Brent Gibbons’s journal round-up for 9th April 2018

Every Monday our authors provide a round-up of some of the most recently published peer reviewed articles from the field. We don’t cover everything, or even what’s most important – just a few papers that have interested the author. Visit our Resources page for links to more journals or follow the HealthEconBot. If you’d like to write one of our weekly journal round-ups, get in touch.

The effect of Medicaid on management of depression: evidence from the Oregon Health Insurance Experiment. The Milbank Quarterly [PubMed] Published 5th March 2018

For the first journal article of this week’s AHE round-up, I selected a follow-up study on the Oregon health insurance experiment. The Oregon Health Insurance Experiment (OHIE) used a lottery system to expand Medicaid to low-income uninsured adults (and their associated households) who were previously ineligible for coverage. Those interested in being part of the study had to sign up. Individuals were then randomly selected through the lottery, after which individuals needed to take further action to complete enrollment in Medicaid, which included showing that enrollment criteria were satisfied (e.g. income below 100% of poverty line). These details are important because many who were selected for the lottery did not complete enrollment in Medicaid, though being selected through the lottery was associated with a 25 percentage point increase in the probability of having insurance (which the authors confirm was overwhelmingly due to Medicaid and not other insurance). More details on the study and data are publicly available. The OHIE is a seminal study in that it allows researchers to study the effects of having insurance in an experimental design – albeit in the U.S. health care system’s context. The other study that comes to mind is of course the famous RAND health insurance experiment that allowed researchers to study the effects of different levels of health insurance coverage. For the OHIE, the authors importantly point out that it is not necessarily obvious what the impact of having insurance is. While we would expect increases in health care utilization, it is possible that increases in primary care utilization could result in offsetting reductions in other settings (e.g. hospital or emergency department use). Also, while we would expect increases in health as a result of increases in health care use, it is possible that by reducing adverse financial consequences (e.g. of unhealthy behavior), health insurance could discourage investments in health. Medicaid has also been criticized by some as not very good insurance – though there are strong arguments to the contrary. First-year outcomes were detailed in another paper. These included increased health care utilization (across all settings), decreased out-of-pocket medical expenditures, decreased medical debt, improvements in self-reported physical and mental health, and decreased probability of screening positive for depression. In the follow-up paper on management of depression, the authors further explore the causal effect and causal pathway of having Medicaid on depression diagnosis, treatment, and symptoms. Outcomes of interest are the effect of having Medicaid on the prevalence of undiagnosed and untreated depression, the use of depression treatments including medication, and on self-reported depressive symptoms. Where possible, outcomes are examined for those with a prior depression diagnosis and those without. In order to examine the effect of Medicaid insurance (vs. being uninsured), the authors needed to control for the selection bias introduced from uncompleted enrollment into Medicaid. Instrumental variable 2SLS was used with lottery selection as the sole instrument. Local average treatment effects were reported with clustered standard errors on the household. The effect of Medicaid on the management of depression was overwhelmingly positive. For those with no prior depression diagnosis, it increased the chance of receiving a diagnosis and decreased the prevalence of undiagnosed depression (those who scored high on study survey depression instrument but with no official diagnosis). As far as treatment, Medicaid reduced the share of the population with untreated depression, virtually eliminating untreated depression among those with pre-lottery depression. There was a large reduction in unmet need for mental health treatment and an increased share who received specific mental health treatments (i.e. prescription drugs and talk therapy). For self-reported symptoms, Medicaid reduced the overall rate screened for depression symptoms in the post-lottery period. All effects were relatively strong in magnitude, giving an overall convincing picture that Medicaid increased access to treatment, which improved depression symptoms. The biggest limitation of this study is its generalizability. Much of the results were focused on the city of Portland, which may not represent more rural parts of the state. More importantly, this was limited to the state of Oregon for low-income adults who not only expressed interest in signing up, but who were able to follow through to complete enrollment. Other limitations were that the study only looked at the first two years of outcomes and that there was limited information on the types of treatments received.

