Healthy Food, Unhealthy Food and Obesity∗ Xiaoyong Zheng† and Chen Zhen‡ North Carolina State University and RTI International Abstract By conducting a systematic demand analysis for unhealthy and healthy food using data from both the United States and Japan, we seek additional evidences to examine whether the latent behavioral mechanisms embedded in two “price effects” explanations of the rising obesity problem are in fact operative. Our findings lend little support to the hypothesis that substitution between healthy and unhealthy food induced by relative price changes is a major cause of the obesity epidemic in the United States. Instead, falling food price in general is likely to be one of the many causes. Keywords: Obesity; Food demand; Demand System Estimation JEL Classification Codes: I10; I18; Q11
I. Introduction Obesity has become a growing public health issue in the United States. The number of adults who are obese has climbed from 15 percent in 1980 to 30.5 percent in 2000 (Flegal et al, 2002) and it is blamed for about 112,000 premature deaths annually in the United States. In response, a number of economic studies have contributed to understanding why more Americans have become substantially more overweight in recent decades. Several possible explanations are proposed. At center are a couple of “price effects” explanations. Lakdawalla and Philipson (LP) (2002) point out that over the past several decades, due to innovations in agricultural production technology, the price of food relative to income has declined significantly, causing higher quantity of ∗
We thank Mary Muth for comments on an earlier draft. Department of Agricultural and Resource Economics, North Carolina State University, Campus Box 8109, Raleigh, NC, 27695. Phone: 919-515-4543, Email:
[email protected]. ‡ RTI International, 3040 Cornwallis Rd, PO Box 12194, Research Triangle Park, NC, 27709. Phone: 919541-7023, Email:
[email protected]. †
food being consumed per capita, leading to increases in individuals’ Bodily Maxx Index (BMI). Along the same line, Chou, Grossman and Saffer (CGS) (2004) find that food prices in fast-food and full-service restaurants and in grocery stores are all negatively correlated with individuals’ BMI, lending further support to LP’s conclusion that falling food prices may be one of the primary reasons for the rising obesity problem. Gelbach, Klick and Stratmann (GKS) (2007) propose yet another explanation that during the past few decades, healthy food has become more expensive relative to unhealthy food. They find a statistically significant positive relationship between price of unhealthy food relative to healthy food and individuals’ BMI using data from the National Health Interview Survey (NHIS). Based on this evidence, they hypothesize that as unhealthy food becomes relatively cheaper compared with healthy food in the United States, people substitute away from healthy food toward unhealthy food. Because unhealthy food tends to be dense in energy, if over-consumed, it tends to cause overweight and obesity (Drewnowski and Darmon, 2005). The contributions of our paper to the obesity discussion are twofold. First, we evaluate the above two price-effect explanations using an alternative approach. If the negative relationship between food prices and individuals’ BMI found by LP and CGS is indeed causal, we expect the own-price demand elasticity of food to be large in magnitude; and if the statistically significant relationship between BMI and relative price of healthy and unhealthy food is indeed caused by substitution between healthy and unhealthy food as GKS argue, we expect healthy food and unhealthy food to be substitutes. Put it differently, a statistically significant, negative and sizable own-price demand elasticity of food would lend support to LP and CGS’s conclusions; and a positive and large cross-price demand elasticity between healthy and unhealthy food would lend support to GKS’s conclusion. On the other hand, finding of an inelastic food demand or gross complementarity between healthy and unhealthy foods would cast doubts on the own-price and cross-price effect explanations, respectively. Therefore, our approach essentially seeks additional evidences to examine whether the latent behavioral mechanisms embedded in the two explanations are in fact operative. Such an approach is suggested and employed in a recent study by Fang et al (2007) to test whether there is a
1
positive effect of life expectancy on investment in health. Second, we compile new price and expenditure series for healthy and unhealthy foods in the United States (1967-2004) and Japan (1963-2003) and for the first time, estimate the demand for healthy food, unhealthy food, and other nondurables as a system. Although the two countries had strikingly similar trends in the price of healthy food relative to unhealthy food and in income growth, their experience in obesity is wildly distinct with Japan having the lowest rate of obesity while the United States having one of the highest in the world. By comparing differences in consumer preferences recovered from the demand system estimation, we attempt to provide some additional insight into this important issue. We find evidence supportive of the own-price effect explanation of LP and CGS, but little evidence for the cross-price substitution effect argument by GKS. Because of the small estimated cross-price elasticity between healthy and unhealthy foods, our results suggest that a “Twinkie tax” on unhealthy food only work to the extent that it reduces unhealthy food consumption through the own-price effect and have limited effect on promoting healthy food consumption, unless it is coupled with a healthy food subsidy.
