CONSPUMA and CPUMA0010 identify the most detailed areas that can be consistently delineated in IPUMS USA microdata for this period. As this post details, CONSPUMA bridges 1980, 1990, and 2000 PUMA definitions, so it’s available through the 2011 ACS (the last sample to use 2000 PUMA definitions). CPUMA0010 bridges 2000 and 2010 PUMA definitions, so it’s available for 2000 samples up through the most recent ACS sample.
To extend your series to 2013, it’s necessary to bridge these two periods by creating a crosswalk from CONSPUMA and CPUMA0010. With knowledge of GIS software or with spatial analysis packages in R or other similar tools, you can spatially overlay IPUMS USA’s GIS boundary files for each of these. Note that these shapefiles are based on different versions of TIGER/Line features. As a result, you’ll get many slivers (i.e. invalid intersections among PUMAs where PUMA boundary representations are slightly different). You’ll want to try to identify and ignore such slivers in your final crosswalk.
If you don’t have a spatial analysis package, you can still create a crosswalk by using the PUMA composition files (available through the Geographic Tools page) by identifying common components of PUMAs across time. However, these composition files are limited in detail; some PUMAs could have the same components, but if the boundaries of those components changed at any time, then the PUMA boundaries would change without any change in the composition files.