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Fast food prices and adult body weight outcomes: evidence based on longitudinal quantile regression models.

I. INTRODUCTION

Average adult body mass index (BMI: weight in kilograms divided by height in meters squared) in the United States increased approximately 12% between the 1960s and 2004 (Regal et al. 2009) and approximately one third of the U.S. adults were estimated to be obese in 2007-2008 (Flegal et al. 2010). At the same time, the proportion of expenditure on food away from home out of total food expenditure more than doubled between 1960 and 2008 from 19.7% to 41.4% (USDA 2011).

In particular, the proportion of sales of food away from home at limited service restaurants increased from 9.7% to 37.1% between 1963 and 2008 (USDA 2011). Data on nationwide surveys of food consumption patterns and household expenditures also show a marked upward trend in total energy intake derived from away-from-home sources, in particular for fast food outlets (Guthrie, Lin, and Frazao 2002: Nielsen, Siega-Riz, and Popkin 2002; Stewart et al. 2004). Fast food consumption was found to be associated with higher total energy intake and higher intake of fat, saturated fat, carbohydrates, sugar, and carbonated soft drinks and lower intake of micronutrients and fruit and vegetables (Binkley. Eales, and Jekanowski 2000; Bowman et al. 2004; Bowman and Vinyard 2004; French et al. 2001; French, Hamack, and Jeffery 2000; Paeratakul et al. 2003) and has been associated with higher body weight (Binkley, Eales, and Jekanowski 2000; Bowman and Vinyard 2004; Guthrie, Lin, and Frazao 2002).

Recently, researchers have explored the importance of food prices as a modifiable economic contextual factor to combat the obesity epidemic given that food prices have fallen, whereas the opportunity cost of physical activity has risen over time (Cutler, Glaeser, and Shapiro 2003; Lakdawalla, Philipson, and Bhattacharya 2006). Particularly, understanding the effect of fast food prices on body weight is important because it provides evidence on the extent to which food pricing policies such as taxes on energy dense foods may be effective policy tools to reverse such an epidemic.

Lower fast food prices have been reported to be statistically significantly associated with higher weight outcomes among adolescents (Auld and Powell 2009; Powell 2009; Powell et al. 2007) and children in low-socioeconomic families (Powell and Bao 2009). Particularly, the price elasticity of body weight outcomes with regard to fast food prices was found to be heterogeneous over the conditional distribution of BMI for adolescents in a cross-sectional analysis with larger associations at higher BMI quantiles (Auld and Powell 2009). However, the evidence is not as consistent for adults. Chou, Grossman, and Saffer (2004) reported that higher prices of full-service restaurants and fast food restaurants (BMI only) were statistically significantly associated with lower BMI and obesity prevalence among adults. However, another study found that the association between fast food prices and adult weight was statistically insignificant (Beydoun. Powell, and Wang 2008).

This study builds on the previous studies and examines the heterogeneous relationship between fast food prices as a proxy for energy dense food away from home and adult body weight outcomes in the United States using data for adults drawn from a nationally representative longitudinal study. We estimate an individual fixed effect quantile regression model of the linear measure of BMI on food prices to estimate changes in the nature, direction, and magnitude of the relationship between fast food prices and body weight outcomes over the conditional distribution of BMI.

The quantile regression model allows capturing any changes in the conditional dispersion of BMI associated with fast food prices, whereas typical mean estimation such as ordinary least squares (OLS) only accounts for changes in the mean value. If, for example, fast food prices are associated with individuals' weight only in the top or bottom of the distribution of BMI, the conditional distribution of BMI from OLS estimation would become thinner and wider without any changes in the mean value. This restriction of OLS for linear BMI also relates to nonlinear models with categorical clinical weight classifications. The estimated proportion of clinical weight classifications remains the same if fast food prices are associated with BMI for only individuals in the top or bottom of the BMI distribution (Auld and Powell 2009). Therefore, accounting for possible heterogeneity in the relationship between food prices and BMI among adults in a longitudinal data framework using a quantile regression model helps to accurately identify the relationship of fast food prices with individual body weight outcomes, providing new evidence to help formulate effective pricing policy measures to combat the obesity epidemic.

