## Parker Rogers and Richard Evans, Department of Economics

The purpose of this project was to estimate a function that describes who are the recipients of inheritances among different age and income groups and to incorporate that function into a dynamic macroeconomic model to simulate the effects of inheritances on wealth inequality in the United States.

Our project provides a more detailed way of modeling the dynamics of inheritances in macroeconomic models. Currently, many dynamic macroeconomic models incorporate how inheritances are distributed using two methods. Each method represents an extreme assumption that is almost assuredly not true.

The first method of inheritance distribution gives all of the inheritances left from a dying individual to individuals who are in their same income group. This method fails to model many altruistic wealth transfers that occur in the economy as well as any distribution of that wealth to other income groups. For example, it fails to simulate individuals who give an altruistic inheritance to poorer family members who belong to a different income group. This hinders the accuracy of the model in predicting the effect of inheritances on wealth inequality, and may lead to incorrect predictions of the effects of certain policy implementations.

The second method of inheritance distribution splits the inheritances from all individuals equally among all income groups. This method assumes that all income groups receive equal inheritances, which does not accurately portray inheritance behavior according to macroeconomic data.

Our model will provides a cutting-edge distribution of inheritances among different age and income groups that reflects the behavior of Americans by using data in the Survey of Consumer Finances (SCF).

The results from our project were promising. Using the programming language Python, we gathered fifteen years of data from the Survey of Consumer Finances, a triennial survey conducted by the Federal Reserve, to more accurately determine which Americans receive inheritances. The results from our computation are exciting. Here is a graph depicting the distribution of inheritances, as a percentage of total inheritances, given among different age and income categories,where ability types one through seven are different income groups categorized using the following annual income amounts: 1: Under $15000, 2: $15000 – $24,999, 3: $25,000 – $49,999, 4: $50,000 – $74,999, 5: $75,000 – $99,999, 6: $100,000 – $250,000, 7: $250,000 or more.

Notice the peak located between ages 55 and 65 on Illustration 1. This is consistent with other literature that analyzes only the relationship between age groups and rates of inheritance reception.

With the data gathered, we used a Multivariate Kernel Density Estimator to approximate a smoothed distribution of inheritances among these different age and income groups. The fitted result is seen in Illustration 2.

With this smooth fitted kernel we can use this distribution with any model specifications. For example, if a model calls for only two income groups and two age groups, we can alter the distribution to portray how inheritances are distributed among those specified age and income groups.

After fitting this distributional form, we put the distribution into the model proposed by Jason Debacker et al. in his paper Dynamic General Equilibrium Tax Scoring Model. By plugging our data-driven distribution of bequests into their model, we were able to more accurately predict the effect that inheritances have on wealth inequality.

By applying this accurate and flexible distribution of inheritances to dynamic macroeconomic models, we can better predict the effects that inheritances have on wealth inequality. These predictions can have substantial policy implications as we can see how certain policy changes, like changing the estate tax, will affect the distribution of wealth.