Five years after the global economy was falling at its fastest rate, Western economies are still failing to gain much-needed momentum, despite the efforts of central bankers on both sides of the Atlantic.

The challenges facing the United States and Europe were evident on Thursday, with the latest figures on growth from Washington showing signs of underlying weakness as the European Central Bank unexpectedly cut interest rates to a record low, reflecting the threat of deflation.

At first glance, the 2.8 percent annualized growth rate estimated for the United States for the third quarter might appear somewhat rosy. It was the fastest quarterly increase in output so far this year, and well above the 2 percent change economists had expected. But nearly a full point of that jump was caused by a buildup in inventory, which is likely to sap expansion in the current quarter. The annual rate of growth in consumer spending slowed sharply to 1.5 percent, the weakest quarterly increase in more than two years, while spending by the federal government fell 1.7 percent.

Last month’s government shutdown did not take place until after the period surveyed in the report, but the decline in federal spending in July, August and September showed how the across-the-board budget cuts imposed by Congress this year were beginning to bite. Over the last four quarters, federal spending cuts have shaved annual growth by half a percent, according to Dean Maki, chief United States economist at Barclays.