II. METHOD

A. Estimation Model

To begin our empirical work, we estimate a cross-sectional OLS model as shown in equation (1) to use as a reference for our main model of quantile regression.

(1) [BMI.sub.ict] = [[alpha].sub.0] + [[alpha].sup.PFF][PFF.sub.ct] + [[alpha].sup.PFH][PFH.sub.ct] + [[alpha].sup.X][X.sub.ict] + [[epsilon].sub.ict]

where the subscripts i, t. and c stand for individual, year, and county, respectively. The [alpha]'s are parameters to be estimated. [epsilon] is a time-varying error term that is assumed to be normally distributed. PFF and PFH, respectively, denote the price of fast food and overall food at home price in county c at year t. X denotes a vector of individual and household characteristics.

As a reference for the individual fixed effect quantile regression estimates, we estimate an individual fixed effects OLS model with only time-varying covariates to control for time constant unobserved individual heterogeneity as shown below:

(2) [BMI.sub.ict] = [[beta].sub.0] + [[beta].sup.PFF][PFF.sub.ct] + [[beta].sup.PFH][PFH.sub.ct] + [[beta].sup.X][X.sub.ict] + [[mu].sub.i] + [[upsilon].sub.ict]

where [mu] is time-invariant unobserved individual heterogeneity and v is a standard residual. The [beta]'s are parameters to be estimated.

Our main estimation model of interest is a quantile regression model on the association of fast food price with BMI. Quantile regression allows for different marginal effects of fast food prices on BMI by quantiles of the entire conditional distribution of BMI (Koenker and Hallock 2001). Quantile regression is particularly useful if the distribution of the linear response variable changes differently following the changes in regressors (Hao and Naiman 2007). For example, if only individuals with BMIs in the 90th percentile or greater are sensitive to fast food prices, the typical OLS model based on the conditional mean functions would be centered on a small positive value. Similarly in nonlinear probability models, the proportion of obese people will not change if only individuals at the top 90th or greater percentile are sensitive to fast food price. Therefore, quantile regression provides a fuller picture of the heterogeneous relationship between fast food price and body weight outcomes (Koenker and Hallock 2001). The estimation for the quantile regression is:

(3) [q.sub.[tau]]([BMI.sub.ict]) = [[delta].sub.[tau].sup.0] + [[delta].sub.[tau].sup.PFF][PFF.sub.ct] + [[delta].sub.[tau].sup.PFH][PFH.sub.ct] + [[delta].sub.[tau].sup.X][X.sub.ict] + [[epsilon].sub.ict]

where [tau] denotes the t th quantile of the conditional distribution of BMI. Our main interest is to show how the parameter [[delta].sub.[tau].sup.PFF] changes in different quantiles of the entire conditional distribution of BMI.

Exploiting the longitudinal nature of our data, we modify Equation (3) to estimate a quantile regression with individual fixed effects to control for the time-constant individual heterogeneity as shown in Equation (4):

(4) [q.sub.[tau]]([BMI.sub.ict]) = [[delta].sub.[tau].sup.0] + [[delta].sub.[tau].sup.PFF][PFF.sub.ct] + [[delta].sub.[tau].sup.PFH][PFH.sub.ct] + [[delta].sub.[tau].sup.X][X.sub.ict] + [[alpha].sub.i] + [[epsilon].sub.ict]

where a is time-invariant unobserved individual heterogeneity and [epsilon] is a standard residual. Although we allow variations in estimates by the quantile [tau] of interest for all time-varying covariates, the time-constant individual heterogeneity is fixed in all quantiles. That is, a shifts the location of response variable, i.e., BMI, of the conditional quantiles of interest (Koenker 2004).

We bootstrap all standard errors. All the estimations are run separately by gender. We also run subpopulation analyses by poverty status and whether any children are present in a household. Individuals in the bottom tertile of per capita household income are defined as low income, compared to the rest of the sample which is considered as non-low income. The survey design is addressed by applying weights, to adjust for unequal probabilities of sampling and by using robust standard errors to adjust stratification and clustering within strata.

B. Data

Individual-level data are drawn from the NLSY79, a nationally representative sample of 12,686 persons aged 14 to 22 years at the initial survey in 1979. The final sample of 10,116 women and 10,008 men is obtained from 23,796 women and 23,941 men who completed interviews between 1992 and 2002 after dropping women who were pregnant at the time of interview and missing in other covariates.

