Constructing risk preference

The next step to my Possible Topic#2 (although the preliminary result was not too encouraging) is to construct individual risk preference coefficients.

A respondent was asked this question:

You have an equal chance of receiving either Rp1.6 million per month or Rp400 thousand per month, depending on how lucky you are. Option 1 guarantees you an income of Rp800 thousand per month. Which option will you choose?

If he chooses (2), the riskier option, then we assume that he prefers (2) to (1). That means U(2) > U(1).

We assume a constant relative risk aversion (CRRA) utility function (following Binswanger 1980, Holt and Laury 2002, Kimball, Sahm and Shaphiro 2009, Cameron and Shah 2009, and many more):

W^(1-r)/ 1-r

where r is the Arrow-Pratt coefficient of relative risk aversion defined as:

- WU''(C) / U'(C)

Hence, for the above gamble, we can write the individual's preference as:

0.5(1600^(1-r)/ 1-r) + 0.5(400^(1-r)/ 1-r) - (800^(1-r)/ 1-r) > 0

Solving the inequality, we get r < 1.

Now, let's say the individual chose the safer option for the follow-up question:

You have an equal chance of receiving either Rp1.6 million per month or Rp200 thousand per month, depending on how lucky you are. Option 1 guarantees you an income of Rp800 thousand per month. Which option will you choose?

The solution is r > 0.3058. So, for this individual, we conclude that his risk aversion lies between 0.3058 and 1, or 0.3058 < r < 1. Higher r implies a greater risk aversion, while lower or negative value of r implies a more risk-loving behavior.

Not-so-encouraging results

A first shot to see if my Possible Topic#2 might work. The results, unfortunately, are not so encouraging.

Here's why. The first of the hypothetical risk question is a filter to sort out ‘irrational’ individuals, or to make sure that they understood the question:

Suppose you are offered two ways to earn some money. With option 1, you are guaranteed Rp800 thousand per month. With option 2, you have an equal chance of either the same income, Rp800 thousand per month, or, if you are lucky, Rp1.6 million per month, which is more. Which option will you choose?

By the way, the questions were asked to adult individuals, and there are around 29 thousand of them in this category. If the respondent answered (1), the interviewers would make sure if they stood by their choice or wanted to switch. Even after the follow-up question, 42 percent respondents are 'irrational' - meaning they opted for a certain Rp800 thousand, even if the other option would not make them worse off. The number, for me, is too high and will pose a serious potential bias in the analysis.

After completing a series of further questions, the 'rational' individuals are categorized into for groups, from the most risk-averse to the most risk-loving. Half of them belong to the most risk-averse group; about a quarter are most risk-loving, 14 percent are somewhat risk-loving, and less than 10 percent are somewhat risk-averse (see picture). The distribution implies that the variations across group are quite small, which lead to a question whether we can see an interesting story from that.

And there are some other concerns I got from various discussions:

• Since these are not true experiments but hypothetical, the noise may be big to infer anything.
• These are hypothetical risk question about money/income. But people may have a different answer if it involves health. So applying this type of gamble to health behavior may not be correct.

It is too early to kill of the topic completely, but it does not give me an 'Eureka moment' either. So I am now shopping for another possible topic.

Possible topic#2 - Risk Preference, Time Preference and Health-related Decisions

Second attempt. So the motivations are:

• Developing countries have lower quality of health: lower life expectancy, higher infant (and adult) mortality rate, etc. Is it because of supply constraint (availability of public services)? Household budget constraint? Or because people value ‘good health’ less?
• Budget constraints causes households or individuals highly prefers today’s income than long-term human capital investment (high discount rate). This could lead to fewer amount of HH budget allocated for own and/or children’s health
• Lower valuation of future health means individuals would engage in riskier health behavior, such as smoking, less exercise, bad dietary habit, not having health insurance
• Policy relevance: a) if risk and time preference do explain less investment on health and riskier behavior, then policies that promote changes in behavior/valuation will be relevant, b) otherwise, improving income/well-being will be the more relevant approach.

Fortunately, new set of questions in IFLS-4 enables to do the analysis of individual's risk preference and discount rate. Discount rate could me measured using questions on whether the respondent prefers a lower amount of money now or a higher amount one year (five years) later. Risk preference coefficients can be calculated from hypothetical questions of a choice between a job that guarantees a certain amount of lifetime income, and another job that gives the individual a 50-50 chance of a getting a higher or lower amount than the previous one.

Once the discount rate is constructed, I can use it as one of the explanatory variables for parent's (mother's) investment in their children's health. The underlying hypothesis is higher discount rate explains lower investment in health.

There will be two main groups of individuals to analyze. The first one is pregnant women. The particular variables to analyze are: 1) number of months of elapsed pregnancy before going to the health service, 2) smoking behavior during pregnancy, and 3) utilization/number of visits to health service during pregnancy. The second group will be children aged 5-15 years, whose variables of interest are their immunization record (completion, delays), utilization of health services and anthropometric measures.

Risk preference coefficient will be used to analyze individual's health-related risky decisions. Focusing on adults, the variables of interests are smoking habit, utilization of preventive health care, access to health insurance, Body Mass Index (a proxy for health status, which is the outcome of behavior, and possibly eating habit. The underlying hypothesis is that higher individual's risk preference lead to riskier health behavior.

Update: supervisor kind of like this idea. She thought this is an interesting topic. One concern is whether I could get enough variations in the data to lead to something. We'll see.

Discarded Topic#1

Update: Possible Topic#1 is now Discarded Topic#1. Supervisor didn't agree, on the basis that 'they have been written for too many times. Oh, well.

Possible topic#1 - Health, Nutrition and Rural Household Welfare

Some motivations for looking at the link between health, nutrition and the welfare of rural households:

• Health and nutrition are important aspects of basic needs, while one of the main goals of economic development is to expand the capacity to obtain basic needs, especially for the poor people.
• The productivity of low-income people is strongly correlated with improved health and nutrition.
• Improving health and nutrition are important means in itself, as well as an instrument for improving welfare.

Behrman and Deolalikar in Handbook of Development Economics (1988) provided a good framework to start with. It is a modified household-farm decision making model, which was based on earlier works by Barnum and Squire (1979) and Singh, Squire and Strauss (1986).

Based on this, I intend to look at three specific issues:

1. Household demand function and income elasticity of nutrient (calorie).
2. Estimating the return of improved nutrient intake (calorie) and health status (Body Mass Index, anthropometric measures), evaluated in terms of: a) farm profit, b) individual wages, and c) output/productivity
3. Estimating the impact of healthy environment (clean water, improved sanitation) on children health status (as a proxy for human capital accumulation).