Although measured remittances by migrant workers have soared in recent years, macroeconomic studies have difficulty detecting their effect on economic growth. This paper reviews existing explanations for this puzzle and proposes three new ones. First, it offers evidence that a large majority of the recent rise in measured remittances may be illusory -- arising from changes in measurement, not changes in real financial flows. Second, it shows that even if these increases were correctly measured, cross-country regressions would have too little power to detect their effects on growth. Third, it points out that the greatest driver of rising remittances is rising migration, which has an opportunity cost to economic product at the origin. Net of that cost, there is little reason to expect large growth effects of remittances in the origin economy. Migration and remittances clearly have first-order effects on poverty at the origin, on the welfare of migrants and their families, and on global gross domestic product; but detecting their effects on growth of the origin economy is likely to remain elusive.