BMI our dependent variable, is measured as self-reported weight in kilograms divided by self-reported height in meters squared. In the NLSY79, height information was collected only three times, in 1981. 1982, and 1985, whereas a respondent's current weight was collected in every round of the survey. Because the respondents were between 20 and 28 years old in 1985, height in 1985 is used as the respondents' adult height based on the assumption that height typically stops changing by those ages (Cawley 2004).

The fast food price, the variable of interest, is obtained from the American Chamber of Commerce Researchers Association (ACCRA) Cost of Living Index reports. These reports contain quarterly information on prices across more than 300 U.S. cities and have been used in a number of previous studies (Auld and Powell 2009; Chou, Grossman, and Saffer 2004; Sturm and Datar 2005). These price data are matched to the NLSY79 sample based on the closest city match available in the ACCRA data using the NLSY79 county-level geocode identifier which is the smallest level of available geographic identifier. Observations for which price matches are not available from the same or contiguous county are not included in the analyses. Further, a price match indicator is included in the estimation to control for price matches based on a contiguous versus exact county match. A fast food price index is generated based on the following three items available in the ACCRA data: a McDonald's Quarter-Pounder with cheese, a thin crust regular cheese pizza at Pizza Hut and/or Pizza Inn, and fried chicken (thigh and drumstick) at Kentucky Fried Chicken and/or Church's Fried Chicken. We also control for a food-at-home grocery price index, which is based on all of the food and nonalcoholic beverage grocery products available in the ACCRA data set including the following 23 items: bananas, lettuce, potatoes, canned sweet peas, canned tomatoes, canned peaches, frozen corn. T-bone steak, ground beef, sausage, frying chicken, canned chunk light tuna, whole milk, eggs, margarine, grated parmesan cheese, white bread, corn flakes, shortening, sugar, coffee, frozen orange juice, and soft drinks. Both price indices are weighted based on expenditure shares provided by ACCRA derived from the Bureau of Labor Statistics (BLS) Consumer Expenditure Survey. All prices are deflated by the BLS Consumer Price Index (CPI) (1982-1984= 1).

Other individual-level covariates drawn from the NLSY79 include the following: age with its square term, race (non-Hispanic Black and Hispanic, with non-Hispanic White as the reference category), marital status (married, with not married as the reference category), the number of children (none, 1, 2, and 3 or more), level of highest completed education (less than high school, some college, and more than college, with high school as the reference category), work status (part time and full time, with nonworking as the reference category), the extent of urbanicity of the respondents' residence (suburban and rural, with urban as the reference category), real total net family income (a composite income figure from a number of income sources for household members related to the respondent by blood or marriage), year indicators from 1992 to 2002.

III. RESULTS

Weighted summary statistics for the variables in the estimation models are presented in Table 1. BMI, the dependent variable, is on average 26.6 and 27.5 units for women and men, respectively. The real fast food price, a proxy measure of energy dense food away from home, is averaged at $2.75 between 1992 and 2002 for both genders. The average real food at home prices between 1992 and 2002 is $1.11 in our sample. Approximately, 25% and 20% of the sample are non-Hispanic Black and Hispanic, respectively, for both genders. Slightly less than one half of women and one quarter of men in our sample have some college or higher education. Inflation adjusted real family income is, on average, $30,779 for women and $32,296 for men, respectively. Women and men had 1.5 and 1.1 kids, respectively, on average, in our sample. Slightly more than a quarter of women (28.9%) do not have any children, whereas over a half of men (54.6%) have no children.
TABLE 1

Weighted Summary Statistics

 Mean (Standard
 Error
 (/Frequency

 Women Men
Variables (N= 10,116) (N = 10,008)

Dependent variable

BMI 26.61 (6.25) 27.50 (4.58)

Independent variable of
interest

Fast food prices 2.75 (0.20) 2.76 (0.20)

Covariates

Price of food at home 1.11 (0.11) 1.11 (0.11)

