What fraction of new businesses die out within a year? Is there a simple way to figure out how many new businesses appear and disappear each year in the US economy?
It seems a key question to figure out how the economy is changing over time, although I suppose the data is potentially messy...
The Business Dynamics Statistics (BDS) of the Census provides annual measures of business dynamics (such as job creation and destruction, establishment births and deaths, and firm startups and shutdowns) for the economy and aggregated by establishment and firm characteristics. The use of the LBD as its source data permits tracking establishments and firms over time. In particular, BDS provides information on Establishment openings and closings and Number of startups and firm shutdowns. 

The following figure is based on BDS and from Haltiwanger, John, Ron Jarmin, and Javier Miranda, (2009) "Business Dynamics Statistics: An Overview".



Note: SUSB means Statistics of U.S. Businesses from Census firms as well.