Monetary Policy Under Pegged Exchange Rates

The paper introduces a two-country macroeconomic model designed to analyze the impact of money supply changes on key economic variables. A defining characteristic of this model is its incorporation of both sticky and flexible price sectors within each country. This dual-sector approach is a departure from simpler one-sector models and aims to provide a more nuanced understanding of short-run economic responses. The model focuses on examining the short-run effects of money supply changes on exchange rates, home and foreign real and nominal interest rates, and production across different sectors and countries. A central finding is that money supply changes produce liquidity effects—a decrease in the money supply raises real and nominal interest rates—both within and across countries, generating cross-country real-interest differentials. Further, the model demonstrates how a country can maintain a degree of independent monetary policy, even when its exchange rate is pegged to another country, challenging conventional wisdom about the limitations of monetary policy under pegged exchange rate systems. The model also refutes the commonly held belief that credible exchange rate target zones severely constrain short-run monetary policy.

The paper highlights limitations in existing theoretical models regarding exchange rate determination and the effects of monetary policy. It criticizes the inadequacy of existing models in explaining short-term exchange rate fluctuations. Current models, whether based on sticky prices or equilibrium approaches, struggle to account for empirical evidence showing a mean-reverting component in exchange rates with a half-life of approximately three years. The authors also point out that existing models fail to explain the observed differences in relative price behavior across different exchange rate systems. Critically, none of these models can fully elucidate the short-run independence of monetary policy that countries appear able to exercise under pegged exchange rates or systems with limited exchange rate flexibility, such as the European Monetary System (EMS). This paper offers an alternative theoretical framework to better understand and explain these observed phenomena, focusing particularly on the role of monetary disturbances in influencing interest rates and exchange rates.

The paper's two-sector model, incorporating both sticky and flexible prices, offers several advantages over existing one-sector models. It generates significantly different predictions about the relationships between money supply changes, interest rates, international interest rate differentials, and exchange rates. The model suggests that credible limits on exchange rate fluctuations impose less stringent constraints on short-run monetary policy than previously believed. This calls for a re-evaluation of the causes of exchange rate changes, whether primarily monetary or real disturbances. The model also proposes new ways to understand the connections between exchange rates and changes in interest rates, international interest rate differentials, the balance of trade, output, and employment. Its applicability extends beyond positive analysis, enabling welfare analysis of different exchange rate systems and monetary policies within those systems. Furthermore, it proposes new channels for the international transmission of monetary policy and how this transmission differs across various exchange rate systems. The model provides a powerful tool for analyzing these complex interactions which were inadequately explained by previous models.

This section contrasts the current model with existing sticky-price and equilibrium exchange rate models, highlighting its ability to explain phenomena not captured by previous frameworks. It presents a model where a country can manipulate its monetary policy to induce short-run changes in real and nominal interest rates, create international real-interest differentials, and alter its inflation rate, all while maintaining a pegged exchange rate. This contradicts traditional viewpoints asserting the loss of monetary independence under pegged exchange rates. The model proposes that countries often have a range of monetary policies available, each with varying effects on other real and nominal economic variables, and identifies an interval of money-supply changes where the exchange rate remains pegged. The treatment of price stickiness, as acknowledged by the authors, is not a focus of the model; instead, the model concentrates on the implications of these price stickiness assumptions. The paper's focus is on negative monetary shocks, with the understanding that positive shocks would yield opposite effects under the assumptions of quantity-demanded output determination.

This section lays the groundwork for analyzing the effects of money supply changes within a closed-economy context where nominal prices exhibit stickiness. The model incorporates the assumption that some sectors have predetermined nominal prices in the short run, while others have flexible prices. This is a key departure from models that assume uniform price flexibility. The introduction of sticky prices is treated as a ‘black box’ as there is no widely-accepted theory explaining why many nominal prices are slow to adjust. The model then examines the impact of a small, unanticipated, and permanent change in the money supply. It focuses on understanding how such a change influences nominal prices within the flexible-price sectors, analyzing the conditions under which these prices 'overshoot' (rise above long-run equilibrium levels) or 'undershoot' (fall below long-run equilibrium levels) in the short run. A critical finding is that only a relatively small sticky-price sector is needed to generate liquidity effects of the magnitude observed in empirical data. This portion of the research offers an alternative model of liquidity effects that contrasts with models developed by other researchers such as Feurst, Lucas, and Christiano and Eichenbaum.

