Change in the Rate of Time Preference

Table 23 Steady State Body Weight with a Change in ρ

United States Turkey Chile

Baseline -10% +10% Baseline -10% +10% Baseline -10% +10%

Body Weight (kg) 111 115 107 86 90 83 85 88 83

GDP 2.03 2.10 1.96 1.67 1.74 1.60 1.70 1.74 1.66

Thailand Egypt Mexico

Baseline -10% +10% Baseline -10% +10% Baseline -10% +10%

Body Weight (kg) 60 60 59 74 77 71 61 62 60

GDP 1.14 1.15 1.12 1.34 1.40 1.30 1.40 1.45 1.38

The rate of time preference is estimated using interest rates. In the case of a pandemic, consumers are likely to have two different, and opposite, responses.

There is the possibility that consumers consume less today due to an antici-pated risk of loss of future income. Those who can afford it, constitute more precautionary savings for the future. To represent this type of consumer, I in-crease ρ by 10% to reflect a inin-crease in impatience. There is also the possibility that consumers will consume more today out of fear of death or fear that the supply of food and other essential items will soon run out (i.e toilet paper). To represent this type of consumer, I decrease ρ by 10% to reflect an decrease in impatience. In most countries, in particular high GDP/capita countries, such as the United States, Turkey, and Chile, even a small change in the rate of time preference causes a significant change in body weight.

In the sensitivity analysis, I simulate large permanent changes in BMR, the tax to output ratio, annd the rate of time preference. In reality, while the pandemic is a large economic shock, the permannent chagnes that it involves are likelty to be lower than what is simulated, suggesting that my resultrs are pretty robust.

6 Conclusion

The empirical evidence shows a positive relationship between income and obesity using singular increases in income such as government transfers, but it lacks evidence of a dynamic relationship between income growth and the rise in obesity. The goal of this thesis is to quantify the positive relationship of income growth and obesity prevalence. To this end, I extend the Ramsey (1928), Cass (1965), and Koopmans (1965) (RCK) model to account for body weight by including the Schofield (1985) equation. This thesis develops and simulates a dynamic model of the relationship between income growth and increased obesity prevalence in six different countries across the world. Those countries are the United States, Thailand, Chile, Turkey, Egypt, and Mexico. There are three main results of my work.

First, all countries except Thailand reach steady state levels of body weight that are classified as overweight or obese. I find that countries with a higher relative GDP/capita such as the United States, Turkey, and Chile all reach higher relative average BMIs than the low per capita GDP countries, which are Thailand, Mexico, and Egypt. In the long run, the model predicts an average BMI above the obesity threshold of 30 for the United states, Turkey, and Chile. The United States, which is clearly the richest of these countries even has a predicted average obesity of 38 which is considered Class 2, morbidly obese. Furthermore, Mexico, which is the highest GDP of the low GDP/capita countries, has a predicted average BMI of 25, which is considered overweight in the long run. The only country that has a predicted average BMI that is within a normal range (<24.99) is Thailand with a predicted BMI of 22.

Second over time in all studied nations, we see an increasing obesity preva-lence as the economy transitions from less developed to more developed. Though the model predicts growth in body weight over time as income increases, some

countries reach overweight or obesity at a faster rate than others. There is a range of 3.8 years for Egypt to 8 years for the United states to reach an over-weight level. This is especially significant when compared to a low GDP/capita country such as Mexico, which reaches this same threshold towards about 15.5 years into the transition. It appears that after a country reaches the overweight level, the time to reach the obese threshold is much shorter. It takes the United States only 11.6 years to reach its obese threshold which is only 3.6 years after it reaches the overweight threshold. In general, this means that when countries are on a path to reach a high standard of living, they are more prone to reaching obesity levels. There are however discrepancies in how fast they reach over-weightness, which also means some countries’ economies development is more or less conducive to rapidly reaching an overweight threshold.

