The J Curve and Japan’s Current Account

Japan Situation
Since Abe’s election in December 2012, the Japanese Yen has dramatically depreciated against the major currencies (USDJPY is up 25%, now trading at 104.30). However, the Ministry of Finance reported on Tuesday that Japan’s current account posted its largest deficit on record in November, printing at 592.8Bn Yen (well above analysts’ expectations of 368.9Bn Yen). The country’s balance of trade goods and services (one of the major components of the current account) widened to ¥1.29tr in November, posting its 17th consecutive deficit as a weaker Yen is pushing import costs.

According to analysts, Abenomics is definitely working as they say that Japan trade’s and current account balances are still in the first stage of a J-Curve effect…

The J-Curve effect
In economics, the J Curve effect is the term used to describe the impact of currency devaluation on a country’s Current Account (Balance of Trade). A weaker currency should definitely boost exports (as they become cheaper) and therefore the country should show a positive Current Account (BoT). However, due to the low price elasticity of demand for the imports and exports in the immediate aftermath, currency depreciation doesn’t have an instantaneous positive impact on the current account (BoT).
If we apply the theory of the J Curve, observations show that in the short term period following currency devaluation, the current account and BoT of that country will decline as the higher exchange rate will firstly correspond to more costly imports and less valuable exports, but as soon as elasticity grows, it will start to improve eventually to better levels.

Theory: Marshall-Lerner
There are many studies which attempt to estimate the J-curves, but we are going to stick with the most famous one, the Marshall-Lerner Condition.
Assume the trade balance in foreign currency terms is expressed as the following equation:

Bf = pfx X – pfm M

Therefore, a change in th trade balance after a sharp depreciation can be denoted as:

ΔBf= (pfx ΔX + X Δpfx) – (pfm ΔM + M Δpfm)                       (0)

With      Vfx = pfx X, the Foreign value of exports                                        (1)
and        Vfm = p fm M, the foreign value of imports                                     (2)
Hence, if we replace (1) and (2) in (0), we have the following equation:

ΔBf = Vfx (ΔX/X + Δpfx/pfx) – Vfm (-ΔM/M – Δpfm/ pfm)           (3)

We can define the elasticities of demand/supply of exports/imports in the following equations:

ex =(ΔX/X) / (Δphx/phx), Home export supply elasticity
ηx =(ΔX/X) / (Δpfx/pfx), Foreign export demand elasticity
em =(ΔM/M) / (Δpfm/pfm), Foreign import supply elasticity
ηm = – (ΔM/M) / (Δphm/phm), Home import demand elasticity

* * *

In mathematics, the formula for the elasticity of Y with respect to X is

e Y X = (dY/dX) * (X/Y),

Where (dY/dX) is the derivative of Y with respect to X

* * *

We know domestic and foreign are related as the following:

pfm = phm r,           with r the exchange rate

With equation (3) and all elasticities expressions, I have now the following expression:

 Vfx * (nx-1) / (1+nx/ex)  +  Vfm * { nm(1+1/em) } / { (nm/em) + 1 }       (4)

ML Condition (MLC):
As it was well defined in Professor Brooks’ dissertation (Currency Depreciation and the Trade Balance, Economics), if prices are fixed in seller’s currencies, then the supply elasticities are infinite:

ex = em = ∞

Definition (Elasticity): As a reminder, the two extremes cases of elasticity are:
– Perfectly inelastic supply, where elasticity = zero
– Perfectly elastic supply, elasticity = ∞ (type of good such that small changes in price cause large changes in quantity supplied)

(Source: IBT Institute)

If we compute equation (4) limit, we have the following equation:

ΔBf = Vfxx – 1) + Vfmm)            (5)

Furthermore, if we assume that Vfx = Vfm (Foreign currency value of exports = Foreign currency value of imports,

ΔBf > 0   eq.   Vfxx – 1) + Vfmm) > 0
ΔBf > 0   eq.   Vfmx – 1) + Vfmm) > 0
ΔBf > 0   eq.   ηx + ηm > 1

In other words, the foreign currency value of the BoT will improve if the sum of the import and export demand price elasticities is greater than unity.
This is known as the Marshall-Lerner condition (see graph below)

(Source: Marshall Lerner’s Blog)

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