Education may reduce risk of dementia through passive reserve, by increasing neural substrate. We tested the hypotheses that education is associated with thicker cortex and reduced rates of atrophy in brain regions related to literacy and intellectual ability. Healthy older adults and those with mild cognitive impairment were categorized into high (≥18 years) and low (≤13 years) education groups. Higher education was associated with thinner cortices in several areas, but one-year atrophy rates in these areas did not differ by education group. These results do not support a passive reserve model in which early-life education protects against dementia by increasing cortical thickness. Connectivity and synaptic efficiency or other lifestyle factors may more directly reflect cognitive reserve.