The Oswald hypothesis is that home ownership reduces mobility and through that channel results in poorer labor market outcomes. There has been only limited previous evidence on the Australian case. Here we use data from the first four Australian censuses of the twenty-first century, aggregated at the smallest geographical areas for which statistics are released. We propose testing the Oswald hypothesis by estimating the effect of home ownership on the full-time employment rate. Modelling the unemployment rate, as is often done in testing the hypothesis, produces implausible results with respect to the control variables, most likely due to the limitations of the official definition of unemployment. We find that, in modelling the full-time employment rate, the control variables for educational and demographic factors have the theoretically plausible effects, while variables capturing rates for both outright home ownership and with mortgage home ownership are positively related to full-time employment rates, with the effect of the former stronger than the latter. Our findings strongly contradict the Oswald hypothesis.