Liquidity, Assets and Business Cycles

Equity price is cyclical and often leads the business cycle by one or two quarters. These observations lead to the hypothesis that shocks to equity market liquidity are an independent source of the business cycle. In this paper I construct a model to evaluate this hypothesis. The model is easy for aggregation and for the construction of the recursive competitive equilibrium. After calibrating the model to the US data, I find that a negative liquidity shock in the equity market can generate large drops in investment and output but, contrary to what one may conjecture, the shock generates an equity price boom. This response of equity price occurs as long as a negative liquidity shock tightens firms' financing constraints on investment. Thus, liquidity shocks to the equity market cannot be the primary driving force of the business cycle. For equity price to fall as it typically does in a recession, a negative liquidity shock must be accompanied or caused by other shocks that reduce the need for investment sufficiently and relax firms' financing constraints on investment. I illustrate that a strong negative productivity shock is a good candidate of such concurrent shocks.Liquidity; Asset prices; Business cycle

Efficiency Improvement from Restricting the Liquidity of Nominal Bonds

This paper addresses why it is beneficial for a society to restrict the use of nominal bonds as a means of payment for goods. The model has a centralized asset market and a decentralized goods market. Individuals face matching shocks that affect the marginal utility of consumption, but they cannot insure, borrow or trade assets against such risks. The government imposes a legal restriction to prohibit nominal bonds from being used as a means of payment in a subset of trades. I show that this partial legal restriction can improve the society's welfare. In contrast to the literature, the efficiency role of the restriction exists in the steady state and it does not require the households to be able to trade assets after receiving the shocks. Moreover, even when lump-sum taxes are available, the efficiency role continues to exist under a condition that induces optimal money growth to be above the Friedman rule.Nominal Bonds; Money; Efficiency; Return dominance

Search Theory; Current Perspectives

In this article I briefly review recent developments in search theory. Particular attention is given to the framework of directed search. I first illustrate the inefficiency that arises in the equilibrium of standard (undirected) search models. Then I provide a formulation of directed search and show that the resulting equilibrium eliminates the inefficiency. Examples of directed search with price posting and auction are provided both for the market with a finite number of individuals and for a large market. After describing the application of search models in monetary theory, I conclude with a remark on the future research.Search; Efficiency; Unemployment

Frictional Assignment

This paper examines the time-consuming process of matching the two sides of a market each having diverse characteristics. This is cast in a labor market setting where workers of different skills need be matched with different machine qualities to produce output. I characterize the efficient allocation and then show that it can be decentralized by a competitive framework. A prominent feature of the frictional assignment is that each skill level is associated with a market tightness in addition to a machine quality. The differential market tightness as an additional allocative device implies that the assignment is not always positively assortative, i.e., high quality machines are not necessarily assigned to high skills even though machine qualities and skills are complementary in production. The market mechanism that decentralizes the efficient assignment has the feature that firms post wages to attract workers in addition to choosing machine qualities. A steady state is established and numerical exercices are used to show that the differential market tightness for different skills is also quantitatively important for the wage function and wage distribution. Ce papier étudie le processus coûteux en temps d'appariement des deux côtés du marché, chacun ayant des caractéristiques diverses. Ceci est placé dans un marché du travail où les travailleurs ont des qualifications qui doivent être appariées avec différents qualités de machine pour la production. Je caractérise l'allocation efficace puis montre qu'elle peut être décentralisée dans un cadre concurrentiel. Un trait saillant de l'assignation frictionnelle est que chaque niveau de qualification est associé à un degré d'étroitesse du marché en plus d'une qualité de machine. L'étroitesse du marché différenciée en tant qu'instrument supplémentaire d'allocation implique que l'assignation n'est pas toujours positivement assortative, par exemple que des machines de haute qualité ne sont pas nécessairement assignées à des travailleurs hautement qualifiés malgré que qualité et qualification soient complémentaires dans la production. Le mécanisme de marché qui décentralise l'assignation efficace a la particularité que la firme affiche des salaires qui attirent des travailleurs en plus de choisir les qualités de machine. Un état stationnaire est établi et des exercices numériques sont utilisés pour montrer que le différentiel d'étroitesse du marché pour les différentes qualifications est également quantitativement important pour la fonction de salaire et la distribution des salaires.Frictional matching; Market tightness; Skills; Machines; Wage distribution

Liquidity, Interest Rates and Output

This paper integrates limited participation into monetary search theory to analyze the liquidity effects of open market operations. The centralized bonds market features limited participation and shocks to government bond sales, while the decentralized goods market features bilateral matches. Unmatured bonds can be used together with money to purchase goods in a fraction of matches, but in other matches a legal restriction forbids the use of bonds as the means of payments. In this economy, a shock to bond sales has two distinct liquidity effects. One is the immediate liquidity effect on the bond price and the nominal interest rate. The other is a liquidity effect in the goods market starting one period later, i.e., the effect on the amount of unmatured bonds circulating in the goods market. Thus, even independent shocks can affect the household s money allocation between the two markets, affect real output and the term structure of interest rates, and cause nominal interest rates to be serially correlated. I establish the existence of the equilibrium and, with numerical examples, examine equilibrium properties.Liquidity; Interest rates; Money; Search.

