House prices and female labor force participation

Is there a causal connection between house prices and labor force participation of married women? The simple correlation between house prices and married women's labor force participation across U.S. metro areas is positive. Plausible, informal arguments have been advanced to support causation in either direction: prices raising participation (negative income effects of higher house prices lead more married women to work) or participation raising prices (richer two-earner households bid up the price of scarce housing). I construct an equilibrium model of location, labor supply and real estate (land) prices within a metro area which predicts that (1) metro areas with exogenously less buildable land will have higher house prices and more labor force participation of married women, while (2) metro areas with married women exogenously more prone to work will have higher house prices. Using geographic instruments for housing supply, I find little evidence of a positive effect of house prices on married women's labor force participation, but a somewhat greater possibility that house prices raise their earnings. Likewise, an instrument for married women's labor supply reveals no consistent significant causal effect of two earner households on housing prices, although the possibility of a positive effect cannot be ruled out.