This new NBER paper looks quite interesting. Suppose that I am an inventor and I create a blood test that correctly detects your probability of having cancer .5 years from now. For my test to accurately predict your future risk probability, a trained nurse must administer the blood sampling. As I debut my product, I will make sure that the qualified nurse does the test. The Scaling up problem is that if my test starts to sell by the millions, its accuracy will decline because there aren't enough qualified nurses to administer my test.
So, this isn't a case of constant returns to scale. As my production rises, the quality of my product declines and the RCT economists would say that my pilot study's average treatment effect over-states the average treatment effect as I scale up the size of my market.
But is this true? In a rational expectations model, If I can pre-commit that my product will be "big" (both in scale and with regards to its benefits if administered by a well trained nurse), then young nurses will train to be experts in my technology and will obtain the human capital necessary to operate my product. In this case, diminishing returns to my product may not kick in. I cannot credible signal my future success then a co-ordination failure will occur and the empirical researcher will observe that the average treatment effect declines with my scale of production (because I can't find qualified nurses to administer it).
Alternatively, suppose that I only roll out my product in California. High quality nurses may start to move to California because they can work with my technology and deliver results. In this case, my product's average treatment effect will not decline with the scale of my sales.
So, when there is a complementarity between a treatment (such as my blood test) and human skills --- the key issue for scale up is "rational expectations and market size" or "migration and general equilibrium".
Scarce inputs will not remain scarce for long if we receive a "heads up" of rising demand (i.e high nurse earnings for skilled nurses) or high demand in given spatial location (i.e nurse salaries for high skilled nurses in California). As usual, the shape of the supply curve in the long run versus the short run plays the key role here. RCT results can be scaled up if the complementary input is elastically supplied. If it isn't then you must ask, why isn't it? What is the barrier to entry?
Note that this is a blog post. I am ignoring "essential heterogeneity" of those at risk to be treated. Instead, I am focusing on the endogenous determination of the treatment's quality (not the demander's response to this treatment). #supplymatters