The permanent income hypothesis implies that people save because they rationally expect their labor income to decline; they save a rainy day. It follows that saving should be at least as good a predictor of declines in labor income as any other forecast that can be constructed from publicly available information.The paper tests this hitherto ignored implication of the permanent income hypothesis, using quarterly aggregate data for the period 1953-84 in the U.S. A vector autoregression for saving and changes in labor income is used to generate an unrestricted forecast of declines in labor income. In the VAR, saving Granger causes labor income changes as one would expect if the PIH is true. The mean of the unrestricted forecast is far from the mean of saving, but the dynamics of the two series are quite similar.The paper presents both formal test statistics and an informal evaluation of the fit of the permanent income hypothesis. By contrast with most of the recent literature, the results here are valid when income is nonstationary.

Darius J. Conger, John M. Campbell, Jr., Simultaneity in the Birth Rate Equation: The Effects of Eduction, Labor Force Participation, Income and Health, Econometrica, Vol. 46, No. 3 (May, 1978), pp. 631-641

[In this paper, the authors develop a simultaneous equation model of birth rates composed of four estimated equations. This work differs from past research in that it considers the simultaneous relationship between birth rates and income and includes the cost of fertility as an explanatory factor. This cost is measured by the female labor participation rate under the assumption that income foregone due to fertility is a significant opportunity cost.]