One of the classic predictions of urban economic theory is that high-income and low-income households choose different residential locations and therefore, conditional on workplace location, have different commuting patterns. The effect of household income on commuting distance may be positive, because of an increased demand for housing as house prices are lower further from workplace locations, or negative, because of an increase in the value of travel time. In addition, the sign of this effect may depend on the location of residential amenities relative to workplaces. Empirical tests of this effect are not standard, due to reverse causation and lack of good control variables. To address reverse causation, this effect is derived using changes in household income and distance through residential moves keeping workplace location constant. Our results contradict previous results in the literature. We show that for Denmark, conditional on the workplace location, the income elasticity of distance is negative and in the order of 0.18. This elasticity is larger for single-earner than for dual-earner households. Conditional on that the household moves residence between municipalities, the elasticity is suggested to be around 0.60.