Testing the law of one-price in the US gasoline market: a long memory approach

This paper aims to shed new light on "law of one-price " in the United States' gasoline market over the period June-2003-December-2019. Specifically, we test for convergence of the retail prices of gasoline in different US PADDs, states and cities using the Local Whittle estimator (LW) and its variants (Robinson 1995, Shimotsu and Phillips 2005). Mean/trend reversion of the relative price of each unit will imply convergence toward the average price in the US thereby offering support for the law of one-price. LW estimators allow us to consider the case where relative gasoline price are fractionally integrated process and may display long memory implying a slow process of convergence. The results obtained generally offer support for the law of one-price albeit with significant differences in the rate of convergence between PADDs, States and Cities. In detail, a slow convergence (long memory process) is observed for PADD3 (Gulf Coast), PADD5 (West Coast) and then confirmed at the level of States (California, Texas and Washington) and at the level of Cities (Los Angeles, San Francisco and Houston). Among the cities, two of four empirical model employed find a slow convergence process is also in the cities of New York, Cleveland and Miami.