This subsection delves into the mechanism by which liquidity effects arise in the closed-economy model with sticky prices. The analysis explores the relationship between changes in the money supply, the elasticity of substitution in consumption, and the degree of relative risk aversion. It shows how a fall in the money supply impacts prices in both sticky and flexible price sectors. The model demonstrates that the percentage change in the flexible-price sector's price is dependent upon the elasticity of substitution in consumption, being smaller when this elasticity is greater than one, and larger otherwise. A key result is that a fall in the money supply increases the one-period interest rate if and only if the degree of relative risk aversion is greater than one. The presented numerical results from the authors' previous closed-economy paper indicate that considerable liquidity effects can occur even with just a small fraction of GDP exhibiting sticky nominal prices. In this closed-economy setting, a decrease in the money supply results in higher nominal and real interest rates, reduced aggregate GDP, and differing effects on the output of the sticky- and flexible-price sectors, setting the stage for the subsequent extension to a two-country model.

This section extends the analysis from a closed economy to a two-country model under a flexible exchange rate system. The model maintains the distinction between sectors with sticky and flexible prices, allowing for a more realistic representation of price dynamics in an international setting. The foreign money supply is held constant while the home country's money supply is unexpectedly varied to observe the effects. The model begins from a steady-state equilibrium with constant money supplies, then analyzes the effects of a small, unanticipated, permanent decrease in the home country's money supply. This setup allows for a direct examination of how international interactions and price rigidities influence the transmission of monetary shocks across borders. The assumption of sticky prices in one sector and flexible prices in another sector within each country remains central to understanding the dynamic interactions within this framework. The model assumes that nominal prices in certain sectors (specifically, those producing good X in both countries) are chosen one period in advance, highlighting the role of predetermined prices in short-run responses.

Because the model departs from a representative household assumption, it introduces a rationing rule to determine how goods are allocated in cases of excess demand or supply. This rule specifies how buyers from each country prioritize purchasing goods based on prices in both countries and the current exchange rate. The rule prioritizes buyers from their own country in excess demand situations and buyers purchasing from the lowest-priced seller in excess supply situations. This rationing mechanism is essential for understanding the complex patterns of international trade and price adjustments in the model. The model examines different sub-cases based on whether there is excess supply or demand for good X in each country and the resulting trading patterns. These sub-cases demonstrate how international trade flows can emerge and how prices interact across borders. In contrast to a closed-economy model, the two-country model allows for international trade to emerge in equilibrium and influences the impact of monetary policy shocks.

The analysis explores the world equilibrium under various scenarios, beginning with an equal wealth equilibrium. The model demonstrates how even a small unanticipated decrease in the home country’s money supply results in a variety of complex equilibrium outcomes. The different sub-cases highlighted (e.g., home country excess supply, international trade of good X) detail how the relative prices of goods and the exchange rate respond to the monetary shock. The interaction of sticky prices in one sector and flexible prices in another influences the short-run outcome, leading to outcomes that deviate from models that assume uniform price flexibility. The model explicitly analyzes scenarios where the home country exports good X due to the interplay of predetermined nominal prices and flexible exchange rates, revealing new channels through which monetary policy impacts international markets. This analysis sheds light on how international trade and wealth distribution impact the equilibrium and the effectiveness of monetary policy in a two-country setting.

