are then calculated as the sum of the annual effects. The growth rates used in the calculations are annual rates, not growth from the beginning year in the study period, so the percent change from year to in the economic variable nationwide for all industries combined is , while the national and regional industry-specific percent changes are and , respectively. Esteban-Marquillas Model In 1972, J.M. Esteban-Marquillas extended the traditional model to address criticism that the regional share effect is correlated to the regional industrial mix. In the Esteban-Marquillas model, the regional share effect itself is decomposed into two components, isolating a regional shift component that is not correlated to the industrial mix. The model introduced a then-new concept to shift-share analyses, a homothetic level of the economic variable within an industry. This is the theoretical value of the variable within an industry assuming the region has the same industrial mix as the nation. In the Esteban-Marquillas model, the calculations of the national share and industrial mix effects are unchanged. However, the regional share effect in the traditional model is separated into two effects: a new regional share effect that is not dependent on the industrial mix, and an allocation effect that is. The allocation effect indicates the extent to which the region is specialized in those industries where it enjoys a competitive advantage. Formula The regional change in the variable within industry between the two years and is defined as the sum of the four shift-share effects: national growth effect (), industry mix effect (), regional share effect (), and allocation effect (). The beginning and ending values of the economic variable within a particular industry are and , respectively. The beginning value of the regional homothetic variable within a particular industry is . It is based on the regional and national values of the economic variable across all industries, and respectively, and the industry-specific national value . Each of the four shift-share effects is defined as a percentage of either the beginning value of the economic variable, the homothetic variable, or the difference of the two. The total percent change in the economic variable nationwide for all industries combined is , while the national and regional industry-specific percent changes are and , respectively. Arcelus Model In 1984, Francisco Arcelus built upon Esteban-Marquillas' use of the homothetic variables and extended the traditional model even further. He used this method to