Inner needle drop is a natural occurance in pines and other evergreens in the fall. The following is more information.
White pines with inner needles turning yellow are not dying, they are just experiencing normal fall yellowing and leaf drop. While evergreens do not loose all their leaves in the fall, individual leaves/needles do not last on the tree forever. If trees are small, you can shake them and loosen the needles. You will end up with a nice pine straw mulch below the trees.
In some years, the natural needle drop will occur in a relatively short period of time, with rapid and noticeable browning of the older needles, which leads to fears the tree is dying. In other years, people don't even notice it happening, because the browning is spread over a long period of time.
The symptoms are normal for the fall. Pines and arborvitaes normally shed their oldest needles in the Fall. White pines usually retain their needles for one to two years. The older needles, those towards the center of the tree, turn yellow before dropping. Older arborvitae leaves turn a reddish brown. Natural needle discoloration may be more noticeable on trees that have experienced root stress due to less than optimal growing conditions. Extended dry periods during the summer months, as well as sites with poorly drained, heavy clay soils may accentuate root stress to pines. Since the newest growth (this year's needles) are still green and healthy in appearance, you can be assured that this yellowing phenomenon is a natural one.
Fall needle drop in pine. Photo from the Plant & Pest Digital Library at Purdue University.
Information from the Ornamentals Hotline Newsletter from UD Cooperative Extension and Gail Ruhl and Jeff Burbrink, Purdue University.