Paul Krugman recently characterized the current pace of trade activity as worse than that during the Great Depression. And indeed, Barry Eichengreen and Kevin O’Rourke have been diligent in illustrating how this is the case, most recently in this September VoxEU post. Caroline Freund ([pdf] here) as well as the IMF in its most recent World Economic Outlook (Box 1.1) attribute the sharp drop-off in world trade to high income elasticities, in part associated with the high degree of vertical integration that characterizes the globalized world economy. Below, I want to examine that explanation from the perspective of the US data. This follows up on several of my recent posts on the subject. [0] [1] [2] [3]

First, let’s take a look at the exports-to-GDP and imports-to-GDP ratios.

Figure 1: Non-agricultural goods exports to GDP ratio (blue), and non-oil goods imports to GDP ratio (red). NBER recession dates shaded gray. Source: BEA, GDP 2009Q2 3rd release of 30 Sep 2009, NBER, and author’s calculations.

Figure 2: Log real non-agricultural goods exports to GDP ratio (blue), and log real non-oil goods imports to GDP ratio (red). NBER recession dates shaded gray. Source: BEA, GDP 2009Q2 3rd release of 30 Sep 2009, NBER, and author’s calculations.

What is clear is that in nominal terms, there has been a trend increase in trade openness, with a big (although not completely unprecedented) break at end-2008. However, nominal ratios incorporate terms of trade changes (think oil price increases in 2008); using log real ratios (I take logs because ratios of chain weighted indices don’t have a ready interpretation), one sees the jagged movements smoothed out, but trends intact.

What these graphs hint at is a break in the pace of integration. To investigate this issue more formally, I estimate error correction models for both non-agricultural goods exports and non-oil goods imports.

For exports, the specification is:

Δ exp _t = θ ₀ + ρ exp _t-1 + θ ₁ y^* _t-1 + θ ₂ r _t-1 + σ ₁ Δ exp _t-1 + σ ₂ Δ y^* _t-1 + σ ₃ Δy ^*_t-2 + σ ₄ Δ r _t-1 + v _t

Note that the rest-of-world GDP variable (y^*) is the export weighted real GDP calculated by the Federal Reserve Board, for 1970q2-07q4; the 2008q1-09q2 data I estimated using a regression of first differenced GDP on a current and four lags of first differenced industrial country industrial production.

(Data sources: BEA 2009q2 3rd release for imports, exports, GDP; Federal Reserve Board for broad index of real dollar value; personal communication/Fed for rest-of-world export weighted GDP; and IMF International Financial Statistics for industrial country industrial production (nsa).)

I estimate an error correction version of this model over the 1973q3-2009q2 period, wherein there is a long run relation between the levels of imports, income and the real dollar.

In this specification, the long run elasticities are given by the ratio θ _i/ ρ . When this model is estimated over the 1973q3-2008q4 period, one obtains sensible estimates (in that higher foreign income or a weaker dollar induces greater exports in the long run).

This specification fits fairly well, with an adjusted R-squared of 0.34, and the serial correlation test again failing to reject. The long run coefficients are significant, as is the reversion coefficient (ρ).

One way of evaluating whether the 2008q4-09q1 observations are anomalous, in a statistically significant sense, is to examine the recursive residuals. A recursive residual is the time t prediction error based upon the regression estimated up to time period t-1, but using time t values of the X variables. Figure 3 depicts the 95% standard error band; an observation outside that band suggestive structural instability in the regression equation.

Figure 3: Recursive residuals from standard model of exports error correction specification, 1974q1-2009q1. +/- two standard error band (red dashes).

For imports, an analogous specification is estimated:

Imp = α ₀ + α ₁ y + α ₂ r

Where Imp is real imports, y is real income, and r is the real value of the dollar.

Δ imp _t = β ₀ + φ imp _t-1 + β ₁ y _t-1 + β ₂ r _t-1 + γ ₁ Δ imp _t-1 + γ ₂ Δ y _t-1 + γ ₃ Δ r _t-1 + u _t

The specification fits fairly well, with an adjusted R-squared of 0.35. The long term coefficients are statistically significant, while the reversion coefficient (φ) is also significant and negative.

The recursive residuals are shown in Figure 4:

Figure 4: Recursive residuals from standard model of imports error correction specification, 1974q1-2009q1. +/- two standard error band (red dashes).

One observation is that using a fairly flexible econometric form (the ECM) with pretty high estimated income elasticities, I cannot track the downturn in exports and imports. (The estimated short run export income elasticity is 2.8, while the import income elasticity is 1.8.)

Now, what is true is that a constant parameter specification such as these cannot accomodate the time variation that Freund stresses — namely that income elasticities in the 2000’s have been substantially higher than in the previous decades.

If one restricts the sample to 2000q1-09q2, the short run export income elasticity falls to 2.5, but rises to 2.5 for imports. Nonetheless, the one-step ahead recursive residuals test still rejects stability for 08q4 and 09q1.

It’s possible that the addition of other regressors would, in conjunction with a shorter sample, eliminate this instability in the equations. Pursuing that avenue remains for future research.

A couple of other interesting results arise from the full sample estimation. The long run price elasticity of exports is 1.4, while that for imports is 0.6. These are substantially higher than those I’ve reported in the past [5]; however, these estimates are subject to considerable uncertainty. The 90% confidence interval for the long run exports price elasticity is [0.56,2.22] (recalling the long run elasticity is the ratio of two coefficients).