Tobacco regulation and cost-benefit analysis: how should we value foregone consumer surplus? American Journal of Health Economics [PubMed] [RePEcPublished 23rd January 2018

This second article addresses a very interesting theoretical question in cost-benefit analysis, that has emerged in the context of tobacco regulation. The general question is how should foregone consumer surplus, in the form of reduced smoking, be valued? The history of this particular question in the context of recent FDA efforts to regulate smoking is quite fascinating. I highly recommend reading the article just for this background. In brief, the FDA issued proposed regulations to implement graphic warning labels on cigarettes in 2010 and more recently proposed that cigars and e-cigarettes should also be subject to FDA regulation. In both cases, an economic impact analysis was required and debates ensued on if, and how, foregone consumer surplus should be valued. Economists on both sides weighed-in, some arguing that the FDA should not consider foregone consumer surplus because smoking behavior is irrational, others arguing consumers are perfectly rational and informed and the full consumer surplus should be valued, and still others arguing that some consumer surplus should be counted but there is likely bounded rationality and that it is methodologically unclear how to perform a valuation in such a case. The authors helpfully break down the debate into the following questions: 1) if we assume consumers are fully informed and rational, what is the right approach? 2) are consumers fully informed and rational? and 3) if consumers are not fully informed and rational, what is the right approach? The reason the first question is important is that the FDA was conducting the economic impact analysis by examining health gains and foregone consumer surplus separately. However, if consumers are perfectly rational and informed, their preferences already account for health impacts, meaning that only changes in consumer surplus should be counted. On the second question, the authors explore the literature on smoking behavior to understand “whether consumers are rational in the sense of reflecting stable preferences that fully take into account the available information on current and expected future consequences of current choices.” In general, the literature shows that consumers are pretty well aware of the risks, though they may underestimate the difficulty of quitting. On whether consumers are rational is a much harder question. The authors explore different rational addiction models, including quasi-rational addiction models that take into account more recent developments in behavioral economics, but declare that the literature at this point provides no clear answer and that no empirical test exists to distinguish between rational and quasi-rational models. Without answering whether consumers are fully informed and rational, the authors suggest that welfare analysis – even in the face of bounded rationality – can still use a similar valuation approach to consumer surplus as was recommended for when consumers are fully informed and rational. A series of simple supply and demand curves are presented where there is a biased demand curve (demand under bounded rationality) and an unbiased demand curve (demand where fully informed and rational) and different regulations are illustrated. The implication is that rather than trying to estimate health gains as a result of regulations, what is needed is to understand the amount of demand bias as result of bounded rationality. Foregone consumer surplus can then be appropriately measured. Of course, more research is needed to estimate if, and how much, ‘demand bias’ or bounded rationality exists. The framework of the paper is extremely useful and it pushes health economists to consider advances that have been made in environmental economics to account for bounded rationality in cost-benefit analysis.

2SLS versus 2SRI: appropriate methods for rare outcomes and/or rare exposures. Health Economics [PubMed] Published 26th March 2018

