This paper examines the impact of Airbnb on the local rental housing market. Airbnb provides landlords an alternative opportunity to rent to short-term tourists, potentially leading some landlords to switch from long-term rentals, thereby affecting rental housing supply and affordability. Despite recent government regulations to address this concern, it remains unclear how many and what types of properties are switching. Combining Airbnb and American Housing Survey data, we estimate a structural model of property owners' decisions and conduct counterfactual analyses to evaluate various regulations. We find that Airbnb mildly cannibalizes the long-term rental supply. Cities where Airbnb is more popular experience a larger rental supply reduction, but they do not necessarily have a larger percentage of switchers. Affordable units are the major sources of both the negative and positive impacts of Airbnb: they cause a larger rental supply reduction, which harms local renters; they also create a larger market expansion effect, which benefits local hosts who own affordable units and may be economically disadvantaged. Policy makers need to strike a balance between local renters' affordable housing concerns and local hosts' income source needs. We also find that imposing a linear tax is more desirable than limiting the number of days a property can be listed. We propose a new convex tax that imposes a higher tax on expensive units and show that it can outperform existing policies in terms of reducing cannibalization and alleviating social inequality. Finally, Airbnb and rent control can exacerbate each other's negative impacts.