Tuesday, March 24, 2009

Fitting the Theory to a Model

Fitting the Theory to a Model

In 2005, Blanchard, Giavazzi, and Sa (The US Current Account and the Dollar) attempt to quantify the extent of dollar depreciation necessary to achieve equilibrium in the current account. They arrive at the conclusion that this depreciation would need to be on the order of 40-90%. They arrive at this conclusion by estimating that the dollar would need to depreciate by 15% to improve the trade deficit by 1%. At the time (February 2005), the US trade deficit was about 5% of GDP and they calculated payments on the US external net debt at the time to add an additional 1%. Thus, they theorized that the dollar would need to depreciate by 6*15%=90% in order to achieve Current Account Balance. Acting as an offset, valuation effects (due to the increase in dollar value of US owned foreign assets) would make the necessary depreciation only 65%.
A quick word on valuation effects: A tempting argument for our current environment is that we won’t have to worry about interest payments on our net foreign debt because the interest rate on treasuries is so low. Although treasury yields are low, the relevant comparison is to US owned foreign assets, which have seen a large decrease in their principal value. This is what lies behind the deterioration in the net foreign asset position of the US in 2008 (Figure 2). Investors who are getting a small return on their principal are doing better than investors who are getting a small return of their principal! However, (if and) when other asset markets offer an expectation of positive return, then yields on US treasuries will rise commensurately. In addition, I think that if the dollar depreciated to the point that foreigners were being finessed out of 8 trillion dollars in net wealth (through the valuation effect) that this offset would in turn be offset by foreigners demanding incredibly high interest rates on US assets.
Since the paper was written, the trade deficit has actually decreased by approximately 35% or about 2% of GDP. While the dollar has depreciated by roughly 20% versus the Yuan and 10% versus the Yen, the trade weighted exchange rate has actually appreciated by 4% from the time the paper was written. So what could be going on? The theory stated by Blanchard et all implied that the dollar would have to depreciate by approximately 30% to achieve a 2% reduction in the trade deficit as a percent of GDP. The answer lies in further shifts in asset preference toward US assets. This shift occurred to a lesser degree through continued pegging by Saudi Arabia and other large petroleum exporters, and mainly through the panicked rush into treasuries and dollar assets seen in the last 6 months. Before the financial panic started, the value of the dollar had actually decreased against the trade weighted basket by 15%, and the Trade Balance had just started to decrease as a percent of GDP. Thus, the theory that an asset preference shift is wholly responsible for the dollar appreciation is consistent with the statistical facts. Significantly, while a shift in asset preference toward US assets appreciates the dollar in the short run, it causes the eventual steady state of the dollar to decrease still further.
At this point I will find it useful to start referring to a phase diagram (Figure 3). The phase diagram shows the dynamic path of the dollar.

A Movement in Equilibrium or a Shift?
When citizens prefer to invest in their own country’s assets (i.e. home bias and α+α*-1>0), we would expect to associate an increase in net debt with a shift of wealth abroad and a depreciation of the dollar. This is what the equilibrium condition ( dE/dt=0) tells us. However, in spite of a large increase in net debt in 2008, there was a significant appreciation of the dollar. This speaks again to the likelihood that the appreciation was due to a shift in asset preferences, as opposed to a movement in equilibrium.
I refer the reader again to the Blanchard paper for more details on steady state conditions and the more detailed dynamics of the system. However, I will briefly note the three most salient points for my arguments:
1. The stable saddle path runs from the north-west quadrant to the south-east quadrant.
2. Shift in asset preferences toward US assets causes the dE/dt=0 locus to shift to the right causing an immediate appreciation of the dollar and increase in net foreign debt level (in the figure, an increase in "F") of the US. This movement also shifts the equilibrium debt position of the US out (increases) and shifts the equilibrium exchange rate down (further depreciation).
3. Although dE/dt=0 and dF/dt=0 appear linear, they are not linear in the limit, so that in both cases the locus would cross the x-axis only when net debt was infinite. The fact that there is historical precedent for important currencies to reach near worthlessness suggests that in practice, this distinction may be a formality.

In Figure 3 above, we start at a hypothetical equilibrium at point “1”. Each shift out in the asymptote is caused by some mechanism which causes a portfolio shift toward US assets. For simplicity, I model the dF/dt=0 asymptote as stationary; it would be expected to shift under certain conditions such as a change in the US interest rate or a shift in the trade deficit (Blachard, Giavazzi, Sa 2005). I hypothesize a shift from “1” to “2” to be caused by an exogenous increase in the demand for dollars for “transaction liquidity” purposes. In the phase diagram, I then model the dollar as beginning to depreciate and the net debt position beginning to increase as it heads for the equilibrium point at “2a”. Next, I model the “flight to safety trade” trade as a shift to point “3”. Again the currency starts to depreciate toward a new equilibrium. The pegging associated with export-growth strategies is denoted by the shift toward point “4” on the graph. Finally, the asset allocation shift associated with the 2008 financial panic is represented as a shift to point “5”, which is our current position.
I believe that the dynamics of the system are so skewed that the natural dynamic adjustment of the system could lead the dollar to be essentially worthless (point 6a). The path to equilibrium associated with this adjustment is a relatively slow depreciation accompanied by an ever increasing level of the net foreign debt position. Another option that is possible is an immediate and unexpected depreciation of the dollar, which would lead us to point 6b. Since much of the foreign claim to US assets is priced in dollars, a depreciation in dollars simultaneously reduces the net foreign debt of the US. Foreign assets held by US citizens would increase in dollar value, so the net foreign debt position would decrease. Since the level of US borrowing in foreign denominated currency is close to nil, we have the luxury of this possibility. Undoubtedly, taking this path would lead to onerous future terms on debt for the US However, this would be negated by a new level of competitiveness of US industry and the US would naturally run a Current Account surplus. Note that in this case we would shift to the south-east quadrant and the stable saddle path would then lead us to an appreciating currency and lower levels of net debt!
Of note, there are at least two possible ways for arriving at point 6b. One possibility would be for the US to announce its intention to devalue the currency, renounce the role of reserve currency, and suggest a discontinuous change in exchange rates (on the order of 90% depreciation.) A determined and extreme increase of the money supply could discourage competitive devaluation (a first-mover advantage of sorts). The other possibility is the possibility that was presented in the first part of the paper: foreign countries abandon pegs and shift asset preferences back to their own foreign markets. Whether this occurs due to a domestic or foreign decision, the net result is a discontinuous shift back to an equilibrium level of exchange rate that is determined strictly by money supply and production of goods and services.

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