Final answer:
The Bureau of Economic Analysis (BEA) compiles statistics on the balance of trade and monitors economic performance, which can contribute to understanding the business cycle's phases. However, the NBER is specifically known for dating the business cycle's peaks and troughs.
Step-by-step explanation:
The agency responsible for putting together business cycle information, including the identification of peaks and troughs, in the United States is the Bureau of Economic Analysis (BEA), a part of the U.S. Department of Commerce. While the BEA compiles statistics on the balance of trade using data from merchandise importers and exporters, surveys on international trade in services, and tracks investment flows and travel information, tracking the business cycle specifically is usually associated with the National Bureau of Economic Research (NBER). However, among the given options, the BEA closely monitors economic performance and provides detailed analyses of GDP and related indicators, which contribute to understanding the business cycle's phases.