The Balassa-Samuelson (BS) effect analyses the relationship between the increase in productivity realised in the traded goods sector and the real exchange rate appreciation. It owes its name to the important contributions made by Bela Balassa (1964) and Paul Samuelson (1964). In particular, it captures the impact of higher productivity growth in terms of internationally traded goods – typically manufactures – on the relative prices and then on the real equilibrium exchange rate (Q), defined precisely by the ratio between the price index of tradable goods (PC) and the price index of non-traded goods (PN). In general, the BS effect explains why the prices of tradable goods tend to converge (net of transaction prices) at the international level, while this is not true for the prices of non-tradable goods, which indeed tend to be higher in richer countries (or in countries where the labour productivity in the tradable sector is higher). 
The underlying logic to the BS effect can be summarized as follows. Let’s assume that the law of one price (LOOP) holds for all internationally traded goods. In growing economies, it is plausible to consider that productivity growth is concentrated precisely in the production of these goods. This leads to an increase in wages that is not necessarily accompanied by an increase in prices. Unlike the non-tradable sector, the demand for higher wages leads to higher  prices and consequently to a rise in the CPI. Since the LOOP will continue to be respected and the nominal exchange rate remains constant, the joint work of these forces results in an appreciation of the real exchange rate. The experience of Japan in the post-conflict phase is often cited as an example of the existence of the BS effect.
In order to illustrate the mechanism that links the growth of labour productivity (pml) to the dynamics of the real exchange rate (Q), we consider an open economy with two sectors, that of traded goods (whose production level is indicated by YC) and non-traded goods (whose production level is indicated by YN). Both productions use two inputs, capital and labour, which are internationally immobile. Let’s assume further that work is perfectly mobile between the two sectors in the same country. This assumption implies the equality of the wages paid in the two sectors within the same country. Both sectors are perfectly competitive; therefore any input receives a remuneration equal to its marginal product.

Let’s consider the situation described by Figure 1 (taken from Colombo and Lossani, 2003). The graph on the left shows:
- the production possibility frontier (drawn under the hypothesis of decreasing marginal productivity), which represents the maximum production of tradable goods (YC) which the economy is able to produce for any given level of output of the non-tradable sector (YN); 
- the relative price line (whose slope is given by the ratio between the price of tradable goods (PC) and the price of non-tradable goods (PN)); 
- the equilibrium point D0 where the marginal rate of transformation is equal to the price ratio.
The graph on the right shows: 
- on the vertical axis, the marginal productivity of labour in both sectors (pmlN and pmlT ); 
- on the horizontal axis, the workforce in the two sectors (LCand LN); 
- the equilibrium in the labour market where real wage w equals the labour marginal productivity.
Let’s consider now the effects of productivity growth in the tradable goods sector. In the graph on the left, there is a "non- neutral" translation in the production possibility frontier: the same level of production of non-traded goods (YN) is now compatible with a higher output of traded goods (YC). In the graph on the right, the curve pmlC shifts to the right. The changed conditions in the labour market result in an increase in the equilibrium wage that implies a consequent increase in the level of prices of non-traded goods (PN). On the contrary, the level of prices of tradable goods (PC) does not change, since the increase in wages is accompanied by an increase in productivity. 
The increase of PN ,PC equal, entails:
- a decrease in  the slope of the relative price line which is now tangent to the new production possibility frontier, thus determining new production levels  for the two goods; 
- a real exchange rate appreciation () proportional to the weight given to non-traded goods in the calculation of the general price index. 
Balassa (1964) also stressed an important empirical regularity. The comparison between developed and developing countries shows that productivity differentials are much higher in the tradable goods sector than in the non-traded goods sector. Let's consider a scenario that includes advanced economies and developing economies. It seems logical to assume that the differential in favour of the first in terms of labour productivity is greater in the tradable goods sector rather than in the non-tradable goods sector. Given that international trade determines an equalization of the prices of internationally traded goods, the lower productivity in the most backward economies results  into lower wages and thus lower prices for non-tradable goods.
In general, if a country experiences a higher productivity growth  than that experienced in other countries, its real exchange rate tends to appreciate. This result has been corroborated by many empirical analyses.

Empirical evidence on the BS effect

Over the years, the empirical literature has provided equivocal contributions on the BS effect. Heston, Nuxoll and Summers (1994) consider the price differential of tradable and non-tradable goods by using data from the International Comparison Program (ICP). By means of various econometric methods, this study produced strong evidence of how the relationship between non-tradable and tradable prices and income is consistent with what the BS effect foresees.
De Gregorio, Giovannini and Wolf (1994), in a study conducted on panel data of forty-OECD countries and aimed to analyse the weight of demand factors (e.g. public expenditure) in generating deviations from PPP, showed that changes in terms of trade exert a more important role in explaining the short-term fluctuations of the real exchange rate rather than the BS effect. In a similar analysis, but conducted on data from Asian countries, Chinn (2000) illustrated how both phenomena - demand factor and BS effect - explain little about the movements of the real exchange rate.
More recently, Lothian and Taylor (2008), by analyzing data on the U.S.A., the UK and France over the period 1820-2001, identified a statistically significant BS effect for the pound-dollar exchange rate (but not for the French franc-pound), which explains about 40% of the deviation from its long-term value. 
Balassa B., (1964), "The purchasing-power parity doctrine: A reappraisal" The Journal of Political Economy, Vol.72, pp. 584-596.
Colombo E. and Lossani M. (2003), Economia Monetaria Internazionale, Carocci editore, Roma.
Harrod R. (1939), International Economics, University of Chicago Press, Chicago.
Lothian J.R. and Taylor M.P. (2008), "Real Exchange Rates Over the Past Two Centuries: How Important is the Harrod-Balassa-Samuelson Effect", Economic Journal, Vol. 118, Issue 532, pp. 1742-1763.
Rogoff K. (1992), "Traded Goods Consumption Smoothing and the Random Walk Behavior of the Real Exchange Rate", Monetary and Economics Studies, Vol. 10, PP. 1-29. 
Rogoff K., (1996), "The purchasing-power parity puzzle" Journal of Economic Literature, Vol 34, pp. 647-668.
Samuelson P.A. (1964), "Theoretical notes on trade problems", The Review of Economics and Statistics, Vol 46, pp.145-154.
Sarno L. and Taylor M.P. (2002), The Economics of exchange rate, Cambridge University Press, Cambridge, UK.