Shift-share analysis

Shift/share analysis is a technique sometimes used for retrospectively decomposing changes, usually in employment, in a set of urban areas or regions. Regional scientists widely use the technique to examine the sources of employment growth or decline.

We have a study area in which employment and population are growing (or declining; the technique works the same way in either case and it saves words to make the growth assumption.) Total employment in our area is "e", and that in the "i^th" activity is "e_i" . We have a larger frame reference area, usually the nation, where total employment is "E", and that in the "i^th" activity is "E_i" . The shift-share model says that growth in the study area’s "i^th" activity employment is a function of:

* The study area’s share of national (or regional) growth.
* The mix change in activities.
* And the shift change of activities toward the study area.

This says that change in employment in the study area’s "ith" activity from time "t" to time "t+n" can be measured:

:$e\_i^\{t\; +\; n\}\; -\; e\_i^t\; =\; share;change\; +\; mix;change\; +\; shift;change$

or

:$e\_i^\{t\; +\; n\}\; -\; e\_i^t\; =\; e\_i^t\; left\; [${E_{}^{t + n} } over {E_{}^t - 1} ight] + e_i^t left [ {E_i^{t + n} } over {E_i^t - E^{t + n} } over {E^t } ight] + e_i^t left [ {e_i^{t + n} } over {e_i^t - E_i^{t + n} } over {E_i^t } ight]

As this brief discussion suggests, shift-share analysis may be viewed as adding explicit considerations to economic base analysis. Economic base analysis asks how an area shares in national growth. Shift-share goes on to look at the changing mix of activities and at whether activities are shifting toward or away from the study area.