Customer Relationship and Sales

I construct a search model to formalize the intuitive idea that sellers hold sales to attract buyers and build customer relationships. The market consists of a large number of buyers and sellers. All sellers sell a homogeneous good and all buyers have the same publicly known valuation of the good. Buyers know the terms of trade offered by sellers before choosing which seller to visit. A buyer is related to a seller if the buyer just bought a good from the seller and the relationship is broken if the buyer fails to continue to buy from the seller. Sellers are restricted to offer the same price to all buyers, but they are allowed to give priority to their related buyers. I prove that there is an equilibrium in which a seller gives priority to the related buyer and a buyer makes repeat purchases from the related seller. In the equilibrium, a seller who does not have a related buyer posts a low (sale) price to attract the buyers who are unrelated to any seller and, once the seller is related to a buyer after a trade, the seller will post a high (regular) price to sell only to the related buyer. The fraction of related sellers is endogenous in the equilibrium. I calibrate the steady state of the model to the data and find that the sale price represents a sizable markdown, and the regular price a sizable markup, on the marginal cost. With the calibrated model, I examine comparative statics and dynamics of the equilibrium with respect to changes in the cost of and the demand for the good.Sales; Customer relationship; Directed search

Welfare Improvement from Restricting the Liquidity of Nominal Bonds

In this paper I examine whether a society can improve welfare by imposing a legal restriction to forbid the use of nominal bonds as a means of payments for goods. To do so, I integrate a microfounded model of money with the framework of limited participation. While the asset market is Walrasian, the goods market is decentralized and the legal restriction is imposed only in a fraction of the trades. I show that the legal restriction can improve the society's welfare. In contrast to the literature, this essential role of the legal restriction persists even in the steady state and it does not rely on households' ability to trade unmatured bonds for money after observing the taste (or endowment) shocks.Nominal Bonds; Liquidity; Money; Efficiency.

Directed Search for Equilibrium Wage-Tenure Contracts

I construct a theoretical framework in which firms offer wage-tenure contracts to direct the search by risk-averse workers. All workers can search, on or off the job. I characterize an equilibrium and prove its existence. The equilibrium generates a non-degenerate, continuous distribution of employed workers over the values of contracts, despite that all matches are identical and workers observe all offers. A striking property is that the equilibrium is block recursive; that is, individuals' optimal decisions and optimal contracts are independent of the distribution of workers. This property makes the equilibrium analysis tractable. Consistent with stylized facts, the equilibrium predicts that (i) wages increase with tenure, (ii) job-to-job transitions decrease with tenure and wages, and (iii) wage mobility is limited in the sense that the lower the worker's wage, the lower the future wage a worker will move to in the next job transition. Moreover, block recursivity implies that changes in the unemployment benefit and the minimum wage have no effect on an employed worker's job-to-job transitions and contracts.Directed search; On-the-job search; Wage-tenure contracts

Directed Search for Equilibrium Wage-Tenure Contracts

I analyze the equilibrium in a labor market where firms offer wage-tenure contracts to direct the search of employed and unemployed workers. Each applicant observes all offers and there is no coordination among individuals. Workers' applications (as well as firms' recruiting decisions) are optimal. This optimality requires the equilibrium to be formulated differently from the that in the literature of undirected search. I provide such a formulation and show that the equilibrium exists. In the equilibrium, individuals explicitly tradeoff between an offer and the matching rate at that offer. This tradeoff yields a unique offer which is optimal for each worker to apply, and applicants are separated endogenously according to their current values. Despite such uniqueness and separation, there is a non-degenerate and continuous wage distribution of employed workers in the stationary equilibrium. The density of this distribution is increasing at low wages and decreasing at high wages. In all equilibrium contracts, wages increase with tenure, which results in quit rates to decrease with tenure. Moreover, the model makes novel predictions about individuals' job-to-job transition and comparative statics.Directed search; on the job; wage tenure contracts

Frictional Assignment, Part II: Infinite Horizon and Inequality

In this paper I study the assignment between machines of heterogeneous qualities and workers of heterogeneous skills in an infinite-horizon economy with matching frictions. I characterize first the efficient assignment and then the decentralizing market equilibrium. The efficient allocation assigns a unique machine quality and market tightness to each skill. This efficient allocation is saddle-path stable and the assignment along the stable path is constant over time. The efficient assignment is not positively assortative when machine qualities and skills are not sufficiently complementary with each other. Moreover, efficient wage rates are increasing functions of the skill level when the assignment is positively assortative, but not always so when the assignment is not positively assortative. Nevertheless, the social value of workers always increases in the skill level.Matching; Frictions; Efficiency; Inequality.