How High Do Income Elasticities Have to Be to Explain the Recent Import Drop-off?

There’s been a debate over the cause of the trade flow drop-off, with varying explanations being offered. Broadly speaking, the explanations are (1) trade credit and credit crunch more broadly, (2) enhanced vertical specialization implying higher income elasticities, and (3) compositional effects (the trade dependent sectors were those most highly affected in the latest recession). Without necessarily offering definitive evidence one way or the other, I wanted to quantify the extent to which income elasticities had to be higher in order to rationalize the movements observed in US data.


Figure 1: Actual q/q change in log real goods imports ex-petroleum, in Ch.2005$ (black), fit using equation estimated over 1989q1-08q2 data (blue), over 1989q1-09q3 data (red), over 1989q1-09q3 data and including dummy for last recession (green). NBER defined recession dates shaded gray, assumes last recession ends 2009q2. Source: BEA, 2009q3 2nd release, NBER, and author’s calculations.

Figure 1 depicts the q/q (not annualized) change in real non-oil goods imports over the past twenty years. The drop in this current recession far exceeds that occurring in the previous two recessions, despite the fact that that same vertical specialization could arguably been in place as well.

I try to match the drop, first by estimating an error correction model over the 1989q1-08q2 period.

Δ imp t = β 0 + φ imp t-1 + β 1 y t-1 + β 2 r t-1 + γ 0 Δ imp t-1 + γ 1 Δ y t + 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 0.51 (it differs from the specification in this post in that contemporaneous GDP growth enters). The long term coefficients are statistically significant, while the reversion coefficient (φ) is also significant and negative. The sum of γ0 + γ1 = 2.42. Even with this fairly high short run income elasticity, the import decline is underpredicted by 10.6 percentage points on a nonannualized basis (see the blue line).

Using the entire sample (89q1-09q3), the sum of the γ coefficients is 3.82. The adjusted R2 rises to 0.64. Yet the underprediction of the decline (as shown in red) is still 6.6 percentage points.

One way to directly evaluate the import elasticity necessary to account for the observed decline in imports is to interact the changes in GDP (both contemporaneous and lagged) with a dummy for this current recession. Here I assume the recession ends at 09q2.

The resulting estimate fits extremely well, with an adjusted R2 of 0.71. The sum of the γ coefficients is 1.82, and (according to the estimates on the interaction terms) rises to 6.93 (!) during this current recession. Then the underprediction is only 3.6 percentage points.

Is it plausible that the income elasticity of non-oil imports has rise so much? That question is dealt with at length in the recent VoxEU volume on the trade collapse. If indeed the trade elasticities observed during the recession persist, then the resurgence in US imports will indeed be very strong — at least in the short to medium term (the econometric specification I used did not allow for the long run elasticity to vary; this is 2.68 in the last specification).

Of course, not all is the same as before the crisis. While the dollar is not as weak as just before the Lehman bankruptcy, it is substantially weaker than it was in, for instance, 2006.

5 thoughts on “How High Do Income Elasticities Have to Be to Explain the Recent Import Drop-off?

  1. Cedric Regula

    “Of course, not all is the same as before the crisis. While the dollar is not as weak as just before the Lehman bankruptcy, it is substantially weaker than it was in, for instance, 2006.”
    The dollar may be the positive thing in the current environment if we continue on with default worries in the Middle East, Venezuela(need to pump more oil), and the PIGS.
    But other sea changes are:
    1) The US Macro Consumer needs a jobful recovery, which is unlikely for quite some time.
    2) Personal Savings Rate was near zero, has increased, and many are saying that needs to continue and maybe even increase.
    3) Our health care cost reduction initiative seems to cost a trillion, and they are looking for somewhere to stick the bill. The US consumer, US worker, and/or US taxpayer are prime targets.
    4) Global warming will cost anywhere from a little money to a lot of money, depending on how much cure they think we can afford.
    5) Taxes are going up.
    6) Interest rates are going up, unless of course they can figure out how to engineer a new inflation index.

  2. RicardoZ

    Is anyone else amused that formulas are now designed after the results are known. The formula is assumed to be correct so if the data changes and the results are not what you want, it must be because some variable just needs a tweak.
    Menzie maybe you should have been a climatologist.
    (Menzie, I am just kidding. I understand what you are doing, and besides, you are not nearly as bad as the climatologists.)

  3. AWH

    I suggest you add inventories to your analysis. There is a high quarterly correlation both for total imports and major components. The inventory drop this cycle was large.

    the inventory induced import surge now is likely to be large, and tempoary of course.

    trade finance probably had mainly indirect effects on US imports but was catastrophic in other world areas as your cited study suggests. cross border finance (mostly trade finance) to some areas fell by 1/2

    My out of date modeling findings and forecast assumptions had an income elasticity coefficient of about 3X but also including inventory variable.

    not all that far from your 3.8X?

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