DSDR KB:

There does not seem to be a question on "How much is your car worth?"

There is a summary of consumption questions in the PSID:

One of the consumption categories is 'transportation' and under this falls vehicle loan payments, down payment for vehicle. There is also a series of questions about vehicle leases. This summary is available here:

http://psidonline.isr.umich.edu/Data/SL/ConsumptionQsinPSID_1968-2005.pdf

There is also a value of vehicle question, but it is is not ideal. It was asked in 1989 and 1994 and the text is:

What about the value of what you own on wheels, like cars, trucks, a motor home, a trailer, or a boat. What are they worth all together, minus anything you still owe on them?

This is available in the Data Center.