Methods

        We used a shift-share analysis to distinguish between likely causes of changes in California’s share of U.S. trade. In this appendix, we provide some background on the calculations underlying the analysis.

        Shift-share analysis begins with the observation that California’s share of U.S. trade flows into a particular customs district, by a particular mode of transportation, of a particular commodity, from a particular country, can be computationally calculated as follows:

where l indexes U.S. customs districts, i indexes mode, j indexes commodities, and k indexes countries. If V indicates either the value or the weight of trade flows, the terms on the right-hand side of the equation are then defined as:

and is district l’s share of U.S. imports or exports of goods shipped by mode i, commodity j, from or to country k,

and is mode i’s share of U.S. imports or exports of commodity j, from or to country k, and is commodity j’s share of U.S. imports or exports from or to country k,

and is country k’s share of all U.S. imports or exports.

        Any change in one of California’s trade shares, T^l_ijk can then be broken down into the portion attributable to changes in flows into California’s customs districts, changes in the modal choice of shippers, changes in the commodity composition of U.S. trade flows, or changes in the country composition of those trading with the United States. Although changes in flows through California’s customs districts may result from changes in modal choice, or country or commodity composition of U.S. trade, this analysis removes these factors before ascribing any change in share to elements fundamental to the demand for port services; these changes may result from technological change (bigger ships need deeper ports, or airplanes are able to fly greater distances), relocation of internal markets, or some other change in the demand for port services in California, for instance, relative user fees or costs associated with congestion.

        The decomposition is with respect to changes in trade flows between two time periods and is calculated as follows:

where ∆ indicates the change in the share over time and X indicates the average of the share in the two time periods. As a shorthand, we can write:

By adding up these changes in different ways, we are able to discern the proximate sources of the total changes in California’s share, T. For instance,

indicates the contribution of changes in the pattern of port demand to changes in customs district l’s share of U.S. trade. This can be more or less than the district’s actual change in share depending on the influence of changes in modal choice or the commodity and country composition of trade.