This section details the approach used to analyze the short-run effects of a decrease in the home country's money supply. The analysis relies on numerical calculations using a non-linear equation solver, as analytical solutions are not readily available for the model's CES utility function. This numerical approach is necessary to capture the complexities of the model's interactions between sticky and flexible prices and the resulting non-linear responses. The analysis begins from an established steady-state equilibrium. The 'Old SS' (old steady state) values serve as the starting point for observing the short-run ('SR') effects of the monetary shock, with the nominal price of good X held fixed for one period to reflect price stickiness. The 'New SS' (new steady state) values represent the long-run equilibrium after the monetary shock has fully propagated. The 'percent' column quantifies the percentage deviation of each variable from its new steady-state level in the short run, highlighting the short-run dynamics in comparison to the long-run equilibrium. This approach allows the researchers to quantitatively assess the model's predictions.

The numerical results show that an unexpected decrease in the home country's money supply produces a substantial short-run impact. Specifically, the home country's nominal interest rate increases by 53 basis points (interpreted as a quarterly model with one-quarter nominal price stickiness). This finding aligns with the concept of liquidity effects, demonstrating the model's ability to replicate observed interest rate responses to monetary shocks. The model further illustrates the impact on output, showing a decrease in output in the sticky-price sector (Good X). The extent of the price adjustment in the flexible-price sector (Good Y) is influenced by the elasticity of substitution between the goods. The model also captures the phenomenon of price overshooting or undershooting relative to the long-run equilibrium, illustrating the short-run dynamics of price adjustments. In the short-run, the home currency appreciates, and combined with the price stickiness assumption, good X becomes cheaper in the foreign country than at home creating excess demand in the foreign country and excess supply in the home country. The model’s non-linearity is evidenced in the differing magnitudes and directions of changes across various variables.

The analysis continues by exploring additional short-run effects and conducting sensitivity analysis. The results highlight a rise in the marginal utility of income (lambda) in the short run, reflecting households' desire to smooth consumption over time. This increase in marginal utility contributes to the rise in the nominal interest rate. The analysis also demonstrates that the closed-economy liquidity effect is about twice as large as the liquidity effect observed in the two-country model. The model showcases how expected deflation, caused by anticipated future price adjustments, amplifies the rise in the real interest rate. The effects of changing parameters, specifically the elasticity of substitution (σ) and the share of the sticky-price sector, are also investigated. The results demonstrate how varying these parameters influences the magnitudes of the real effects of the money supply change. This sensitivity analysis provides a crucial assessment of the robustness of the model’s predictions and illustrates the model’s ability to capture differences in real effects based on structural factors.

This section directly addresses the long-standing debate in international monetary economics concerning a country's ability to maintain monetary independence when its exchange rate is pegged to another country's currency. While central bankers often claim such independence is possible, and empirical evidence supports this view, existing theoretical models generally suggest a loss of monetary autonomy under pegged exchange rates. This research challenges the conventional view by demonstrating that, within the context of the model, short-run monetary independence can exist even under a pegged exchange rate. This is a significant departure from traditional theoretical models which typically predict a direct trade-off between exchange rate stability and monetary policy autonomy. The model demonstrates that there is a range of money supply changes available to the policymaker that will not result in a change of the pegged exchange rate, contradicting established models of exchange rate determination.

The model reveals that, contrary to common belief, maintaining a pegged exchange rate does not eliminate all flexibility in short-run monetary policy. The key insight is the existence of an interval of money supply changes—a range of possible monetary policy actions—that the foreign country can utilize while keeping the exchange rate fixed. This range of policy options is a novel finding that contrasts sharply with existing theoretical frameworks. Each choice within this interval has differing implications for other real and nominal economic variables. The model illustrates that production, consumption, international trade patterns, international borrowing, and both real and nominal interest rates are all affected by the specific choice of monetary policy. The authors demonstrate the model's flexibility by providing several examples of this range of policy options, showcasing the trade-offs involved in making these policy choices, and emphasizing that not only the magnitude, but also the direction of changes in many economic variables, depends on the monetary policy choice.

