Published on Development Impact

A Stata package for estimating correlated random coefficient models

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Guest post by Jeffrey Michler and Emilia Tjernström


As researchers interested in technology adoption, we are often confronted with an empirical puzzle: why are adoption rates so low for so many high-potential technologies? The classic example in Sub-Saharan Africa is hybrid seed: whether it is hybrid maize in Kenya or improved sorghum in Zimbabwe, adoption rates of these high-yielding seeds are much lower than adoption rates of similar technologies in Asia or Latin America.

About ten years ago, Tavneet Suri, then a graduate student at Yale (now Associate Professor at MIT), proposed a clever explanation for this empirical puzzle. Maybe we had been looking at the wrong outcome variable! If the benefits and costs to adoption are heterogeneous across households, judging a technology’s suitability by its average returns could be misleading.

The role of heterogeneity
Suri’s paper ( 2011 - published; 2009 - ungated working paper version) examines the adoption decision for hybrid maize in Kenya and finds that the choice to adopt (or not!) is rational once she adequately controls for observed and unobserved heterogeneity at the household level. In other words, those households who have a comparative advantage in cultivating hybrid maize tended to adopt while those with a comparative advantage in cultivating traditional varieties tended not to adopt.

So the empirical puzzle was a puzzle no more! It only appeared to be a puzzle when researchers failed to account for selection into adoption that was driven by unobserved household heterogeneity.

Suri’s solution to the puzzle is intuitive and has had a substantial impact on the development literature (250+ citations), but it is not entirely new. Gary Becker and Barry Chiswick first discussed the idea that an individual’s choice to adopt a technology – in their case the choice to seek more schooling – is correlated with her or his returns to adoption ( Becker and Chiswick, 1966).

The difficulty has always been in measuring or controlling for this heterogeneity in the rate of return to adoption. Heckman and Vytlacil (1998) and Wooldridge (2003) developed instrumental variable approaches to controlling for what are called correlated random coefficients (CRC).

What was really new and innovative about Suri’s research was that she developed an alternative method for estimating these types of models. The approach, which is structural in nature, uses a set of reduced-form parameters to recover the structural parameters of interest using an optimal minimum distance estimator. The structural approach to identifying the CRC model has several advantages over the instrumental variables approach.

First, it does not require the selection of an instrument and the inevitable defense of the exclusion restriction. Rather, identification relies on a linear projection of the individual's rate of return onto his or her history of adoption. This is similar to the correlated random effects (CRE) method, pioneered by Mundlak (1978) and Chamberlain (1984), which has become a staple of panel data analysis.

Second, the approach allows the researcher to test how important a role an individual's rate of return (comparative advantage in Suri's terminology) plays in the adoption decision.

Third, the approach allows us to recover the distribution of the rate of return for post-estimation analysis. All of these are major improvements over the old way of estimating CRC models.

A new Stata command
Despite the numerous advantages, the method has not been widely adopted. We suspect that one reason might be that the coding and/or computational costs outweigh the benefits for many researchers. Therefore, together with Oscar Barriga Cabanillas and Aleksandr Michuda, we decided to lower the cost of adoption by developing a Stata package – mve – that allows users to estimate these models ( Barriga Cabanillas, Michler, Michuda, and Tjernstrom, 2017).

The package allows users to estimate Suri’s CRC model, along with more standard CRE models, and provides a variety of estimation options. Additionally, the package allows for up to five rounds of panel data and can accommodate additional endogenous regressors.

We hope that the package will prove useful to folks who want to estimate returns to adoption whenever these returns may be correlated with unobservables. This type of situation is common in the study of agricultural technologies, but as Becker and Chiswick demonstrated, similar issues can arise in numerous other empirical applications (e.g., educational, health behaviors, management techniques).

We have both altruistic and selfish reasons for sharing it here: on the one hand, we want to ensure that interested researchers will find out about it, and on the other hand, we would love to receive feedback on the package before we send a final version out for publication!

Getting started
To install the package, download the Stata files and copy them into the folder in which Stata stores .ado files. The location of the folder will depend on the user, but on Windows machines it is often C:\ado\personal.

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