Yodsanklai is referring to the mythical food deserts.
We study the causes of “nutritional inequality”: why the wealthy tend to eat more healthfully than the poor in the U.S. Using two event study designs exploiting entry of new supermarkets and households’ moves to healthier neighborhoods, we reject that neighborhood environments have economically meaningful effects on healthy eating. Using a structural demand model, we find that exposing low-income households to the same food availability and prices experienced by high-income households would reduce nutritional inequality by only 9%, while the remaining 91% is driven by differences in demand. In turn, these income-related demand differences are partially explained by education, nutrition knowledge, and regional preferences. These findings contrast with discussions of nutritional inequality that emphasize supply-side issues such as food deserts.
The term 'Food desert' was used primarily to refer to total healthy food availability within a certain radius, including (especially) healthy food availability in supermarkets.
Yodsanklai appears to have been referring to the availability of healthy prepared foods, particularly restaurant foods. It is entirely possible to live in an area well-served with supermarkets and bodegas and only have 'unhealthy' restaurants to choose from due to the peculiar demands of that area. You can drive through parts of the US and see nothing but greasy spoons or pub food, while the local at-home cooks have access to a wider variety of healthy foods from the markets.
The following is the remainder of the sentence you quoted
> would reduce nutritional inequality by only 9%, while the remaining 91% is driven by differences in demand.
Most of the difference in what the underclass and others eat is because of taste. And Americans spend less of their budgets on food consumed at home than any other nation.
We study the causes of “nutritional inequality”: why the wealthy tend to eat more healthfully than the poor in the U.S. Using two event study designs exploiting entry of new supermarkets and households’ moves to healthier neighborhoods, we reject that neighborhood environments have economically meaningful effects on healthy eating. Using a structural demand model, we find that exposing low-income households to the same food availability and prices experienced by high-income households would reduce nutritional inequality by only 9%, while the remaining 91% is driven by differences in demand. In turn, these income-related demand differences are partially explained by education, nutrition knowledge, and regional preferences. These findings contrast with discussions of nutritional inequality that emphasize supply-side issues such as food deserts.
https://web.stanford.edu/~diamondr/AllcottDiamondDube_FoodDe...