In this paper, Stiglitz gives a verbal argument as follows:
Let us consider verbally what actions of the individuals are required to offset various actions by the firm. Assume the firm decreases its dividend payout ratio. This means that it has more retained earnings, so, if the two basic financial accounting identities are to be satisfied, either it must borrow less (perhaps it even lends) or issue fewer new shares. To make up for the loss in dividends, i.e., to keep the same consumption path, individuals buy fewer new shares in the firm or buy fewer new bonds. Assume the firm simply issued fewer shares. In one case, the value of the equity grew because of issuing new shares, in the other case, the value of the equity grew because of retained earnings. From the point of view of the stockholders, the two are perfectly equivalent. This change in dividend pay-out ratio thus leaves the debt-equity ratio unchanged. On the other hand, if the firm decreases the number of bonds issued, it will lead to a lower debt-equity ratio.
I could understand the logic up to this point. But I don't seem to get what follows:
Then individuals borrow on their own account. One can think of it as if the individual takes the proceeds of the loan to purchase the increased equity in the firm (since the two are exactly equal, this is only a convenient way of looking at it; since all funds are fungible, there is no real connection between the two). The increased borrowing by individuals exactly offsets the decreased borrowing by firms so markets continue to clear. Similarly, if the firm decides to issue more three-year bonds and fewer five-year bonds, the individual can undertake exactly offsetting actions in his own portfolio.
Dividend get reduced, the planned consumption is reduced at that period. The investor wants consumption, what the investor does is to borrow from from the market for the consumption. But why can this be viewed as the individual takes the proceeds of the loan to purchase the increased equity in the firm?