Post-Keynesian growth models are incorporating debt dynamics as an important aspect of the relationship between growth and income distribution. Following these lines, this paper suggests a model in which household savings behavior is determined by a dynamic adjustment of wealth to a targeted level. This assumption results in a model in which household adjusts their wealth to a target wealth to wage ratio. We then run an empirical estimation of our model for different household income brackets and group of ages. We use microlevel data for wealth and wage of US Households available in the PSID (Population Survey Income Dynamics) Database. We find that the model yields statistically significant results for most income and age groups. Furthermore, it is extremely significant for the middle income and middle age households. We also observe that the target wealth to wage ratio is not constant across groups of income and age. This ratio also tends to increase with income and age.