Backus–smith puzzle

What Is the Backus–Smith Puzzle?

The Backus–Smith puzzle, also known as the consumption–real exchange rate anomaly, describes a long-standing empirical observation in international economics that contradicts a fundamental prediction of many standard open-economy economic models. Specifically, it refers to the finding that the correlation between a country's relative consumption and its real exchange rate is often zero or negative, rather than strongly positive as theoretical models of international risk sharing would predict.

This anomaly challenges the notion that, under complete financial markets and perfect risk sharing, countries facing relatively high prices (implying a depreciated real exchange rate) should experience a reduction in their relative consumption, and vice versa. The Backus–Smith puzzle is a key focus within modern macroeconomics, particularly for researchers studying international business cycles and asset pricing.

History and Origin

The Backus–Smith puzzle was first documented in a seminal 1993 paper by economists David K. Backus and Gregor W. Smith. Their work, titled "Consumption and real exchange rates in dynamic economies with non-traded goods," revealed an unexpected empirical regularity that stood in contrast to prevailing economic theory on international risk sharing. Prior to their findings, many models assumed that complete international capital markets would allow countries to perfectly pool idiosyncratic risks. In such a scenario, if one country experiences a negative economic shock, its citizens would smooth consumption by borrowing from abroad, leading to a depreciation of its real exchange rate (goods become relatively cheaper there) and a relative increase in its consumption. Conversely, a positive shock would lead to appreciation and higher consumption.

However, Backus and Smith's empirical analysis of real-world data demonstrated that this expected positive correlation was either weak, zero, or even negative. This empirical challenge highlighted a significant disconnect between theoretical predictions and observed realities in international finance. The puzzle continues to motivate extensive research aimed at developing more robust and empirically consistent international macroeconomic models. Researchers have since explored various potential explanations for the Backus–Smith puzzle, attempting to reconcile theory with the data.

Key Takeaways

• The Backus–Smith puzzle highlights the empirical observation that the correlation between a country's relative consumption and its real exchange rate is typically weak, zero, or negative.
• This observation directly contradicts predictions from standard international economic models that assume complete risk sharing and frictionless markets.
• The puzzle underscores the limitations of simple theoretical frameworks in explaining complex real-world phenomena in international finance.
• Resolving the Backus–Smith puzzle often involves introducing market imperfections, such as incomplete financial markets, non-traded goods, or specific forms of productivity shocks, into economic models.
• It is a central focus of research in international macroeconomics, driving the development of more sophisticated dynamic general equilibrium models.

Interpreting the Backus–Smith Puzzle

Interpreting the Backus–Smith puzzle involves understanding its implications for the underlying assumptions of economic models. Standard theory, particularly those built on the premise of perfect risk sharing across countries, posits that agents in different countries can smooth their consumption paths by trading claims on future income. This implies that if a country's goods become relatively cheaper (its real exchange rate depreciates), its citizens should be able to consume more, leading to a positive correlation between relative consumption and the real exchange rate. The puzzle arises because this strong positive relationship is not consistently observed in real-world data.

The persistence of the Backus–Smith puzzle suggests that certain factors are at play that are not fully captured by these idealized models. These factors might include frictions in international capital markets, the presence of non-traded goods that complicate the measurement and interpretation of the real exchange rate, or other market imperfections such as heterogeneous agents or imperfect information. Researchers often vi⁴ew the puzzle as an indication that either international risk sharing is far from complete, or that the mechanisms through which real exchange rates and consumption interact are more complex than initially theorized.

Hypothetical Example

Consider two hypothetical economies, Home and Foreign, that are theoretically capable of perfect risk sharing.

According to a standard model, if Home experiences a temporary negative shock to its output, its citizens should be able to borrow from Foreign to maintain their consumption levels. This borrowing would typically lead to a depreciation of Home's real exchange rate, making its goods cheaper relative to Foreign goods. Consequently, Home's relative consumption (compared to Foreign) should increase, as its citizens are now effectively richer due to the ability to consume cheaper domestic goods and imported goods at favorable terms. The theory predicts a positive correlation: as Home's real exchange rate depreciates, its relative consumption rises.

However, in a scenario reflecting the Backus–Smith puzzle, empirical data might show a different outcome. Even with a significant depreciation of Home's real exchange rate, its relative consumption might remain unchanged or even decrease. For instance, if Home's real exchange rate depreciates by 5%, but its relative consumption either stays flat or declines by 1-2%, this would illustrate the puzzle. The expected strong positive relationship is absent, suggesting that mechanisms beyond perfect risk sharing, such as trade barriers, incomplete financial markets, or the presence of non-traded goods, are preventing the theoretical outcome from materializing.

Practical Applications

The Backus–Smith puzzle has significant practical implications for policymakers, international investors, and economists engaged in understanding global economic dynamics.

For policymakers, especially central banks and finance ministries, the puzzle highlights the challenges in predicting the effects of exchange rate movements on domestic consumption and the broader economy. If the theoretical link between real exchange rates and consumption is weak or absent, policies aimed at influencing real exchange rates (e.g., through monetary policy or fiscal measures affecting the nominal exchange rate and inflation) might not have the expected effects on welfare and consumption smoothing. This encourages a more nuanced approach to international macro policy, recognizing the role of market imperfections and other factors.

For international investors, the puzzle suggests that simple parity conditions related to consumption and real exchange rates may not hold, impacting arbitrage opportunities and risk management strategies. It underscores the complexity of cross-border investment decisions where deviations from theoretical benchmarks are common.

