RDP 2007-10: Trade Costs and Some Puzzles in International Macroeconomics 2. Method and Data

Obstfeld and Rogoff (2001) present a series of simple models in which a percentage of the good is lost in transport to argue that trade costs can explain these three puzzles. The estimation approach used in this paper uses panel data (across countries and time) to examine the link between trade costs and various measures of the extent of these puzzles (for example, a higher correlation between saving and investment for the Feldstein-Horioka puzzle).

The approach involves running regressions similar to those seen in the existing literature about these puzzles, but also including terms relating to trade costs, which are proxied by cost data based on US imports. These data are used because, firstly, it seems to be close to what Obstfeld and Rogoff's model suggests is most relevant (costs that cause a wedge between prices faced by locals and foreigners).^[8] Secondly, it is one of the few reliable sources for trade costs (Hummels and Lugovskyy 2006).^[9]

To examine whether trade costs play a role in the Feldstein-Horioka puzzle, variations of the following regression are run on data from 1974–2001:

where: t is a year index; i is a country index; I is investment; S is saving; and Y is output. f captures the average transport costs for shipments originating in country i to the US in year t (using data on US merchandise imports from Feenstra 2005). f is defined as the average percentage trade cost including insurance, derived as CIF (cost, insurance and freight) plus duties minus the FAS value (all expressed as a percentage of the FAS value). Results are also reported for measures excluding duties. Apart from the Feenstra trade data, much of the data used in the analysis comes from the World Bank World Development Indicators. This source provides a reasonably standardised collection of cross-country data. However, as with all cross-country data sets, there are likely to be concerns about the reliability of the data and their comparability across countries. The inclusion of fixed effects can be viewed as a way of controlling for some of these cross-country differences. A summary of the key data is provided in Table 1; details about the data and how the variables are defined are provided in Appendix A.^[10]

In short, the regression describes investment as depending upon: (a) country fixed effects (to capture potentially relevant factors that may be relatively invariant over time); (b) saving; (c) saving interacted with trade costs (to allow for the investment-saving relationship to vary with trade costs); and (d) trade costs (as trade costs may be associated with lower investment).

If trade costs provide at least a partial explanation of the puzzle, γ₁ would be expected to be positive. If γ₁ is positive and φ₁ is not statistically different from zero, the results could be interpreted as suggesting that trade costs explain all of the puzzle. However there are a number of reasons why this is unlikely. For example, in real business cycle models with complete markets and no trade costs, shocks can lead to a co-movement of investment and saving. Some of the results in Kehoe and Perri (2002) seem consistent with this.^[11]

One possible concern about estimating a regression like Equation (1) is that with the country fixed effects, the parameters of interest (for example, γ₁ and φ₁ ) are estimated from a small fraction of the variation in the independent variable (in this case, investment). There is some evidence that this is true.^[12] To some extent, the issue is that there is a trade-off between estimating with fewer fixed effects (such as estimating with just country fixed effects) and estimating with more fixed effects (such as with country-decade fixed effects). The former approach may reduce the extent of multicollinearity and is likely to be more informative as it estimates fewer parameters from the same number of observations (assuming the equations are not misspecified). The latter is likely to be more immune from arguments that other factors not included in the regression could explain the apparent correlation between investment and saving.

I also compare the results from estimating Equation (1) to the regression excluding the interaction and trade-cost terms. If trade costs can account for much of the puzzle, the coefficient on investment should be much smaller in a regression of Equation (1) than in the regression without trade-cost terms.

For the purchasing PPP, variations of the following regressions are estimated:

where RER is a real exchange rate index. Here, country fixed effects are not included because to do so in the presence of a lagged dependent variable would result in biased estimates.^[13]

If trade costs are a contributor to the PPP puzzle, the coefficient on the third term, γ₂, is expected to be positive, indicating that higher trade costs increase the persistence of the real exchange rate and decrease the speed of convergence. The model is estimated in both logs, Equation (2), and levels, Equation (3). The former has the advantage of reducing the influence of some observations that are extreme, which may be due to the real exchange rate being poorly measured.^[14]

To examine the effect of trade costs on the international consumption correlation puzzle, variations of the following regression are estimated:

where: C and GDP are consumption and output per capita; and C* and GDP* are world consumption and output per capita (in real US dollars).^[15] Under a simple model of complete insurance, the growth rate of every individual's consumption could be expected to be equal. In this case, the growth rate of national consumption per capita should equal the growth rate of world consumption per capita; alternatively, the ratio of national consumption per capita and world consumption per capita should be constant.^[16] So, if there is no consumption correlation puzzle (that is, there is complete risk sharing), all terms in Equation (4) except the country fixed effects should have coefficients which are equal to zero. Alternatively, with no risk sharing, consumption should move in line with national income (or output). If trade costs explain all of the puzzle, the coefficient on the third term should be positive and the coefficient on the second term should be zero.