II. Data and Econometric Framework The demand system estimated in this study has three goods, the unhealthy food, the healthy food and the other good (includes all other nondurable goods except food), which are denoted as i = 1, 2, 3 respectively. Table A in the Data Appendix lists the food product categories in the unhealthy food class and the healthy food class.1 For estimation purpose, for each good in the United States and Japan, we create a price index pit and an expenditure index eit . Please see the Data Appendix for data sources and details on how these economic variables are constructed. Preliminary analysis of the data indicate that a prominent feature of the price data as well as other variables used in the demand estimation is that even after taking logarithms, there are still clear evidences of drifts and trends of nonstationary behavior. 1
The classifications in Table A closely resemble the ones GKS used in constructing their relative food prices.
2
Adequate inference of the preference parameters requires a demand system model that copes with the nonstationary feature of the data. Popular demand system models like Deaton and Muellbauer’s (1980) AIDS model and the standard translog model (Christensen, Jorgenson, and Lau, 1975) ignore this feature and applying these models to our datasets may lead to spurious regressions and inconsistent parameter estimates. For this reason, we employ the NTLOG (nonstationary translog) demand system recently proposed by Lewbel and Ng (2005) to estimate the preference parameters. The NTLOG demand system is a variant of the standard translog model. It explicitly takes into account the nonstationary feature of the relative prices as well as the possibility of highly autocorrelated errors in the budget share equations and hence best suits our needs here. More specifically, suppose a representative consumer’s indirect utility function in period t takes the translog functional form (1)
U ( p t , et ) =
3 i =1
ai +
1 2
3 j =1
bij ln
p jt et
ln
pit et
where pit is the price of good i, et is the total expenditure on food and other nondurables, and a i and bij are parameters to be estimated. Define ci = aggregation condition
3 i =1
3 j =1
bij and impose the exact
ci = 0 , Lewbel and Ng (2005) show that the aggregate market
shares ( Wit ) equations used in estimation can be written as (2)
Wit = a i 0 + a i1t +
where r jt = ln
p jt et
3 j =1
bij r jt −
3 j =1
c j z ijt + u it
, z ijt = Wit ln p jt , u it is an error term that can be interpreted as a
weighted average of preference heterogeneity (taste) parameters across different individual consumers and t is a linear trend used to approximate deterministic changes in preferences over time.
3
As explained above, (2) cannot be used to estimate parameters in the demand system because the regressors r jt and z ijt are functions of prices and hence are nonstationary as well. To solve the nonstationary problem, Lewbel and Ng recommend estimating (2) in first-differences. Estimation is further complicated by the fact that z ijt is correlated with the error term u it due to the presence of Wit in z ijt . Lewbel and Ng propose to use a GMM estimator based on a set of moment conditions formed by the products of first-differences of the shares equations (2) and suitable instrumental variables. Suppose we have a vector of stationary instrumental variables st that are uncorrelated with the stationary differenced error term ∆u it = u it − u it −1 , then we can form the following moment conditions (3)
E st ∆Wit − a i1 −
3 j =1
bij ∆r jt +
3 j =1
c j ∆z ijt
=0
where i = 1, 2 . Since all the variables in (3) are now stationary, standard GMM inference can be applied. After imposing the symmetry restriction bij = b ji ∀ i ≠ j , the homogeneity condition ci =
3
b , and the exact aggregation condition
j =1 ij
3 i =1 i
c = 0 , there are 7 free
parameters to be estimated. The adding-up constraint means that only two budget share equations need to be estimated. With two estimation equations, each of the instruments in st can be used to form two moment conditions, one for each good. Regarding the choice of instruments, since our objective here is to identify demand parameters, a natural choice is to use food supply shifters. Furthermore, to identify the preference parameters for healthy food separately from unhealthy food, the supply variables should also have differential effects on the costs of healthy and unhealthy foods. GKS use gasoline price to instrument the price of healthy food relative to unhealthy food and argue that gas price is tightly correlated with cost differences in distribution costs between healthy and unhealthy foods. Following this line of argument, we use variables that are directly related to food marketing costs as instruments. This choice is justified on the ground that, for example, marketing healthy food like fruits and vegetables is more expensive than marketing unhealthy food like fats and oils, because 4
the former ones entail higher costs in transportation, refrigeration, labor, packaging, and are much prone to spoilage. We include three marketing cost variables (i.e. gasoline prices, workers’ wages2, and electricity prices) in the instrument set for the United States and Japan. Additional instruments are personal consumption expenditures, disposable income, total population, and a constant. Except for the constant, all instruments are differenced to remove nonstationarity. This gives a total of 14 moment conditions. The two-step optimal GMM is used to estimate the demand system.