This third paper I will touch on only briefly, but I wanted to include it as it addresses an important methodological topic. The paper explores several alternative instrumental variable estimation techniques for situations when the treatment (exposure) variable is binary, compared to the common 2SLS (two-stage least squares) estimation technique which was developed for a linear setting with continuous endogenous treatments and outcome measures. A more flexible approach, referred to as 2SRI (two-stage residual inclusion) allows for non-linear estimation methods in the first stage (and second stage), including logit or probit estimation methods. As the title suggests, these alternative estimation methods may be particularly useful when treatment (exposure) and/or outcomes are rare (e.g below 5%). Monte Carlo simulations are performed on what the authors term ‘the simplest case’ where the outcome, treatment, and instrument are binary variables and a range of results are considered as the treatment and/or outcome become rarer. Model bias and consistency are assessed in the ability to produce average treatment effects (ATEs) and local average treatment effects (LATEs), comparing the 2SLS, several forms of probit-probit 2SRI models, and a bivariate probit model. Results are that the 2SLS produced biased estimates of the ATE, especially as treatment and outcomes become rarer. The 2SRI models had substantially higher bias than the bivariate probit in producing ATEs (though the bivariate probit requires the assumption of bivariate normality). For LATE, 2SLS always produces consistent estimates, even if the linear probability model produces out of range predictions. Estimates for 2SRI models and the bivariate probit model were biased in producing LATEs. An empirical example was also tested with data on the impact of long-term care insurance on long-term care use. Conclusions are that 2SRI models do not dependably produce unbiased estimates of ATEs. Among the 2SRI models though, there were varying levels of bias and the 2SRI model with generalized residuals appeared to produce the least ATE bias. For more rare treatments and outcomes, the 2SRI model with Anscombe residuals generated the least ATE bias. Results were similar to another simulation study by Chapman and Brooks. The study enhances our understanding of how different instrumental variable estimation methods may function under conditions where treatment and outcome variables have nonlinear distributions and where those same treatments and outcomes are rare. In general, the authors give a cautionary note to say that there is not one perfect estimation method in these types of conditions and that researchers should be aware of the potential pitfalls of different estimation methods.

Credits

 

Biased towards bias?

A six hour delay flying home from the Health Economists Study Group conference in Gran Canaria is providing me with ample time to mull over the great issues in life. One of these big issues is of course the trade-off between bias and variance.

Typically the discussion of an empirical economics paper at a conference will focus heavily on the model and estimation method. Often the word ‘endogenous’ echoes round the room as the discussion considers whether the estimator employed is biased or not. This is of course an important consideration for any empirical work; but, the question of efficiency (essentially the variance) of the estimator rarely comes up. Indeed, Andrew Gelman has discussed this predilection among economists elsewhere. So, why don’t we prefer to think in terms of overall error?

As an example consider that fixed-effects (FE) models are generally almost always preferred to random-effects (RE) models among economists. (Although the meaning of these terms varies widely!) This is for reasons of unbiasedness; we teach undergraduates to choose FE if the Hausman test for a difference in FE and RE is rejected. But, RE is more efficient. So the question should be under what conditions is the overall error smaller in the RE model. If much of the variation is between individuals (or whatever the unit of a panel of data is) rather than within individuals, then the efficiency gains of RE may outweigh error due to bias.

To give a more mathematically explicit example consider the use of an ordinary least squares estimator (OLS) versus a two stage least squares (2SLS) estimator. If we have the simple linear model y = xβ + u, the OLS estimator is biased if Corr(x,u)=ρ≠0. In such cases if an instrumental variable, say z, is available, one which is correlated with but not with u, then 2SLS is an unbiased estimator. But what of overall error? If λ is the correlation between and x, and is the sample size, then 2SLS has a lower mean squared error than OLS if

ρ2 λ2 n/(1-λ2 )>1

Thus if the correlation between and u is low or the instruments are weak then OLS should be preferred in many cases. In many cases it comes down to whether the sample size is sufficient.

The same considerations could be made of predictive models for economic evaluation. An ambitious young student (as I was) may want to create an ever more complex model that captures this and that ambiguity in the world. While each addition may reduce bias in the prediction of the outcome it will increase variance. Thus beyond a certain point we will just increase the uncertainty in our predictions.

It could be argued that one of the key goals of research is a decision. Minimising the error in the estimator that informs the decision will lead to a lower probability of making the wrong decision. We should therefore consider overall error. This could be a plug for Bayesian methods; the posterior mean is an estimator that minimises the mean squared error. But, I don’t think Bayesianism is implied by the premises, we should just be less biased towards bias.

Photo credit: PeterPan23

#HEJC for 26/02/2015

The next #HEJC discussion will take place Thursday 26th February, at 11pm London time on Twitter. To see what this means for your time zone visit Time.is or join the Facebook event. For more information about the Health Economics Journal Club and how to take part, click here.