Third, the effect of income growth on body weight is larger in rich than in poor countries. It is important to understand that all countries start at the same level of development and those countries that are primed to reach a higher level of GDP, and thus, average body weight, are those that have higher GDP/capita and growth structures. The United states has an elasticity of 0.252 in year 5 whereas in the same year Thailand has an elasticity of 0.059. This discrepancy means that the US’s average body weight is influenced more by its GDP/capita structure than in Thailand even though they are in the same year of development. The reason they reach different levels of development and average body weight is because of their GDP/capita and growth rates. These elasticities shows the higher the GDP/capita the more of an effect it has on the average body weight in each economy. This observation confirms that the level of GDP/capita influences the obesity prevalence of a country, because all high GDP/capita countries have a higher elasticity than the low GDP/capita countries.

However, we also see a diminishing effect on body weight as income increases in a more developed nation. The model predicts a diminishing effect of income growth on body weight gain. This is observable in both a developed nation, such as the United States, and a developing country, such as Egypt. The effect of GDP growth on body weight gain falls from .0252 to 0.092 within only ten years in the United States. This pattern is the same in Egypt because the effect of GDP growth on body weight gain falls from 0.137 to 0.0008 within the same ten years. The importance of these elasticities is to show the diminishing effect of income growth on body weight gain, which matches the empirical observations by Sobal and Stunkard (1989) and Mclaren and Kuh (2004).

To test the robustness of my results, I conduct a sensitivity analysis that focuses on parameter and policy changes linked to the coronavirus pandemic.

First, I decrease the BMR used in the model by 400 kcal for an individual to reflect a more sedentary lifestyle due to quarantine orders. Though the steady state increase in weight compared to the baseline varies from 18 kilograms for Thailand up to 35 kilograms for the United States, there is a clear increase in each country when BMR is decreased. Next, I change parameters that have an effect on income as well as body weight. My model predicts that a negative effect on income, such as an increase in a tax, causes a decrease in average body weight, but by a smaller magnitude than the tax increase itself. Yet, high GDP/capita nations predicted an average 4.5% decrease in body weight with a 10% decrease lifetime income. The nation with the smallest decrease in body weight is Egypt with a 2.7% decrease in average body weight and the nation with the highest decrease in body weight is Thailand with a 6.6%

decrease in average body weight. If consumers are less impatient and constitute precautionary saving, this also causes an increase in body weight but, again by a small magnitude. With a 10% change in income, the model predicts a range of

values for body weight change between 1.6 and 6.6% for all nations. Generally, for high GDP/capita nations, such as the United States, Turkey, and Chile, a small change in the rate of time preference causes a significant change in body weight. Throughout my sensitivity analysis, I simulate large permanent changes in all of the parameters. In reality, the effects of the pandemic, though large, are not likely to last forever, and thus are likely to ne lower than what is simulated.

This suggests my results are pretty robust.

As with all research, there are some limitations to acknowledge. My model is based on overall consumption choices for households, rather than just food choices. The share of food consumption out of total consumption is fixed in this model, but in reality, this share changes as an economy develops. This means the model overvalues average body weight and average BMI. It is also important to note that there is not a homogenous income in each nation as the model presents. I do not account for socioeconomic differences in the population when predicting average body weight and BMI for each nation. The empirical evidence indicates that obesity prevalence is higher among poor cohorts in richer nations and among rich cohorts in poor countries. There is not a variable in the model that captures the wealth status of different socioeconomic classes in each nation, therefore it is possible that the average BMI and average body weight are over- or undervalued depending on the makeup of the population.

There are still significant points of research in the complex relationship of obesity prevalence and income growth across the globe. A few areas that are lacking in the literature include estimating the welfare effects of obesity. What does it mean to the healthcare system that people are getting heavier and heavier as the nation develops? Are people better off being heavier and wealthier? It would also be interesting to explore a cross-sectional portion of a population as well to attempt to estimate the income threshold that is the turning point

for individuals to consume less food and focus more on health. Finally, it is important to explore potential policy interventions that could slow or prevent the rise in obesity prevalence even as economies develop. Despite some caveats, my thesis clarifies the quantitative effect of income growth on the rise in obesity, which is an important element to consider when designing those policies.

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