Relative prices and Balassa Samuleson e ect

Relative prices and Balassa Samuleson e ect Prof. Ester Faia, Ph.D. Johann Wolfgang Goethe Universität Frankfurt a.m. March 2009 rof. Ester Faia, Ph.D. (Johann Wolfgang Goethe Relative Universität prices and Frankfurt Balassaa.M.) Samuleson e ect March 2009 1 / 19

Relative prices As goods are di erent across countries and since there are costs of trading goods, relative prices are di erent and have long run and short run dynamics For the time being we do not introduce money so prices are measured in goods Prices are de ned in terms of a reference basket and of a numeraire Real exchange rate is the relative price of two similar baskets in two di erent countries, once basket s costs in the two countries have been convertered into a numeraire Samuleson e ect March 2009 2 / 19

PPP and LOP If P 1 P 2 " we say that country one experiences a real appreciation while country 2 experiences a real depreciation Law of PPP (purchasing power parity) says that the real exchange rate has a tendency to return to 1 when the long-run ratio is disturbed for some reason. Why do prices di er? LOP (law of one price) says that absent tari s or other trade barriers, goods should sell at the same price in di erent countries Samuleson e ect March 2009 3 / 19

Empirical evidence on LOP LOP fails empirically Transport costs are so high that in practice goods are not sold at the same price in di erent countries Samuleson e ect March 2009 4 / 19

Balassa Samuelson e ect Assume traded and non-traded (high transportation costs) goods, capital is mobile across countries and sectors, but labour is mobile only across sectors. Relative prices depend on relative demand Output: Y T = A T F (K T, L T ), Y N = A N G (K N, L N ) As workers cannot migrate internationaly but can across sectors ) wages are equalized across sectors Total labour supply is L = L T + L N and capital is also mobile internationaly and across sectors Samuleson e ect March 2009 5 / 19

Assumptions (cont ed) Only tradeables can be transferred into capital and viceversa, non-tradeables cannot As capital can be traded internationaly its marginal product in the traded-good sector is equalized to the world interest rate r Samuleson e ect March 2009 6 / 19

Firms Maximization Call p the relative price of non-tradeables to tradeables. Firms present value of pro ts in the tradable sector is: 1 s t (A T,sF (K T,s, L T,s ) w S L T,s K T,s+1) s=t 1 + r in the non-tradable sector is: 1 s t (A N,sp s G (K N,s, L N,s ) w s L N,s K N,s+1) 1 + r s=t Samuleson e ect March 2009 7 / 19

Firms F.O.C. tradable sector F.O.C. for K T,s and L T,s : A T,s F L (K T,s, L T,s ) = w s A T,s F K (K T,s, L T,s ) = r Samuleson e ect March 2009 8 / 19

Per capita ratios Let us de ne the capital labour ratio: k T = K T L T, k N = K N L N Since the production function is homogenous of degree one, this implies: y T = A T F (k T, 1) = A T f (k T ) In the non-tradable sector: y N = A N g(k N ) = A n g(k N, 1) Samuleson e ect March 2009 9 / 19

Firms F.O.C. in per capita terms Tradable sector: A T f 0(k T ) = r (1) and using wl T + rk T = Y T we get: A T [f (k T ) f 0(k T )k T ] = w (2) In the non-tradable sector: pa N g0(k N ) = r (3) and pa N [g(k N ) g0(k N )k N ] = w (4) Samuleson e ect March 2009 10 / 19

Graphical solution Given r (exogenously given), rms FOC determine uniquely w and p. Which implies that the demand plays no role in determining the relative price p Graphical solution: Samuleson e ect March 2009 11 / 19

Anticipated productivity shifts Consider rst an increases in A T, a ects w(a T, r) which determines MPL. As A T rises, this pushes MPL in the tradeable sector, but since workers can migrate across sectors this also pushes MPL in the non-tradable sectors and wages in the non tradable sector increase. For given k N the relative price p must increase Consider now that A N increases. MPK in the non tradable sector shifts downward: as A N ", MPK ", and for given r, the relative price, p, must fall to maintain equality. The same is true for MPL (as A N ", MPL "). For given w, the price must fall to maitain equality Since both curves shift downward k N remains unchanged but relative p falls Samuleson e ect March 2009 12 / 19

Productivity di erentials A faster productivity growth in the tradable sector makes relative price of non-tradable go up. As A T increases, both MPL and MPK increase as well. Labour migrates from non-tradeable to tradeable sector and p goes up Intermarginal productivity di erences have implications for relative international price levels (exchange rates). Notice that price levels depend on both tradable and non-tradable prices Samuleson e ect March 2009 13 / 19

Harrod-Balassa-Samuelson e ect: Tendency for countries with higher productivity growth in tradeables compared to non-tradeables to have higher price levels Samuleson e ect March 2009 14 / 19

E ect of productivity shocks (cont ed) Assume price level is a geometric average of the prices of tradeables and non-tradeables. P = (1) γ p 1 γ = p 1 γ, P = (1) γ (p ) 1 γ = (p ) 1 γ Domestic to foreign price level ratio is: P p 1 P = p γ Samuleson e ect March 2009 15 / 19

E ect of productivity shocks continued Consider now product allocation: Take logs: Total di erentiation: 1 A T f (k T ) Recall that: And obtain: 1 A T f (k T ) A T f (k T ) = rk T + w pa N g(k N ) = rk N + w lg(a T f (k T )) = lg(rk T + w) ( da T + df (k T ) dk T ) = A T dk T k T ( da T A T df (k T ) dk T + r dk T k T ) = = r 1 dkt rk T + w k T 1 dkt rk T + w k T + dw w + dw w Samuleson e ect March 2009 16 / 19

E ect of productivity shocks (cont ed) Final expression is: da T A T = de ne ˆx = d lg x = dx x, µ LT = w L T Y T The equation above now reads as: w dw A T f (k T ) w  t = µ LT bw and µ LN = w L N Y N Do same passages for zero pro ts in non-traded sector and get: Substitute ŵ = ÂT µ LT into 5 and get: ˆp +  N = µ LN ŵ (5) ˆp = µ LN µ LT  T  N Samuleson e ect March 2009 17 / 19

E ect of productivity shocks As long as µ LN µ LT = 1 (non-tradeable is more labour intensive than tradable secotr) when  T >  N ) ˆp " Samuleson e ect March 2009 18 / 19

In ation di erentials Example Japan: productivity in manufacturing sector, a tradable sector, has been increasing after World War 2, hence prices, ˆp, have been raising Now we know that real exchange rate is: Take logs changes: P P = p p 1 γ ˆP ˆP = (1 γ) (ˆp ˆp µln ) = (1 γ)  T  T µ LT  N ÂN Harrod-Balassa-Samuelson: countries for which  T rises above  N relatively to the other countries experience real appreciation (relative prices of non-tradeable to tradeable rise). This is also called "catch-up" e ect Samuleson e ect March 2009 19 / 19