Race

Non-Hispanic White 0.54 0.56

Non-Hispanic Black 0.25 0.24

Hispanic 0.21 0.20

Married 0.60 0.62

Education

Less than high school 0.79 0.11

High school 0.40 0.42

Some college 0.28 0.23

More than college 0.24 0.24

Area of living

Suburban area 0.65. 0.67

Rural area 0.11 0.12

Urban area 0.83 0.82

Age 36.06 (4.03) 35.93 (4.03)

AFQT score 43.00 (27.52) 44.39 (29.40)

Number of children 1.51 (1.07) 1.13 (1.14)

Having any children 0.29 0.55

Work status

Work part-time 0.27 0.12

Work full-time 0.57 0.82

Family income 30779.28 32296.36

 (23068.70) (23758.54)

Low income 0.33 0.33

Year 1992 0.16 0.16

Year 1994 0.14 0.14

Year 1996 0.18 0.18

Year 1998 0.18 0.18

Year 2090 0.16 0.16

Year 2002 0.18 0.18


Table 2 reports quantile estimates for selected quantiles for the price of fast food with mean estimates for linear BMI as the reference for all sample persons. Our results show that the price of fast food is not statistically significantly associated with BMI at the mean for women. The quantile estimates for women also indicate no statistically significant association across the entire conditional distribution of BMI although the association is negative at the top quantile for both the cross-sectional and longitudinal models.
TABLE 2

Marginal Extent of the Association of Fast Food Prices in
All Sample Persons by Gender

 Mean Quantile

Price of Fast (BMI) q10 q25 q50 q75
Food

Female (N =
10,116)

Cross-sectional 0.233 0.367 -0.034 0.228 -0.009

 (0.571) (0.218) (0.293) (0.405) (0.560)

 [0.024] 10.050] [-0.004] [0.025] [-0.001]

Longitudinal -0.148 0.353 0.166 0.272 0.221

 (0.216) (0.310) (0.202) (0.189) (0.209)

 [-0.015] [0.048] 10.0201 10.029] [0.020]

Mule (N =
10.008)

Cross-sectional -0.106 0.453 0.422 -0.423 * -1.034
 ***

 (0.435) (0.307) (0.265) (0.253) (0.350)

 [-0.011] [0.056] [0.048] [-0.044] [-0.096]

Longitudinal 0.118 0.281 0.110 -0.025 -0.087

 (0.177) (0.239) (0.156) (0.152) (0.169)

 [0.012] [0.035] [0.012] [-0.003] [-0.008]

Price of Fast q.90
Food

Female (N =
10,116)

Cross-sectional -0.664

 (0.826)

 [-0.052]

Longitudinal -0.140

 (0.287)

 [-0.011]

Mule (N =
10.008)

Cross-sectional -1.039 *

 (0.629)

 [-0.086]

Longitudinal -0.052

 (0.222)

 [-0.004]

Notes: All the cross-sectional estimations on BMI control for
the following variables: year fixed effects; price of food at
home; price match indicators (contiguous vs. exact county match):
age with its square term: race (non-Hispanic Black, Hispanic with
non-Hispanic White as the reference group): marital status
(separated, never married, divorced vs. married); the number
of children (none, 1, 2, and 3 or more); work status (part
time and full time with non-working as the reference);
education level (some college or more with high school or
less as the reference); real family income in dollars for
1992: AFQT score as a measurement of intelligence score:
the extent of urbanicity (suburban and rural with urban
as the reference): and. AFDCRANF program participation
in the previous calendar year. All the longitudinal
estimations control for the same covariates as the
cross-sectional models except that individual fixed
effects model does not control for any time-constant
individual characteristics. Mean estimations on BMI
is estimated using OLS. Clustered-corrected standard
enors are in the parentheses. Elasticity of BMI with
respect to the fast food price is reported in brackets.

* Significance at 10%: *** significance at 1%.


For men, the cross-sectional mean estimates show no statistically significant association of fast food prices with BMI. Cross-sectional quantile estimation reveals that a statistically negative association is estimated at the 50th or upper quantiles and the extent of the negative association becomes larger at higher moments. A dollar increase in the price of fast food is associated with 0.4 unit lower BMI at the 50th quantile but is more than twofold higher at the 90th quantile, with an estimated association of 1.04 lower BMI units, corresponding to a price elasticity of--0.08. The magnitude of the OLS estimate is one fourth and one tenth of the quantile estimates at the 50th and 90th quantiles, respectively. These results reveal that the OLS estimate underestimates the negative association of fast food prices with BMI at the higher moments of the conditional distribution of BMI. However, controlling for time-constant individual heterogeneity weakens the relationship of fast food prices with BMI, given that the association is no longer statistically significant and has a much lower magnitude (Table 2).

