Correct Partitioning of Regional Growth Rates: Improvements in Shift-Share Theory *
Bibliographic record
Abstract
This paper demonstrates that the Ray-Srinath model resolves, conceptually and mathematically, the issues that are beyond the traditional shift-share model. It does this by establishing the mathematical links between the traditional and the Ray-Srinath models. Ray-Srinath partitions the traditional regional share rate into a region effect rate and a region-industry interaction rate. The traditional industry-mix rate is split into an industry-mix effect rate and an allocation rate. Four is the minimum number of components if they are to be clean ones. L'etude demontre que le modele Ray-Srinath resout les problemes conceptuels et mathematiques inherents au modele shift-share traditionnel en etablissant les liens mathematiques entre les deux modeles. Le modele Ray-Srinath decompose chacune des deux composantes du modele traditionnel en deux composantes plus raffinees et plus justes. La premiere composante traditionnelle, les conditions regionales, est decomposee en effet de region et effet d' interaction region-industrie. La seconde composante traditionnelle, la composition industrielle, est decomposee en effet de structure industrielle et effet d'allocation. Quatre est le nombre minimal requis pour que les composantes soient propres. Introduction Shift-share analysis has become one of the most widely-used partitioning techniques in regional development studies since it was introduced by Prof. J. Harry Jones in The Royal Commission on the Distribution of the Industrial Population published in 1940. Its appeal is that it provides a very simple method of partitioning regional employment growth into two fundamental components: a partitioning that is crucial to understanding regional growth patterns. The model first measures what it purports to be the contribution to employment growth of the regional industrial structure or industry-mix. The residual employment growth is then termed the regional share. Unfortunately they are incorrectly measured. Nevertheless, all analysts followed his lead, and his approach became the basis for the traditional shift-share model (Dunn 1959; Statistics Canada 1973). Regional analysts will not abandon a well-established technique without proof of its deficiencies. This paper seeks to provide that proof. It demonstrates that the results produced by the traditional model are incorrect, by identifying the precise mathematical relationship between his model and the Ray-Srinath model. In essence what this paper does is prove that when the regional growth rates are partitioned correctly the process results in the splitting of each of the two traditional components into two finer components which are correct mathematically in the sense that they measure what they say they do. The problems with the approach used by Jones are, however, conceptual as well as mathematical, and the conceptual limitations cannot be removed without first correcting the mathematical errors. In particular, regional analysts and policy makers no longer accept that regional disparities in employment growth can be understood properly merely in terms of regional industry-mix and regional shifts in industry. An important role is played by other factors, such as regional differences in firm-size distribution and, in an age of increasing globalization, the regional concentrations of foreign multi-national corporations. The Jones model is limited to testing a single assumption: that regional growth rates are largely controlled by industry mix. The Jones model cannot be extended to analyze these multivariate factors simultaneously. Nor can it be used to examine these regional forces two at a rime as they are interwoven and act together simultaneously. Hence in 1990, Ray and Srinath introduced a new multi-factor partitioning model to analyze regional disparities in employment growth (Ray 1990). It was then used to examine the impact on employment growth in Canada of industry-mix, the size-structure of firms, the level of foreign ownership and regional factors, as well as the interactions among them. …
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".