I also estimate a version using consumption and output measured in PPP terms. Such PPP measures may be more appropriate as they value goods according to common international prices, however, there is no readily available measure of world output on this basis, so I include year fixed effects in order to capture the effect of these omitted terms.

One potential concern with estimating Equation (4) is that it ignores the possibility that the consumption puzzle is explained by consumption of non-tradable goods like housing. There is some evidence that non-tradables can explain the consumption correlation puzzle (Lewis 1996). Partly due to data availability and partly to examine how much of the puzzle can be explained by trade costs alone, my analysis does not take into account the role of non-tradables.

Footnotes

Plausibly, other factors affecting prices faced by foreigners (compared to locals) – such as non-tariff barriers and intranational transportation costs – are positively correlated with the measure used. To the extent that they are uncorrelated, the coefficients estimated may be biased towards zero and may explain the insignificance of some of the statistical results below. Anderson and van Wincoop (2004) provide a rich discussion of issues relating to trade costs such as their measurement. [8]

Analysis of the 1999 data from the IMF Direction of Trade Statistics (DOTS) confirms that these statistics are not a reliable source from which to infer trade costs. In particular, it is not uncommon for the cost insurance and freight (CIF) measure of trade to be less than the FOB measure of the same trade flow, implying a negative trade-weighted trade cost for some countries (even after adding 10 per cent to costs for Australia and Canada, where imports are reported FOB rather than CIF). As the US is the most significant economy in the world, it seems reasonable to think that US costs are likely to be a reasonable proxy for costs applying to a significant portion of world trade. This issue will be discussed further below. [9]

The regressions are generally estimated with dummies using least squares. This will yield reliable estimates if the number of countries is sufficiently large, which I am assuming is true here. [10]

Obstfeld and Rogoff (1996, ch 3) provide additional reasons why trade costs may explain only part of the puzzle. However, the regression results below may, to some extent, control for these other potential explanations of the puzzle, like demographic change, via decade fixed effects. [11]

The concern is that there is a close-to-linear relationship between the main variables of interest (for example, saving interacted with trade costs) and the other right-hand-side variables. A fair amount of this multicollinearity is due to the relationship between the interaction term and trade costs. As discussed in Deaton (1997), a concern could be that including fixed effects (and other controls) increases the noise-to-signal ratio in the independent variable of interest, potentially making the estimates appear insignificant even if the underlying relationship between trade costs and the puzzle is important. The insignificance of some coefficients is consistent with this. [12]

As mentioned previously, Taylor (2000) has discussed how this type of regression is not necessarily inconsistent with PPP. However, a number of authors, including Imbs et al (2005), estimate a linear model similar to Equation (2) and treat the coefficient on the first lag of the exchange rate as indicative of the extent of the PPP puzzle. Even if this is not informative about the PPP puzzle, the results indicate the persistence of the real exchange rate. As the real effective exchange rate is arguably the most relevant for developments in the economy, it is the focus of the analysis, though some robustness checks are done with bilateral real exchange rates. [13]

An alternative approach could be to include trade-cost terms in some of the popular non-linear models such as Exponential Smooth Transition Autoregressive (often referred to as ESTAR; see, for example, Kilian and Taylor 2001). Kilian and Taylor's results provide mixed evidence of whether trade (which is likely to be related to trade costs) explains the speed of adjustment. Countries for which shocks to the real exchange rate have relatively short half-lives (France, Germany, Italy and the United Kingdom) trade less, considering the size of their economy, than two of the other economies in the sample (Canada and Switzerland), but more than the only other country in the sample (Japan). [14]

This specification is similar in spirit to the one in Sørensen et al (2005). [15]

In an economy with a fixed population, where all individuals have identical preferences with constant relative risk aversion, each individual will consume a constant share of world consumption each period (see Obstfeld and Rogoff 1996). This implies that individual consumption growth will be the same across individuals in each time period. Hence, national per capita consumption growth should equal world per capita consumption growth. The specification of Equation (4) has been driven by a desire to use a similar regression to that of Equations (1) to (3), while being similar to previous statistical examinations of the extent of complete insurance (for example, Townsend 1994, chapter 5 of Obstfeld and Rogoff 1996 and Sørensen et al 2005). [16]