Money is perfectly liquid. Other assets are not as liquid as money, but some are more liquid than others. One of the main features of the financial crisis is that some assets became less liquid than they had previously been. I want to look at the channels through which a fall in the liquidity of those assets could reduce aggregate demand.
We can define "liquidity" (or illiquidity) as the cost of a round-trip. Start with money, use it to buy the asset, then sell the asset again for money. How much have you lost in the process? Money by definition is the medium of exchange, and perfectly liquid. All other assets are less liquid. Short-term government bonds are the most liquid, next to money. And commercial paper (private bonds and stocks) are less liquid. Real assets are even less liquid.
Some days I don't want to buy anything. Other days I want to buy a small amount of stuff. Very rarely, I want to buy a large amount of stuff. We could say my preferences for consumption expenditure are stochastic. They look something like U = d.U(C), where d is zero some days, positive other days, and sometimes, rarely, gets very large. Perhaps I can predict how the parameter d will fluctuate over time; perhaps I can't.
We could probably think of firms in the same way. Some days they don't want to buy anything. Other days they want to buy a small amount of stuff. Very rarely, they want to buy a large amount of stuff.
Now think of an inventory-theoretic demand for various types of assets. Just like the Baumol-Tobin inventory-theoretic demand for money, but with more assets than just money and bonds. I will divide my portfolio between many assets: from the most liquid to the least liquid. On average, I will hold a small amount of perfectly liquid money for the frequent small expenditures; some less liquid government bonds for the less frequent medium-sized expenditures; and some even less liquid commercial paper for the rare large expenditures. [Update: even the consumer durables I hold could be sold to finance spending in an emergency.]
Firms may do the same.
In equilibrium, the yields on various assets across the liquidity spectrum will vary inversely with their liquidity, and the velocities of circulation (turnover rates) will vary inversely with liquidity. The most liquid assets will have a low yield, and high velocity. The least liquid will have a high yield, and low turnover.
Now suppose there is an exogenous shock: some assets (commercial paper) become less liquid than they were before. The shock might be the revelation that some of this class of assets were lemons. Knowing that some assets are lemons, people will want to take more effort to get information about an asset before buying it, or else suffer a greater risk that the asset is a lemon. Getting that information (or risking not getting that information) is a transactions cost, and it makes the asset less liquid.
The decline in the liquidity of commercial paper will reduce its value (increase its equilibrium yield) over and above any direct effect from some assets being lemons. In other words, even if it were revealed that some assets were worse than before and others better than before, so that the average fundamental value were the same, the fact that buyers cannot tell which is which, and it is costly to find out, will reduce the value of the whole class of assets. Because people value liquidity.
The initial decline in liquidity will be self-reinforcing. (It has a multiplier effect). With transactions costs higher, people will be less willing to buy and sell commercial paper. The velocity of circulation will fall. That makes the market in commercial paper shallower, with less volume of transactions, and a large quick sale will cause a bigger drop in price. That is because buyers expect, rationally, that a greater percentage of commercial paper offered for sale on the market will be lemons, compared to the percentage in the total stock.
So an initial small decline in liquidity will be magnified into a larger decline in liquidity. It is not impossible that the positive feedback parameter will be greater than one, and the market will freeze up totally, with all paper being held to maturity.
[Update: bank failures will also play a role in making assets less liquid. Banks buy illiquid assets as raw materials, convert them into more liquid liabilities, and make their revenues off the liquidity spread. When the reduction in asset prices reduces banks' capital, this reduces banks' ability to convert less liquid into more liquid assets.}
How will this decline in liquidity affect aggregate demand?
The first effect is a wealth effect. With higher yields on the now less liquid commercial paper, the price of commercial paper has fallen. If agents have finite lives (as in an overlapping generations model), they will reduce their demand for consumption due to a decline in the value of their assets.
The second effect is a substitution effect away from current consumption towards future consumption. If a household needs to sell commercial paper to finance a large purchase, like a new car, the higher yield on commercial paper will increase the incentive to postpone consumption, and save. Likewise, if a firm needs to sell commercial paper to finance new investment, the higher yield will increase the incentive to postpone investment.
Both the wealth effect on consumption, and the substitution effects on consumption and investment, mean that higher yields on the less liquid commercial paper cause aggregate demand to fall.
[Update: and if it were real assets, like houses, that became less liquid, that would directly reduce the prices of real assets, and reduce the demand for investment in newly-produced real assets.]
Now, the decline in aggregate demand will cause a response from the central bank. The central bank will want to lower interest rates to offset that decline, and prevent a recession. But the interest rate on which the central bank normally operates is the interest rate on assets which are nearly as liquid as money, like short-term treasury bills, or overnight reserves of the banking system.
Reducing interest rates on those assets will help, but it might not help enough, even if those interest rates are forced down to zero.
The wealth effect of lower interest rates on very short-term assets is very small, approaching zero in the limit as the term to maturity approaches zero. (The price of an infinitely-lived bond will double if the interest rate halves; the price of a one-year bond will rise by only 5% if the interest rate drops from 5% all the way to 0%).
The substitution effect of lower interest rates on very liquid assets will help increase consumption and investment, but only for those who would finance the marginal expenditure through selling those very liquid assets. That is a small subset of total expenditure.
We can think of "the" interest rate for the IS curve as a weighted average of all interest rates at which the marginal consumption or investment expenditure will be financed. Weighted first by shares in total expenditure; weighted second by the interest elasticity of that expenditure. That "average" interest rate is a very different interest rate from the interest rate on the most liquid assets. If the liquidity spread gets wider, the average interest rate may rise even if the interest rate on the most liquid assets (next to money) falls to zero. And then aggregate demand will fall. We enter a recession, and expected deflation, which raises the average real interest rate further still.
And we can think of "the" interest rate on the LM curve as a weighted average of all interest rate spreads between all assets and zero-interest money. Weighted first by the shares of assets in the portfolio; and second by the interest elasticity of demand for that asset in the portfolio. The fact that some of the total stock of all assets are now less liquid than before means that the average liquidity of all assets is less than it was before. The LM curve shifted left. It is not horizontal at zero. Only a small fraction of the weighted average LM curve is horizontal at zero.
Was it a fall in the Neo-Wicksellian "natural rate of interest" below zero which caused the "liquidity trap"? Depends how you define both terms. But it needn't have been a fall in time-preference, or in the return on investment, that caused the problem. It could have been a fall in liquidity.
And the solution is to increase liquidity. Either take the lemons off the market, or clearly brand them "lemons", or else increase the percentage of money, or money plus liquid bonds, in the portfolio.