Question

Using data from IRS Form 5500 filings by U.S. pension plans, I estimated a model of contributions to pension plans as ln(1+c i)=α 0+U i∗α 1+ PD i∗α 2+ e i Where the subscript i indicates the pension plan, c is employer contributions per participant, U is a dummy that equals one if the plan is a union plan, and PD is a dummy that equals if the plan is participant directed (meaning that the employee decides how to invest the money). Note that employer contributions can equal zero, since some pension plans are funded entirely by employee contributions. I estimated a Tobit and OLS version of the model. The results are below. Sigma represents the standard deviation of the residual. Standard error of coefficients is presented in parentheses below each coefficient. Variable OLS Tobit Union -0.0626*** -0.0676*** (0.012) (0.014) Participant Directed -0.307*** -0.311*** (0.007) (0.008) Constant 5.894*** 5.684*** (0.006) (0.007) Sigma 2.7434 3.226*** Observations 744615 744615 What is the unconditional expected value of Y. That is, E[Y] not E[Y|Y>0].

Answer 1

The unconditional expected value of Y is calculated by summing up all the values of ln(1+c) and dividing by the total number of observations.

Step-by-step explanation:

The question asks for the unconditional expected value of Y, denoted as E[Y]. In the given equation, Y represents ln(1+c), which is the natural logarithm of the employer contributions per participant in a pension plan. To find E[Y], we need to calculate the average value of Y across all observations.

To calculate E[Y], we sum up all the values of ln(1+c) and divide by the total number of observations. In this case, the total number of observations is 744,615.

Therefore, the unconditional expected value of Y is the sum of ln(1+c) divided by 744,615.