The inflation index favored by the Federal Reserve rose moderately in June, and consumer spending remained stable. This is an encouraging sign for officials who hope to cool inflation without damaging the economy. According to data released Friday by the U.S. Bureau of Economic Analysis, the so-called core personal consumption expenditure price index, which excludes volatile food and energy projects, rose 0.2% on a month-on-month basis and 2.6% on a year-on-year basis in June. Consumer spending adjusted for inflation increased 0.2% in June, and the increase in May was upwardly revised.