Frolich and Lechner want to determine the effectiveness of Swiss labor training programs for the subsequent employment and earnings of the unemployed Swiss workers who enroll in the program. The authors take advantage of widespread regional variation in program participation as the source of causal identification. Now in general it is quite common for participation rates to vary across regions or other relevant geo-spatial units – for example poorer areas may have higher rates of participation in anti-poverty programs.
Can we correlate the spatial variation in participation with the spatial variation in the outcomes we care about in order the assess program effectiveness? The ready answer is no because the variation in participation doesn’t satisfy the requirements of a valid instrument: (a) the variation may not be due to exogenous factors so, as a consequence, (b) the characteristics of the local area partly determine the outcomes that the program hopes to influence and hence the variation in program participation doesn’t satisfy the necessary “exclusion restriction” – the spatial variation in program participation is related to the outcomes through many possible channels aside from the effects of the program.
However, Frolich and Lechner note two unique characteristics of their setting:
2. … the Cantonal borders often bisect local labor markets. In many localities in Switzerland (as well as elsewhere) the relevant labor market for workers crosses several administrative boundaries. It is this fact that generates the counterfactual because workers on both sides of the border face the same employment prospects even though they face different training program intensities (as a result of different quotas). If we accept the common labor market argument than the regional variation in participation can be used as a valid instrument.
To operationalize the analysis the authors need to define local labor markets and then search for such markets that are bisected by Cantonal boundaries. So they look for clusters of regional employment offices (REOs, the entities tasked with supervising unemployed workers) that are spread over at least two Cantons. They further narrow their search according to other factors that would suggest a common local labor market, such as whether the two Cantons share a common language and whether the REOs are within no more than 30 minutes of each other by car. This process identified 18 local labor markets around Switzerland with different training quotas on either side of the Cantonal border.
This approach is essentially the recognition of a series of natural experiments created by the rules of the Swiss federal government, akin to the famous analysis of minimum wage effects on teen employment  by Card and Krueger that compared bordering areas of New Jersey and Pennsylvania. Only here in the Swiss case there are 18 experiments, not one, so Frolich and Lechner average across these experiments in order to estimate an average treatment effect.
They find that the receipt of training significantly increases the likelihood of employment. Over the 12-month period following training, a program recipient works two months more than a non-recipient – in the world of job training programs this is a rather large effect. There may also be an increase in earnings (per month worked) though this effect is not precisely estimated.
A couple issues of note.
Second, the authors not only report the IV estimate but the Conditional IV estimated (CIV) (a method first presented in this 2007 paper by Frolich ) that, by conditioning on worker observables, is better able to balance the characteristics of the workers used to estimate the treatment effect. The CIV must make additional assumptions beyond the standard IV case, such as the complete absence of defiers (workers who choose not to participate in areas with high quotas but who would participate in training in low quota areas), which appear reasonable in this context. The impact estimates are slightly greater in magnitude for the CIV than the IV, suggesting that the characteristics of unemployed on either side of the Canton border are slightly different on average and this difference should be accounted for where possible.
This technical paper is a great example of how to leverage spatial variation in treatment intensities to estimate program impacts. But note the fundamental requirements of (a) exogeniety of treatment intensity with respect to the local area and/or (b) a valid exclusion restriction. Many of the proposals I reviewed failed one or both of these requirements. But without these features there is no way to sensibly use the regional differences in program intensity.