The paper for discussion is a working paper published by the Canadian Centre for Health Economics (CCHE). The authors are Koffi-Ahoto Kpelitse, Rose Anne Devlin and Sisira Sarma. The title of the paper is:

The effect of income on obesity among Canadian adults

Following the meeting, a transcript of the Twitter discussion can be downloaded here.

Links to the article

Direct: http://www.canadiancentreforhealtheconomics.ca/wp-content/uploads/2014/08/Sisira-et-al.pdf

RePEc: https://ideas.repec.org/p/cch/wpaper/14c002.html

Summary of the paper

This is the first paper to examine the causal relationship between income and obesity in the Canadian context. To do so, they examined data from five biennial Canadian Community Health Survey (from 2000/01 to 2009/10), a nationally representative survey collecting information on over 100,000 individuals each survey.

Initially, the paper explored the Grossman model, which suggested increasing income would promote healthy lifestyle investments, and thus lead to a negative relationship between income and obesity. Previous studies that examined this link were discussed, some (eg. Lindahl (2005)) demonstrating a negative relationship; some (eg. Schmeiser (2009)) demonstrating a positive relationship; some (eg. Cawley (2010)) finding no evidence of a causal relationship.

Additionally, education and employment were explored. Again, the Grossman model was used as a basis, predicting i) a negative relationship between education level and obesity with a greater income effect amongst educated people and ii) a negative relationship between employment level and obesity. However, regarding education, prior studies discussed have shown “mixed results”, and regarding employment, the authors were not aware of any study to examine this causal relationship, but suggested the relationship was ambiguous.

Finally, the relationship between gender and obesity were discussed. Numerous studies have shown negative association between income and BMI amongst women, but for men, the relationship is unclear (some showing positive relationship, some negative, and some no significant relationship at all). The importance of the effect of obesity on labour market outcomes (outlining the “large” empirical literature showing obese women more likely to suffer discrimination in the labour market) was outlined.

In this study, the authors found that:

  • From 2000/01 to 2009/10, BMI and obesity rates amongst both men and women have risen.
    • For men, the obesity rate rises from 19.48% for those with income below $10k to 26.09% for those with income over $80k.
    • For women obesity falls from 26.71% for those below $10k to 17.38% for those with income over $80k.
  • For men, a 1% rise in household income leads to 0.027 point decrease in BMI (2SLS estimate); 0.084kg reduction and 0.27% point decrease in probability of being obese (linear IV procedure).
  • For women, a 1% rise in household income leads to 0.113 point decrease in BMI (much higher than for men; this used a 2SLS estimate); 0.300kg reduction; and 0.76% point decrease in probability of being obese (linear IV procedure).
  • For men the effect of income on BMI was only demonstrated at higher BMI distribution, while for women the effect of income on BMI was found throughout with a larger effect at higher BMI.
  • Education had a variable relationship amongst both men and women, not consistent with the theoretical prediction that the effect would be larger amongst educated people.
  • The effect of employment for men was mixed, with a negative effect of income on BMI only in employed men and a negative effect of income on obesity probability only in unemployed men.
  • The effect of employment for women was more consistent with theoretical predictions, showing negative effects of income on both BMI and on the probability of being obese across employment status.
  • Higher BMI and probability of obesity was associated with older age, marriage (much greater effect in women), household size (much greater effect in women) and home ownership.
  • Lower BMI and probability of obesity was associated with being widowed/separated/divorced, being an immigrant and living in urban area (in men).

In summary, this study supports the findings of Lindahl, and stands in contrast to Schmeiser, Cawley and other related studies.

Discussion points

  • Why might there be significant variation in findings between the different studies discussed?
  • Are there ways in which unemployment and neighbourhood income might directly influence BMI?
  • Is the set of control variables used in the authors’ models satisfactory?
  • Is it of concern that policies to increase household income could be regarded a pure, explicit public health policy?
  • Are there relevant studies from other countries?
  • To what extent are these findings generalisable?

Can’t join in with the Twitter discussion? Add your thoughts on the paper in the comments below.