Results from subgroup analyses reveal differential patterns of the association of fast food prices with BMI by individuals' income and family status. Among women, we find that a dollar increase in the price of fast food is associated with lower BMI by approximately 1.1 units with a price elasticity of--0.09 at the 90th quantile for low-income women in the individual fixed effect quantile estimation, whereas no such association is found among high-income women. When we subgroup women by the existence of any children, we also find a statistically significant negative association of fast food prices with BMI only among women with any children at the top quantile. A dollar increase in fast food prices is estimated to be associated with lower BMI by 0.8 units with a price elasticity of--0.07 at the 90th quantile in the longitudinal quantile estimation model. The association at the 90th quantile in the cross-sectional model is also statistically significant but is twice as large compared to the longitudinal individual-level fixed effects results (see upper section of Table 3).

For men, higher fast food prices are associated with lower BMI at the 75th quantile only among low-income men or men with any children. BMI is lower by 1.9 and 1.3 units, among low-income men and men with any children, respectively, at the 75111 quantile in the cross-sectional quantile regression model, corresponding to price elasticities of--0.20 and--0.14 in the respective subgroups. However, this negative association of fast food prices with BMI is not statistically significant at the 90th quantile in the respective subgroup models. Also, the statistically significant associations at the 75th quantile in the cross-sectional quantile models in those subgroups become insignificant and substantially smaller in the longitudinal individual fixed effects models (see lower section of Table 3).
TABLE 3

Subgroup Analyses by Poverty Status and Family Structure

 Cross-Sectional

 q10 q23 q50 q75 q90

Female

By income

High 0.190 -0.363 0.496 1.257 0.002
income (0.366) (0.479) (0.601) (0.810) (1.329)
(N = [0.020] [-0.050] 10.0621 [0.161] [0.000]
6.627)

Low 0.096 -0.026 -0.928 -1.751 -2.642
income (0.723) (0.846) (1.203) (1.573) (2.483)
(N = [0.010] [-0.004] [-0.112] [-0.183] [-0.232]
3,489)

Family
structure

No child 0.178 0.287 0.719 0.965 2.047
(N = (0.727) (0.711) (1.034) (1.784) (2.232)
2,452) [0.018] [0.040] [0.090] [0.106] [0.190]

Any child 0.329 -0.226 0.029 0.150 -1.9288
 *
(N = (0.317) (0.511) (0.536) (0.843) (1.101)
7,664)

Male [0.034] [-0.031] [0.004] [0.016] [-0.176]

By income

High 0.757 0.618 -0.165 -1.167 -1.062
income (0.569) (0.437) (0.393) (0.524) (1.074)
(N = [0.076] [0.076] [-0.019] [-0.119] [-0.098]
7,414)

Low -0.092 -0.076 -0.624 -1.937 * -0.519
income (0.819) (0.742) (0.816) (1.050) (1.430)
IN = [-0.009] [-0.010] [-0.073] [-0.201] [-0.048]
2,594)

Family
structure

No child 0.134 0.499 -0.2091 -0.5013 -0.6141
(N = (0.658) (0.555) (0.567) (0.838) (1.497)
5,695) [0.014] [0.O62] [-0.024] [-0.052] (-0.057]

Any child 0.828 0.247 -0.4225 -1.346 -1.3880
 **
(N = (0.524) (0.492) (0.521) (0.643) (0.967)
4,313) [0.092] [0.030] [-0.048] [-0.137] [-0.127]

 Longitudinal
 Individual
 Fixed
 Effects

 q10 q25 q50 q75 q90

Female

By income

High 0.408 0.134 0.301 0.335 0.259
income 10.288) (0.230) (0.215) (0.233) (0.383)
(N = [0.0431 [0.018] [0.038] [0.048] [0.024]
6.627)

