It concerns how the average quality of assets that are for sale in the market changes over time. These dynamics will determine the average asset quality—or, equivalently, the severity of the lemons problem—facing the asset's buyer. These variables therefore determine whether it is optimal to take advantage of the prediction effect in choosing the optimal time for intervention.
The announcement effect is driven by the quality effect and the option value of the intervention. Average asset quality will only increase sufficiently after the intervention to induce trading in the market.
OPTIMAL INTERVENTIONS AND THE ANNOUNCEMENT EFFECT 1. Objective Function
As the market becomes less important, the costs of intervention increase relative to gains from trade. When the quality shock is small (α >1), an announcement effect can occur by delaying the intervention sufficiently and without increasing the price (see Proposition. Consequently, if trade frictions are small (λsufficiently large) or if the market is not too high. important (θ sufficiently large), it is optimal to delay the intervention and rely on the advertising effect.
For a small shock (α >1), it is optimal to delay intervention and rely on the announcement effect when the market is not important and trading frictions are small. First, the magnitude of the notification effect is limited when the intervention is delivered early because a sufficient delay is needed for a notification effect to emerge. Moreover, by Proposition 8, whenever P ∈ (Pmin, Pmax), it is optimal to delay the intervention and increase the price to Pmax in order to induce the announcement effect as much as possible.
As the value of θ increases, it is optimal to keep the price at Pmin but to delay intervention (T > 0) longer and longer. This shows the main trade-off for the optimal policy between the price and the timing of the intervention. MMLR can take advantage of the announcement effect through a higher price and delay intervention.
When the cost weight of the intervention is high, delaying the intervention becomes more attractive when the price increases.
DISCUSSION
The parameter θ shifts the weight between the cost of the intervention and the cost of misallocation. We now prove the second part of the proposition, which states that trade before the intervention can be characterized by two breakpointsτ1(T)≥0 andτ2(T)∈[τ1, T). Since with no tradeα describes an upper bound for α(t), the right-hand side of the condition is always positive so that there cannot be an announcement effect.
The second lemma considers how the net present value of the minimum cost C(VI)e−rT intervention changes by changing this policy in a way that allows us to maintain a constant surplus Γ(T) provided that trading behavior does not change. This net present value is minimized exactly at the inflection point of the minimum cost function defined above. Define the new intervention time with T′=T−∆∈(τ2(T), T) and define the new intervention size corresponding to the marginal policy change z.
With proposition 6, an announcement effect can only occur when the intervention is sufficiently delayed and the option value is sufficiently large. Therefore, any price in the interval (Pmin, P(T)] cannot be optimal as it increases the cost of the intervention without providing additional benefits in terms of inducing trade before the intervention. Using Q=Qmin for any optimal policy, the lower bound by the welfare with any intervention (T, P) is then given by.
This implies that the welfare loss due to postponing the intervention with any policy (T, P) is given by .
Koeppl
Time of Intervention
This implies that for a minimum intervention at any T, there can be no announcement effect, since α(t) < α < 1 for any t < T. The absence of an announcement effect allows us to express the trading profits of a minimal intervention at T explicitly. These gains are achieved through two parts: a steady-state part and a part capturing the transitions associated with an intervention in T.
The first term is a constant and expresses the welfare cost of an asset that is permanently misallocated, while the second term is the gain from going back immediately to a steady state of trade at period T , the time of the intervention, discounted back to period 0 The third is the additional gain from the slow movement (according to κ) of traders from high to low valuation until the intervention takes place. The last period expresses the welfare loss by moving slowly to the steady state after the intervention on T.
This creates the primary trade-off for the policymaker where delaying intervention saves costs, but at the expense of less trading in the market. The optimal intervention time T∗ in an internal solution equates the marginal benefit with the marginal costs of intervention delay. The marginal benefit arises from the cost savings corresponding to the first term in square brackets.
Marginal costs are given in the second term and derive from less trading in the market.
Role of Search Frictions
When search frictions increase, selling pressure dissipates more slowly, which increases the marginal costs of delaying intervention. Therefore, for sufficiently large T, we have that marginal costs decrease as search frictions increase. Therefore, market importance drives the effects of search frictions on the timing of the intervention.
We assume that there is a positive trade surplus for the good but a non-positive trade surplus for lemons.1 Denote the net value of the good for the seller as vsg and for the buyer as vbg > vsg. Consider any contract (p, q), where p is the price paid by the buyer and q is the probability that the seller transfers the asset. We want to show that buyers always prefer a pooling contract or, in other words, have no incentive to separate sellers using lottery contracts (ie, q < 1).
Pool contract with (p, q) Sellers with a good asset will sell at price p if and only if. On the contrary, if vb` = vs`, the problem becomes D.11) which gives exactly the same payout as with a pool contract. If πvbg+ (1 − π)vb`− vsg < 0, then there is only trade in lemons which generates no trade surplus.
It is believed that trading bad assets alone cannot produce a positive trade surplus for buyers.
Set-up
Trade Dynamics
This implies that we have continuous trade for all t < τ , provided that π is sufficiently large and ρ is sufficiently small.
Optimal Interventions
- Set-up
- Minimum Gradual Interventions
- Remarks
This policy could be optimal with respect to the parameter θ, which expresses how important the market is relative to the cost of the intervention. Depending on the parameter values, trading in the market can be interrupted simply due to a time mismatch between buyers. Finally, for γ = 1, buyers who get a lemon will not benefit from the guarantee, as they can obtain a higher value by waiting for the market to trade for a possible positive value.
Note, however, that the threshold provided by the guarantee depends explicitly on how much trading there is in the market, as reflected by vb(γ). For any additional quantity ∆Q = Q − Qmin of lemons purchased at price P, only the proportion (P − Pmin)∆Q provides an additional transfer to lemons, since the market is functioning again after the intervention and the lemon has the expected market value. from Pmin. The market will continue to operate continuously after the sale as the average asset quality in the market remains above the threshold to maintain trading in balance.
The reason is that they can later sell the lemon again on the market. When selling additional lemons lemons back to the market at price v`, the costs of the intervention are then approximately given by1. Of course, MMLR can only resell lemons on the market if future buyers cannot observe which assets were once owned and resold by MMLR.
The reason is that the quality in the market does not improve before T , time intervenes.
Benchmark Calibration
The steady state equilibrium then falls into the range of multiple equilibria so that it matters whether a trader can resell the asset when he receives a liquidity shock.
Low Search Frictions and Small Quality Shock
The reason is that with less search friction there cannot be much trading, as otherwise the quality of assets for sale would fall too quickly to maintain a mixed strategy equilibrium. It also increases trading activity prior to intervention which in turn increases the market price. This is due to a faster decline in the average quality of the assets that are for sale when there are more trades in the market.
We have assumed all along that when traders sell lemons at MMLR, they are out of the market forever. Assume now instead that traders who sell lemons at MMLR can stay in the market and become buyers again after selling to MMLR. An intervention can then have more powerful effects, as it permanently increases market liquidity by increasing the number of buyers in the market from 1 to 1 + Q.
This reinforces the strategic complementarity, since we now have for the value of a lemon after full recovery it. Using the parameter values in Appendix J, Figure K.1 compares the equilibrium trade dynamics for an intervention with and without this liquidity channel. The value function for lemons is almost identical to our benchmark economy, and thus the market price and trade dynamics are only slightly changed by this additional effect.1.
1 It is not clear how relevant the liquidity channel would be empirically, as there could be entry and exit of traders in a specific market. Moreover, the shock to quality may be temporary as MMLR is able to shed some of the purchased assets after recovery, leaving the market tightening unchanged in the long run.
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