BUS606: Operations and Supply Chain Management

The gravity model is the workhorse of empirical international trade. Typically, it is used to obtain econometric estimates of the sensitivity of trade flows with respect to particular trade cost factors, and to run counterfactual simulations based on those estimates. Novy turns the gravity model on its head to develop a methodology for inferring trade costs based on the observed pattern of trade and production. He starts from a variety of theory-based gravity models, and uses simple algebra to derive a theory-consistent expression for bilateral trade costs between two countries. His approach has been applied in a number of recent papers, such as: Jacks et al. on trade costs over the 1870-2000 period; Shepherd, who uses the methodology to assess the effectiveness of trade facilitation programs in APEC and ASEAN; Brooks and Ferrarini on trade costs between India and China; Duval and Utoktham on trade costs in the Asia-Pacific; Miroudot et al. on trade costs in international services markets; and Olper and Raimondi on trade costs in food industries. 

There are three main advantages to the Novy methodology. First, it is "top down", in the sense that it provides an all-inclusive measure of trade costs, covering all factors - even unobservables - affecting exports and imports. Second, its data requirements are limited to the value of domestic and international shipments, which can be approximated using commonly available data from national accounts and standard trade databases. It is not necessary to have policy data on the full range of trade costs in order to properly account for them using this approach. Third, the methodology is theory-based, and relies on an identity relationship rather than econometric estimation. There is thus no risk of omitted variable bias, or other problems that typically plague econometric estimates of gravity models.

Of course, the cost of relying heavily on theory is that if it is incorrect, then the decomposition might also be erroneous. However, Novy shows that the approach used here can be applied successfully to a variety of theoretical models of trade; it obviously captures a deep regularity in the relationship between trade costs, production, and trade flows. He also shows that it is highly robust to the possibility of measurement error.

In ad valorem equivalent terms, Novy's measure takes the following form:

$\bar{t}_{i j t}^{k}=\left(\frac{t_{i j t}^{k} t_{j i t}^{k}}{t_{i i t}^{k} t_{j j t}^{k}}\right)^{\frac{1}{2}}-1=\left(\frac{x_{i i t}^{k} x_{j j t}^{k}}{x_{i j t}^{k} x_{j i t}^{k}}\right)^{\frac{1}{2(s-1)}}-1$

where: $\bar{t}_{i j t}^{k}$ is the geometric average of trade costs facing exports from country i to country j and those facing exports from country j to country i; k and t index sectors and time periods respectively; $\dfrac{t^{k}_{ijt}}{t^{k}_{iit}}$ is the cost of shipping goods from country i to country j relative to the cost of shipping them within country i;  $\dfrac{x^{k}_{iit}}{x^{k}_{ijt}}$ is the value of goods shipped within country i relative to the value of those shipped from country i to country j; and s is a model parameter, usually the elasticity of substitution among product varieties within a sector.

The basic interpretation of equation (1) is straightforward: as the ratio of international trade relative to domestic shipments $(\frac{x_{i j t}^{k} \: x_{j i t}^{k}}{x_{i i t}^{k} \: x_{j j t}^{k}})$ increases, trade costs fall. In other words, trade costs must be lower when countries exhibit a greater tendency to trade with each other rather than with themselves. The precise relationship between trade costs and the ratio of trade to domestic shipments depends on how substitutable the goods in question are: in more homogeneous sectors, the effect on trade costs of a given change in the ratio is dampened.

However, it is important to be clear on a number of other aspects of the interpretation of . First, it represents average trade costs in both directions between i and j. The structure of the model is such 38 that it is not possible to derive expressions for unidirectional trade costs in terms of observables. From a policy perspective, it is therefore important to interpret changes in $\bar{t}_{i j t}^{k}$ cautiously: they might be caused by policy changes in country i, in country j, or in both simultaneously.

Second, as the first part of equation (1) indicates, $\bar{t}_{i j t}^{k}$ depends on the ratio of international trade costs to domestic trade costs  $(\frac{t_{i j t}^{k}} {t_{j i t}^{k} } \: \text {and} \: \frac{t_{j i t}^{k} }{t_{j j t}^{k}})$. One aspect of this connection is that some kinds of "behind-the-border" trade costs are effectively cancelled out in the final measure of average trade costs, namely those that affect domestic and foreign producers in exactly the same way. However, many behind-the-border measures discriminate in fact, if not in law, in the sense that it is more costly for foreign producers to obtain information on procedures, or navigate a path through domestic regulations and institutions. These kinds of differences are captured in $\bar{t}_{i j t}^{k}$. However, when comparing trade costs across countries, it is impossible to separately identify international versus domestic trade costs.

Third, $\bar{t}_{i j t}^{k}$ is an all-inclusive measure of trade costs, in the sense that it takes account of the full range of transaction costs affecting exports and imports. It thus takes account of logistics performance. It is not a measure of protection, like the World Bank's Trade Restrictiveness Indices. It takes account of tariff and non-tariff barriers to trade, but also includes a wide range of other trade cost factors typically captured in gravity models. Examples include geographical distance, and cultural or historical links. As a result, $\bar{t}_{i j t}^{k}$ is generally much larger in magnitude than the rates of protection trade economists are used to dealing with in measures such as the Overall Trade Restrictiveness Index (OTRI) or average applied tariffs.

Once the Novy trade cost measure has been calculated for a range of countries, it is possible to use an econometric decomposition to assess the impact of different factors on the overall level of trade costs. Shepherd adopts this approach to examine the impact of logistics performance on total trade costs in the Maghreb region (Table 5). Logistics costs are captured by a rescaled version of the LPI, 39 in which a higher score indicates poorer performance. Results show that logistics performance is clearly an important determinant of trade costs in this sample of countries: increasing logistics performance by 10% would tend to decrease trade costs by 6.5% in manufacturing and 8% in agriculture.

Table 5: Regression Results Using Log(Trade Costs) as the Dependent Variable, 2007 Only.

To illustrate the relative importance of the various factors as determinants of overall trade costs, Chen and Novy (2010) suggest a variance decomposition approach. The percentage of the observed variance in trade costs accounted for by logistics, for example, is given by the following expression:

$\text { Variance } \%=\beta_{1} \frac{\operatorname{cov}\left[\log \left(\bar{t}_{i j}^{k}\right), \log \left(\overline{\operatorname{Logistlcs}_{i j}}\right)\right]}{\operatorname{var}\left[\log \left(\bar{t}_{i j}^{k}\right)\right]}$

where $\beta_{1}$ is the relevant partial regression coefficient. Applying this approach to the model for manufacturing (Table 5, column 1) shows that logistics accounts for just over 15% of the observed variation in total trade costs. Tariffs, by comparison, account for only 0.6% of the variation in trade costs, but distance accounts for over one-third of the total. Although these are little more than "back of the envelope" calculations, it is clear that as far as policy- related impediments to trade are concerned, logistics is an issue of major quantitative importance. This result lines up well with the existing literature, which tends to suggest that the gains from reforming non-tariff measures - and in particular trade facilitation and logistics - outweigh the gains from comparable tariff reductions.

Clearly, it will be important for future research to expand the country sample used for this analysis to include a broader range of countries. Inclusion of LPI scores for 2007 and 2009 will make it possible to control for a range of country- specific factors using fixed effects, thereby reducing the risk of omitted variables bias. Nonetheless, it seems likely that the basic results presented here will be confirmed, namely that logistics is a very important determinant of bilateral trade costs, accounting for perhaps as much as 15% of the total.