While the model shows the possibility of short-run monetary independence under pegged exchange rates, it also clarifies the conditions under which this independence holds. The model highlights that this independence is contingent upon the behavior of the home country's money supply, which must leave some excess supply for good X in the home country. If this excess supply condition is not met, the foreign country's ability to exercise independent monetary policy while maintaining a pegged exchange rate diminishes. The analysis supports this point through numerical simulations. The model demonstrates how a permanent decrease in the foreign money supply, without adjustments to the new steady-state money supply, will lead to a failure of the exchange rate peg in the long run. However, these tables show that the exchange rate remains pegged in the short run. This emphasizes that the response of variables like nominal interest rates depends not only on domestic monetary policy but also on foreign monetary policy, further underscoring the complexity of international monetary interactions. The high degree of non-linearity observed in the model's response to monetary changes suggests that linear econometric models may misrepresent these relationships.

This extension addresses the assumption of perfect substitutability between goods X produced in the home and foreign countries. The model is generalized to treat good X as a composite of two goods, 'r' and 'q', produced domestically and abroad, respectively. This modification acknowledges that goods from different countries may not be perfect substitutes, incorporating a more realistic element of product differentiation into the analysis. The primary goal is to examine the robustness of the model's predictions, specifically concerning the extent of short-run monetary independence under pegged exchange rates, when this perfect substitutes assumption is relaxed. By introducing imperfect substitution, the model becomes more complex, requiring adjustments to account for the varied responses of international trade to the monetary shock.

A second extension enhances the model by including another good, denoted as 'z', with a relatively small expenditure share. Good 'z' is produced in both countries, has a sticky nominal price in the short run, and is treated as a perfect substitute for good z produced in either country. The inclusion of good 'z' is intended to represent standardized goods sold globally for which there is evidence of sticky nominal prices. This extension serves to make the model more realistic by accounting for different types of goods with different degrees of price stickiness in the economy. The utility function is modified to incorporate the utility derived from consuming good z. By varying the expenditure share allocated to good z, the researchers explore how the model's predictions concerning monetary independence under different exchange rate regimes respond to changes in the relative importance of this specific type of good.

The results of these model extensions demonstrate the robustness of the model’s key findings. Despite the added complexity and more realistic assumptions, the qualitative results remain consistent. Even with the inclusion of the additional good and relaxation of the perfect substitutes assumption, the model continues to show the existence of a range of money supplies that allows one country to maintain a pegged exchange rate while still exercising short-run monetary independence. The size of this range (representing the degree of monetary independence) changes with the specific assumptions about the new good. As the expenditure share of the standardized good z diminishes, the range of permissible money supplies allowing for a pegged exchange rate also decreases. The researchers conclude that their central finding—short-run monetary independence is possible under pegged exchange rates—remains valid even when the model is extended to incorporate more realistic features.

The paper concludes by highlighting the significant contribution of its two-country, two-sector model to the ongoing debate regarding monetary independence under pegged exchange rates. Existing theoretical models, both those based on sticky prices and those employing equilibrium frameworks, fail to adequately account for the empirical evidence showing that countries can sometimes maintain a degree of monetary policy autonomy even when their exchange rates are pegged. The model presented in this paper directly addresses this discrepancy, providing a framework capable of generating results consistent with observed real-world phenomena. The model's ability to demonstrate short-run monetary independence under pegged exchange rates stands in stark contrast to predictions made by previously existing models, and offers a substantial advancement in understanding the complex interplay between monetary policy, exchange rates, and international economic interactions.

The two-country, two-sector model developed in this paper offers several key contributions to the field of international monetary economics. The model demonstrates that even under pegged exchange rates, there can be a substantial range of monetary policy options available to policymakers in the short run, impacting various economic variables. This insight challenges existing theoretical models and provides a more nuanced explanation for observed behavior. The model also offers novel predictions about the transmission of monetary shocks across borders, capturing the complexities of liquidity effects both domestically and internationally. The researchers emphasize the non-linear nature of these relationships, cautioning against using linear models to empirically capture the dynamics of money, interest rates, and exchange rates. The paper suggests several avenues for future research, including incorporating dynamics, uncertainty and risk, and issues of industrial organization and imperfect competition which were simplified for the purposes of this analysis.