III. Results and Discussion The parameter estimates for the United States are collected in the left panel of Table 1. Despite the small sample size, three out of the five bij ’s are statistically significant at the 5% level. The model fits the data reasonably well. The χ 2 test for overidentifying restrictions cannot reject the orthogonality conditions. Ljung-Box χ 2 test cannot reject the hypothesis that there is no serial correlation in the residuals. The negative semi-definitiveness of the Slutsky matrix is satisfied at all data points. Similar results using the Japan data are collected in the right panel of Table 1. Table 2 presents the estimated uncompensated price and expenditure elasticities computed at the sample means. Several results are noteworthy. First, own-price elasticities are all negative and mostly sizable. This indicates that consumers’ demand for food do respond substantially to price changes. This is evidence in support of LP and CGS’ conclusions. Second, in the United States, demand for food is less price- and expenditureelastic than demand for other nondurables, which is expected as food is a necessity. Consistent with a priori expectations, the expenditure elasticity of healthy food is higher than that of unhealthy food. For Japan, demands for both healthy and unhealthy food are very price- and expenditure-elastic. This is consistent with the notion that food is 2
For the United States, we use weekly earning of production workers. For Japan, we use the wage index for the food and tobacco industry.
5
considerably more expensive in Japan than in the United States (Senauer and Gemma, 2006). According to the estimated expenditure elasticities, unhealthy food is a luxury while healthy food is a necessity. These differences between the United States and Japan are likely caused by differences in product composition, quality, culture, and demographics. For example, the healthy food category in the Japan dataset includes noodles, rice, vegetables, and seafood, which have been staple food in Japan for centuries. On the other hand, the unhealthy food category includes Wagyu beef and Japanese cakes and candies which are often considered delicacies rather than staple foods. Therefore, it is very plausible that the listed healthy food items in Table 1 are necessities for the Japanese, while the unhealthy food items are luxuries. Finally, the cross-price elasticities (i.e. degree of substitutions) between unhealthy and healthy foods are not precisely estimated for the United States and Japan, although the point estimates suggest that healthy and unhealthy food are substitutes in both countries. The estimated cross-price elasticities are very similar in magnitude between the two countries. This observation, together with the fact that the U.S. BMI increases at a far faster rate than the Japanese counterpart, provides little support for the hypothesis that substitution between healthy and unhealthy foods caused by relative price changes is an important factor in causing the obesity epidemic in the United States. Some policy makers have contemplated levying the so-called “Twinkie taxes” on unhealthy food items. Proponents of such policies argue that “Twinkie taxes” raise the price of unhealthy food relative to healthy food and would induce consumers to eat healthier. On the other hand, opponents of such policies argue that such tax is extremely regressive, inflicting much greater welfare losses on the poor and elderly than on the young and rich. Our results show that such policies may be effective in reducing demand for unhealthy food, but would have very limited effects on inducing higher healthy food consumption. To encourage higher healthy food consumption and reduce the negative welfare impacts of “Twinkie taxes,” healthy food subsidies may have to be paid at the same time.