Low -0.118 0.350 0.098 -0.493 -1.0736
income (0.695) (0.426) (0.394) (0.430) (0.585)
(N = [-0.012] [0.047] [0.012] [-0.051] [-0.094]
3,489)

Family
structure

No child 0.547 0.379 0.347 0.350 0.423
(N = (0.587) (0.638) (0.689) (0.350) (0.458)
2,452) [0.057] [0.052] [0.044] [0.039] [0.039]

Any child 0.084 -0.123 -0.003 -0.166 -0.7559
 **
(N = (0.278) (0.192) (0.190) (0.207) (0.328)
7,664)

Male [0.009] [-0.017] [0.000] [-0.018] [-0.069]

By income

High 0.072 -0.036 -0.206 -0.241 -0.122
income (0.255) (0.186) (0.170) (0.179) (0.224)
(N = [0.007] [-0,004] [-0.023] [-0.025] [-0.011]
7,414)

Low 0.425 0.148 0.11 0.032 0.135
income (0.467) (0.342) (0.326) (0.364) (0.563)
IN = [0.043] [0.014] [0.013] [0.003] [0.012]
2,594)

Family
structure

No child 0.080 0.073 0.095 0.277 0.204
(N = (0.447) (0.322) (0.309) (0.333) (0.543)
5,695) [0.008] 10.0091 [0.011] [0.029] [0.019]

Any child -0.026 -0.059 -0.198 -0.115 -0.308
(N = (0.368) (0.232) (0.218) (0.249) (0.327)
4,313) [-0.003] [-0.007] [-0.012] [-0.012] [-0.028]

Notes: See notes in Table 2. Additionally note that the bottom
tertile of per capita family income is defined as low income and
the rest are defined as high income


IV. DISCUSSION

An increasing number of studies have recently paid attention to economic contextual environments as important modifiable factors that would potentially impact individual body weight outcomes. In particular, given the substantial increase in food away from home consumption, particularly fast food, that has paralleled the increase in obesity, researchers have examined the association of fast food prices with individual body weight outcomes. The results for adults have been mixed (Chou, Grossman, and Saffer 2004: Beydoun, Powell, and Wang 2008) and previous studies except for Auld and Powell (2009) for adolescents estimate the association at the mean without accounting for potential heterogeneity in the relationship between fast food prices and body weight outcomes (usually measured with BMI). Allowing for a differential relationship of fast food prices with BMI over the entire conditional moment of BMI is important given that the mean estimation does not capture changes in the dispersion of the conditional distribution of BMI with regards to changes in fast food prices. Understanding the differential relationship of fast food prices with BMI across the entire conditional distribution of BMI is also important in foreseeing the potential effectiveness of policy measures relying on fiscal price changes of fast foods. Our study builds on the previous literature and estimates quantile regression models in both cross-sectional and longitudinal settings to advance our understanding of the characteristics of the relationship of fast food prices with body weight outcomes.

Our study results reveal that the OLS estimate for men underestimates the negative relationship of fast food prices with BMI at the 50th and upper quantiles in the cross-sectional models although the statistical significance is lost in longitudinal individual fixed effects quantile regression. Whereas for women fast food prices are not statistically significantly associated with BMI anywhere throughout the conditional distribution of BM1, we find that at the 90th quantile a 10% increase of fast food prices is statistically significantly associated with 0.9% and 0.7% lower BMT among low-income women and women with any children, respectively, in the longitudinal individual fixed effects model. These results show the importance of accounting for the heterogeneity of the relationship of fast food prices with body weight outcomes, particularly for certain populations. In addition, given that the OLS results are substantially larger in magnitude than the individual fixed effects results, our findings also highlight the importance of employing longitudinal data in order to control for any unobserved individual-level heterogeneity that might potentially bias the cross-sectional estimates.

