Anheuser-Busch InBev SA said Budweiser and Bud Light volumes continued to decline in the fourth quarter, but that its efforts to woo drinkers with new lower-carbohydrate and lower-alcohol drinks had started to improve its overall performance in the U. S.

The world’s largest brewer has struggled in recent years, as American drinkers shift to craft beers, Mexican imports, wine and spirits. It has also had to grapple with challenging emerging markets and a huge debt pile from its more than $100 billion acquisition of SABMiller…