6
References
Christensen, L.R., D.W. Jorgenson, and L.J. Lau (1975): “Transcendental Logarithmic Utility Functions,” American Economic Review, 65, 367-83. Chou, S.Y., M. Grossman and H. Saffer (2004): “An Economic Analysis of Adult Obesity: Results from the Behavioral Risk Factor Surveillance System,” Journal of Health Economics, 23, 565-587. Deaton, A.S. and J. Muellbauer (1980): “An Almost Ideal Demand System,” American Economic Review, 70, 312-326. Drewnowski, A. and N. Darmon (2005): “The Economics of Obesity: Dietary Energy Density and Energy Cost,” American Journal of Clinical Nutrition, 82, 265S-273S. Fang, H., M. Keane, A. Khwaja, M. Salm and D. Silverman (2007): “Testing the Mechanisms of Structural Models: The Case of the Mickey Mantle Effect,” American Economic Review Papers and Proceedings, 97, 2, 53-59. Flegal, K.M., M.D. Carroll, C.L. Ogden, and C.L. Johnson (2002): “Prevalence and Trends in Obesity Among US Adults, 1999-2000,” Journal of the American Medical Association, 288, 1723-1727. Gelbach, J.B., J. Klick and T. Stratmann (2007): “Cheap Donuts and Expensive Broccoli: Relative Price Effects on Body Mass Index,” Working Paper, Florida State University. Lakdawalla, D. and T. Philipson (2002): “The Growth of Obesity and Technological Change: A Theoretical and Empirical Examination,” NBER Working Paper. Lewbel, A. and S. Ng (2005): “Demand Systems with Nonstationary Prices,” Review of Economics and Statistics, 87, 479-494. Senauer, B. and M. Gemma (2006): “Reducing Obesity: What Americans Can Learn from the Japanese,” Choices, 21, 4, 265-268.
7
Table 1: Parameter Estimates of the Demand System by Two-Step Optimal GMM U.S. Japan Variables Estimate S. E. Estimate S. E. 0.0867 0.0608 -0.0039 0.0398 b11 0.0230 0.0314 0.0195 0.0816 b12 0.0986** 0.0256 -0.0641 0.1985 b22 -0.0581** 0.0182 0.1026 0.0774 b23 -0.1322** 0.0288 -0.0937** 0.0464 b33
a11 a12 Overidentification χ 2 test statistic Ljung-Box χ 2 test statistic pnsd
0.0005 0.0001 7.5741
0.0007 0.0005 df = 7
-0.0001 -0.0042** 13.0208
0.0006 0.0016 df = 7
1.8948
df = 2
0.3624
df = 2
100
86.84
* denotes significant at 10% level. ** denotes significant at 5% level. For χ
2
test with df =2, the 95%
critical value is 5.99. For χ test with df=7, the 95% critical value is 14.07. psdn: percentage of observations that satisfy the negative semi-definitiveness of the Slutsky matrix. 2
Table 2: Uncompensated Price and Income Elasticities U.S. Japan Variables Estimate S. E. Estimate -0.5226 0.3977 -1.0062** e11 -0.3351* 0.1774 -1.2880* e22 -1.0002** 0.0251 -1.1243** e33
e12 e21 e13 e23 e31 e32 em1 em 2 em 3
S. E. 0.3371 0.6485 0.0836
0.0954 0.0548 0.2342**
0.2107 0.2443 0.0190
0.1020 0.0957 -0.3061**
0.7031 0.2704 0.0635
-0.2516*
0.1402
0.4005
0.2419
-0.1032**
0.0298
-0.0433
0.0298
-0.1390**
0.0226
0.1135
0.1907
0.1930
0.2109
1.2103**
0.2409
0.5319**
0.2019
0.7919**
0.2815
1.2424**
0.0273
1.0542**
0.1150
* denotes significant at 10% level. ** denotes significant at 5% level. good i with respect to the price of good j.
eij is the elasticity of demand for
emi is the expenditure elasticity of demand for good i, where i, j
= 1 (unhealthy food), 2 (healthy food), and 3 (other nondurables).
8