We acknowledge several limitations of this study. First, we draw fast food prices and food prices at home from ACCRA. The ACCRA data have a number of limitations, which include that the data are only collected in a limited number of cities and metropolitan statistical areas; the data are based on establishment samples that reflect a higher standard of living; and, they do not always sample the same cities continuously and hence the data are not fully comparable over time. Given that the ACCRA data do not include rural areas, we are limited in generalizing our findings of the relationship of fast food price with BMI in those areas. Previous studies raise the higher likelihood of the existence of food deserts in rural areas (Neckerman et al. 2009; Bitler and Haider 2009), which may imply limited price elasticities for rural residents and reduced impact of potential tax policies for fast food for those populations. Despite these limitations, the ACCRA data provide national coverage, and, hence, a number of previous studies use these price data (Auld and Powell 2009; Chou, Grossman, and Saffer 2004; Powell, Zhao, and Wang 2009; Sturm and Datar 2005, 2008).

Second, BMI in our data is based on self-reported height and weight. Several previous studies report potential measurement errors in self-reports of height and weight in that height is likely to be over-reported, whereas weight is likely to be under-reported (Danubio et al. 2008; Krul, Daanen, and Choi 2010). A number of studies, including Cawley (2004) have adjusted reported height and weight with measured height and weight information using the third National Health and Nutrition Examination Survey (NHANES III). However, we do not adopt such an approach because the magnitude of the errors in self-reported height and weight in the NHANES III may be different than those in the NSLY79, particularly given that the respondents in the NHANES III were aware that their weight and height would be measured after their self-reports of weight and height (Han, Norton, and Stearns 2009; National Center for Health Statistics 1996). In addition, those studies equivocally have reported that results from such an adjustment are overall robust compared to the unadjusted results (Han. Norton, and Stearns 2009; Cawley 2004).Therefore, we opt to use self-reported height and weight as given in the data.

Finally, while this study controls for permanent individual-level unobserved heterogeneity, we do not control for time-varying unobserv-ables. We control for the permanent portion of the unobserved individual heterogeneity by exploiting the panel nature of our data, which partly controls for the impact of such individual heterogeneity to the extent that those characteristics are time-permanent. Our findings that longitudinal individual fixed effects models having weakened relationship of fast food prices with BMI show that permanent individual heterogeneity partly mediates the relationship of fast food prices and BMI. Nonetheless, our results should be interpreted with caution given that we are unable to control unobserved heterogeneity that may be time-varying. In particular, changing prices may reflect other changes such as changing wages in the locale, busier lifestyles, or other policy changes, etc. (Kuchler, Tegene, and Harris 2005: Schroeter, Lusk, and Tyner 2008; Smith, Lin, and Lee 2010).

The results from this study suggest that a fiscal pricing policy such as a "fast food tax" might have any meaningful impact only in certain populations, specifically among low-income women or women with children who are in the upper tail of the conditional distribution of BML Those subpopulations may be more likely to consume fast food in limited service restaurants when they eat out given their budget or time constraints. Previous studies have reported that the prevalence rate of obesity is higher in low-income populations (Miech et al. 2006) and both income and body weight status tend to transfer from parents to their children potentially through nurturing environments (Behrman and Taubman 1990; Friedman et al. 2005; Whitaker et al. 1997). Therefore, our study results have important policy implications in that fiscal food pricing instruments that increase the price of fast food may be an effective tool for combating the obesity epidemic particularly for those vulnerable populations but may have limited effects on other populations.

At the same time, if fast food is a major source of protein intake in low-income populations as indirectly indicated in the previous literature (Lakdwalla et al. 2006), our results also imply that fiscal policies that raise fast food prices might need to be accompanied by other policies to help those individuals to find affordable substitutes for protein via subsidy programs which would also offset the regressive nature of the tax.

ABBREVIATIONS

ACCRA: The American Chamber of Commerce Researchers Association

BLS: Bureau of Labor Statistics

BMI: Body Mass Index

CPI: Consumer Price Index

NHANES III: Third National Health and Nutrition Examination Survey

OLS: Ordinary Least Squares

doi:10.111/j.1465-7287.2012.00322.x

[c] 2012 Western Economic Association International

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Han: College of Pharmacy, Gachon University, Incheon 406-799, South Korea. Phone 82-10-9334-7870, Fax 8232-820-4829, E-mail eahan@gachon.ac.kr: hanayah2@hotmail.com

Powell: Institute for Health Research and Policy. University of Illinois at Chicago, Chicago, IL 60608, Phone 1-312413-8468, Fax 1-312-355-2801. E-mail powelll@uic.edu
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