In academic research, the Backus–Smith puzzle is a vital empirical regularity that drives the development of new open-economy economic models. Researchers strive to build models that can replicate observed macroeconomic facts, including the puzzle, by incorporating elements such as incomplete markets, non-traded goods, or specific features of consumer preferences. For example, some studies suggest that movements in the nominal exchange rate are a primary driver of the puzzle, moving counter-cyclically with consumption in ways that violate basic risk sharing theory. Others explore how expectations about future productivity can impact the puzzle, particularly in the presence of incomplete financial markets.

Limitations and Critic³isms

The primary criticism and limitation of existing economic theory lies in its inability to consistently explain the empirical facts presented by the Backus–Smith puzzle. Standard international real business cycle models, which often assume complete financial markets and frictionless trade, predict a strong positive correlation between relative consumption and the real exchange rate. However, this theoretical prediction is largely absent in real-world data, leading to the puzzle.

Various solutions and explanations have been proposed to address the Backus–Smith puzzle, each with its own set of assumptions and limitations:

• Incomplete Markets: Many proposed solutions emphasize the role of incomplete international capital markets. If countries cannot fully insure against idiosyncratic shocks, their consumption behavior may deviate from the perfect risk-sharing benchmark. However, simply introducing incomplete markets is often not enough; specific forms of incompleteness or additional frictions are usually required to fully account for the puzzle.
• Non-Traded Goods: The ²presence of non-traded goods (services, housing, etc.) is a key feature in the original Backus and Smith paper and subsequent research. The idea is that changes in the prices of non-traded goods can affect the real exchange rate without necessarily leading to the predicted consumption response if consumers face different baskets of goods across countries. However, the specific assumpti¹ons about the utility function and elasticity of substitution between traded and non-traded goods are crucial.
• Preference Shocks or Habit Formation: Some models introduce shocks to consumer preferences or assume habit formation in consumption. These can alter the optimal consumption path and its relationship with the real exchange rate. While they can sometimes generate the observed correlations, the magnitude of such shocks or the strength of habit formation required may be implausibly large or difficult to empirically verify.
• Nominal Rigidities and Exchange Rate Behavior: A significant area of criticism points to the role of nominal rigidities and the behavior of the nominal exchange rate. Research suggests that nominal exchange rate movements, rather than inflation differentials, are the main source of the Backus–Smith puzzle, moving counter-cyclically with consumption. This implies that models need to better account for the dynamics of nominal variables and their interaction with real macroeconomic aggregates.
• Data and Measurement Issues: Some criticisms revolve around data quality and measurement. Different definitions of consumption, varying methods for calculating real exchange rates, and the challenges of accurately measuring cross-country economic activity can influence empirical results.

Despite numerous attempts, a single, universally accepted solution that fully resolves the Backus–Smith puzzle and is consistent with all other international economic growth facts remains elusive, continuing to make it a fertile area for research.

Backus–Smith Puzzle vs. Backus-Kehoe-Kydland Puzzle

While both the Backus–Smith puzzle and the Backus-Kehoe-Kydland (BKK) puzzle emerged from the work of David K. Backus and colleagues in the early 1990s, they address distinct, though related, anomalies in international macroeconomics.

The Backus-Kehoe-Kydland puzzle (BKK puzzle), documented by Backus, Kehoe, and Kydland in 1992, refers to the observation that the correlation of consumption growth rates across countries is lower than the correlation of output growth rates. Standard international business cycles models with complete risk sharing predict the opposite: that consumption should be highly correlated across countries because agents can pool their income risks, leading to smoother consumption paths globally even if output fluctuates domestically. The BKK puzzle highlights the limited extent of international risk sharing in practice.

In contrast, the Backus–Smith puzzle (consumption–real exchange rate anomaly), identified by Backus and Smith in 1993, focuses on the relationship between relative consumption and the real exchange rate. It notes that theoretical models predict a strong positive correlation (countries with cheaper goods should consume relatively more), but the empirical correlation is found to be weak, zero, or negative. While Backus and Smith's work on non-traded goods partially helped explain the BKK puzzle, it simultaneously gave rise to this new anomaly. The BKK puzzle is about how much consumption co-moves across countries, whereas the Backus–Smith puzzle is about how relative consumption correlates with the relative prices of goods between countries.

FAQs

Why is the Backus–Smith puzzle considered a "puzzle"?

It is considered a "puzzle" because observed economic data on consumption and real exchange rates contradict a clear prediction from widely accepted economic theory regarding international risk sharing. Theories suggest a strong positive correlation, but empirical evidence shows a weak, zero, or even negative one.

What are the main factors theorized to explain the Backus–Smith puzzle?

The primary explanations explored by economists include incomplete financial markets, the presence of non-traded goods, various market imperfections like transaction costs, and certain types of productivity shocks or consumer preferences that are not fully captured by simpler models.

Does the Backus–Smith puzzle apply to all countries?

The puzzle has been observed across various country pairs and regions, particularly among developed economies. While the exact magnitude of the correlation may vary, the general finding of a weak or negative relationship, contrary to theoretical predictions, is a widespread empirical regularity in international economics.

How does the Backus–Smith puzzle relate to the balance of payments?

The Backus–Smith puzzle primarily concerns the relationship between consumption and relative prices (real exchange rates) rather than the trade balance or capital flows. However, since the real exchange rate and consumption patterns are influenced by international trade and capital movements, the puzzle indirectly highlights complexities in how these components interact within the broader balance of payments framework.