Let's consider the United States in the time of major westward expansion and "Amerindian removal": the century 1760 to 1860 before the Civil War. We have U.S. output-per-worker growth then at about 1.0% per year, in contrast to British output-per-worker growth at about 0.5% per year. We have the U.S. population and labor force growing at 2.5% per year, from 2.5 to 30 million. Our conclusion:
An America penned behind the Appalachians would probably have seen its living standards and productivity levels not growing at 1% per year from 1760 to 1860 but shrinking. For the $ \gamma = 3.0 $ benchmark case, living standards and productivity levels would have shrunk at a pace of -0.325% per year had population growth been the historical 3% per year.