Editing Balassa–Samuelson effect (section)

==Theory==
The Balassa–Samuelson effect depends on inter-country differences in the relative [[productivity]] of the tradable and non-tradable sectors.

===Empirical "Penn Effect"===
By the [[law of one price]], entirely [[tradable]] goods cannot vary greatly in price by location because buyers can [[arbitrage|source from the lowest cost]] location. However, most [[Service (economics)|service]]s must be delivered locally (e.g. [[hairdressing]]), and many manufactured goods such as furniture have high transportation costs or, conversely, low value-to-weight or low value-to-bulk ratios, which makes deviations from the law of one price, known as [[purchasing power parity]] or PPP-deviations, persistent. The Penn effect is that PPP-deviations usually occur in the same direction: where incomes are high, [[Consumer Price Index|average price levels]] are typically high.

===Basic form of the effect===
The simplest model which generates a Balassa–Samuelson effect has two countries, two goods (one tradable, and a country-specific nontradable) and one factor of production, labor. For simplicity assume that productivity, as measured by marginal product (in terms of goods produced) of labor, in the nontradable sector is equal between countries and normalized to one.

<math>MPL_{nt,1}=MPL_{nt,2}=1</math>

where "nt" denotes the nontradable sector and 1 and 2 indexes the two countries.

In each country, under the assumption of competition in the labor market the wage ends up being equal to the value of the marginal product, or the sector's price times MPL. (Note that this is not necessary, just sufficient, to produce the Penn effect. What is needed is that wages are at least related to productivity.)

<math>w_1=p_{nt,1}*MPL_{nt,1}=p_{t}*MPL_{t,1}</math>

<math>w_2=p_{nt,2}*MPL_{nt,2}=p_{t}*MPL_{t,2}</math>

Where the subscript "t" denotes the tradables sector. Note that the lack of a country specific subscript on the price of tradables means that tradable goods prices are equalized between the two countries.

Suppose that country 2 is the more productive, and hence, the wealthier one. This means that

<math>MPL_{t,1}<MPL_{t,2}</math>

which implies that

<math>p_{nt,1}<p_{nt,2}</math>.

So with a same (world) price for tradable goods, the price of nontradable goods will be lower in the less productive country, resulting in an overall lower price level.

===Details===
A typical discussion of this argument would include the following features:
*Workers in some countries have higher [[productivity]] than in others. This is the ultimate source of the income differential. (Also expressed as productivity growth.)
*Certain labour-intensive jobs are less responsive to productivity innovations than others. For instance, a highly skilled [[Zürich]] burger flipper is no more productive than his [[Moscow]] counterpart (in burger/hour) but these jobs are services which must be performed locally.
*The fixed-productivity sectors are also the ones producing non-transportable goods (for instance haircuts) – this must be the case or the [[labour intensive]] work would have been [[Offshoring|off-shored]].
*To ''equalize local wage levels'' with the (highly productive) Zürich engineers, Zürich fast food employees must be paid more than Moscow fast food employees, even though the burger production rate per employee is an international constant.
*The CPI is made up of:
**local goods (which in richer countries are more expensive relative to tradables), and
**tradables, which have the same price everywhere
*The (real) [[exchange rate]] is pegged (by the [[law of one price]]) so that tradable goods follow PPP (purchasing power parity). The assumption that PPP holds only for tradable goods is testable.
*Since money exchange rates will vary fully with tradable goods productivity, but average productivity varies to a lesser extent, the (real goods) productivity differential is less than the productivity differential in money terms.
*Productivity becomes income, so the real income varies less than the money income does.
*This is equivalent to saying that the money exchange rate exaggerates the real income, or that the price level is higher in more productive, richer, economies.

===Equivalent Balassa–Samuelson effect within a country===
The average asking price for a house in a prosperous city can be ten times that of an identical house in a depressed area of the ''same country''. Therefore, the [[real exchange rate|RER]]-deviation exists independent of what happens to the ''nominal exchange rate'' (which is always 1 for areas sharing the same currency). Looking at the price level distribution within a country gives a clearer picture of the effect, because this removes some complicating factors:
# The [[econometrics]] of [[purchasing power parity]] (PPP) tests are complicated by [[Exchange rate|nominal exchange rate]] noise. (This noise would be an econometric problem, even assuming that the exchange rate volatility is a pure [[Standard error (statistics)|error term]]).
# There may be some real economy border effects between countries which limit the flow of tradables or people.
# [[Monetary]] effects, and exchange rate movements<ref group=note>There may be a causal link from exchange rates to productivity, as well as (or instead of) the opposite direction of causation (from productivity to RERs) given by the BS-hypothesis model. [[Michael E. Porter]]'s ''The Competitive Advantage of Nations'' says that currency depreciations can reduce growth, and that 'overvalued' currencies can contribute to domestic productivity growth by 'forcing' efficiency improvements in the tradables sector (by exposing it to international competition at unfavourable [[terms of trade]]). In fact, [[Singapore]] gave "Competitive Appreciation" as the official reason for the high [[SGD]] policy. (Lu & Yu 1999). Other mechanisms through which RERs can affect productivity growth have been advanced, such as the idea that structural transitions caused by exchange rate volatility have a disruptive effect on the real economy. There is some econometric evidence that the [[causality]] from exchange rates to productivity is more significant than the reverse, i.e. the BS-effect. (For instance, {{Citation |last=Strauss |first=Jack |year=1999 |title=Productivity Differentials, the Relative Price of Nontradables and Real Exchange Rates |journal=[[Journal of International Money and Finance]] |volume=18 |issue=3 |pages=383–409 |doi=10.1016/S0261-5606(99)85003-7 }}.)</ref> can affect the real economy and complicate the picture, a problem eliminated if comparing regions that use the same [[currency]] unit.
# [[Taxes]] are very different in many countries, whereas in a same country taxes are usually equal or similar.

A pint of [[pub]] beer is famously more expensive in the south of [[England]] than the north, but supermarket [[beer]] prices are very similar. This may be treated as [[anecdotal evidence]] in favour of the Balassa–Samuelson hypothesis, since supermarket beer is an easily transportable, traded good. (Although pub beer is transportable, the pub itself is not.) The BS-hypothesis explanation for the price differentials is that the 'productivity' of pub employees (in pints served per hour) is more uniform than the 'productivity' (in foreign currency earned per year) of people working in the dominant tradable sector in each region of the country ([[financial services]] in the south of England, [[manufacturing]] in the north). Although the employees of southern pubs are not significantly more productive than their counterparts in the north, southern pubs must pay wages comparable to those offered by other southern firms in order to keep their staff. This results in southern pubs incurring a higher labour cost per pint served.