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Balassa-Samuelson Hypothesis
In this section, we delve into the relationship between the real exchange rate and productivity through the Balassa–Samuelson hypothesis, aiming to analyze the factors contributing to the long-term depreciation of Japan's real exchange rate.
In general, goods and services can be categorized into tradable goods (tradables), those that can be exchanged with foreign countries, and non-traded goods (nontradables), those that cannot. It is reasonable to assume that certain services, like haircuts, are nontradables since people are unlikely to travel abroad solely for cheaper haircuts.
6 General prices, therefore, comprise both prices of tradables and nontradables.
Tradables are subject to foreign trade; therefore, their prices are influenced by competitive forces.
7 Consequently, the real exchange rate is determined by the disparity between domestic and foreign prices of nontradables. That is, in a bilateral comparison, the greater the increase in the price of nontradables relative to tradables in a country, the more the real exchange rate appreciates.
The real exchange rate can be expressed in a formula
8 : 𝐸 = 𝑆𝑃/𝑃∗ , where 𝐸 denotes the real exchange rate, 𝑆 represents the nominal exchange rate (market rate), 𝑃 indicates the price level in the home country, and 𝑃∗ represents the price level in other countries. Prices can then be further expressed in terms of tradables and nontradables as 𝑃 = 𝑃𝑇 1−𝜔𝑃𝑁 𝜔, where 𝑃𝑇 denotes the prices of tradables, 𝑃𝑁 denotes the prices of nontradables, 𝜔 symbolizes the weight of nontradables in the home country, and 𝜔∗ signifies the weight of nontradables in the foreign country. Then, 𝐸 = 𝑆𝑃𝑇 1−𝜔𝑃𝑁 𝜔/(𝑃𝑇 ∗1−𝜔∗ 𝑃𝑁 ∗𝜔∗ ). By transforming this formula into logarithms and organizing it, we obtain the following expression: 𝑒 = (𝑠 + 𝑝𝑇 − 𝑝𝑇 ∗ ) + 𝜔(𝑝𝑁 − 𝑝𝑇 ) − 𝜔∗(𝑝𝑁 ∗ − 𝑝𝑇 ∗ ), assuming the law of one price for tradeables, i.e, 𝑠 + 𝑝𝑇 − 𝑝𝑇 ∗ = 0 , the real exchange rate can be simplified as 𝑒 = 𝜔(𝑝𝑁 − 𝑝𝑇 ) − 𝜔∗(𝑝𝑁 ∗ − 𝑝𝑇 ∗ ), representing the ratio of the relative prices of tradables and nontradables .
Furthermore, we explore the relationship between the real exchange rate and productivity. Assuming that the productivity is equally determined by real wages, 𝐴𝑇 = 𝑊/𝑃𝑇 , indicating the productivity of tradables where 𝑊 denotes the nominal wages and 𝐴𝑁 = 𝑊/𝑃𝑁, which represents the productivity of nontradables. If we substitute the logarithms of both equations, 𝑝𝑇 = w − 𝑎𝑇 and 𝑝𝑁 = w − 𝑎𝑁 , into the above expression for the real exchange rate, we derive 𝑒 = 𝜔(𝑎𝑇 − 𝑎𝑁) − 𝜔∗(𝑎𝑇 ∗ − 𝑎𝑁 ∗ ), signifying that the real exchange rate reflects the difference in the productivity ratio of tradables and nontradables between two countries. Consequently, the real exchange rate appreciates more in a country where the productivity of tradables increases more than that of nontradables.
This hypothesis, known as the Balassa–Samuelson hypothesis, posits that the real exchange rate is determined by reflecting bilateral differences in the productivity of tradables and nontradables. Its mechanism can be illustrated with an example:9 Let us consider a scenario where the productivity increases in an industry producing tradables in the home country. This increase in the productivity could result in a decline in the selling price of the tradables because the increased productivity allows for cheaper production. Alternatively, the selling price of the tradables may remain unchanged, but the wages of the workers involved in their production are raised.
First, we examine the case where the home country's tradable industries lower the prices of the goods and services it produces due to higher productivity. The intensified price competition in the home tradable industries may exert downward price pressure on foreign tradable. If there is no change in productivity in the foreign tradable industries, sales in those industries might decline, leading to a decrease in wages for workers in the foreign tradable industries. If the lower wages cause workers in the tradable industries to switch to the nontradable industries, the labor supply in the nontradable industries will increase, resulting in downward pressure on wages in the nontradable industries. As nontradable industries, such as service industries, are often labor-intensive, and labor costs constitute a significant portion of production costs, lower wages can lead to lower prices. Consequently, the decline in the price of tradables due to their productivity growth can trigger a chain reaction of declining wages and prices in the foreign country.
Likewise, if the home country's tradable industries raise the wages of workers instead of adjusting the selling price, the labor supply in the nontradable industries may decrease as workers in the industries seek employment in the tradable industries for higher wages. Consequently, there will be upward pressure on wages in the nontradable industries, leading to higher prices of nontradables and causing a general rise in prices in the home country.
6 The classification of services does not inherently designate them as nontradables. For instance, when considering educational services, it becomes evident that a significant population of foreign students enroll in universities, resulting in the export of educational services.
7 Regarding tradables, the law of one price cannot be universally assumed to hold true. For instance, when companies establish different markups (the ratio of selling price to marginal cost) for tradables depending on the country of sale, that is, when they adopt the pricing-to-market strategy, it deviates from the principle of one price (Itskhoki, 2021).
8 See Schmitt-Grohe, Uribe and Woodford (2022), Itskhoki (2021), Kawai et al. (2003), and others.
9 The following description is based on Shimizu et al. (2016).