Time Inconsistency Problem Research Articles

Price setting in forward-looking customer markets

If consumers form habits in individual goods, firms face a time-inconsistency problem. Low prices in the future help attract customers in the present. Firms, therefore, have an incentive to promise low prices in the future, but price gouge when the future arrives. In this setting, firms benefit from “committing to a sticky price.” If consumers have incomplete information about costs and demand, the firm-preferred equilibrium has the firm price at or below a “price cap.” The model therefore provides an explanation for the simultaneous existence of a rigid regular price and frequent “sales”.

Quality uncertainty and time inconsistency in a durable good market

In a durable good monopoly where consumers cannot observe quality prior to purchase and product improvement occurs exogenously over time, I show that uncertainty in quality may resolve the time inconsistency problem (even for low levels of product improvement). Higher dispersion in quality creates greater demand for future product by increasing the incentive of buyers with inferior quality realizations to repeat purchase and this, in turn, reduces the incentive of the seller to cut future price. For various levels of product improvement, I characterize the range of quality uncertainty for which the market equilibrium is identical to one where the monopolist can credibly precommit to future prices. I also show that the presence of quality uncertainty can lead to no trading in the primary good market. Further, in contrast to the literature on the Coase conjecture, inability to precommit to future prices can reduce social welfare as a result of the market closure.

Intergenerational Risk Sharing in Time-Consistent Funded Pension Schemes

Intergenerational risk sharing by funded pension schemes may increase welfare in an ex ante sense. However, it also suffers from a time inconsistency problem. In particular, young generations may be unwilling to start participating in a pension scheme if this requires them to make huge transfers to older generations. This paper explores if limiting the transfers between generations can make a funded pension scheme time-consistent. The paper finds that this is possible indeed in a more or less realistic economic environment; it is not the case in general however. The form of the time-consistent scheme (how strong are the limits to transfers) is found to be very responsive to the economic environment. The time-consistent scheme offers lower welfare than the original time-inconsistent scheme, but higher welfare than a defined-contribution scheme without any intergenerational risk sharing.

THE TIMING OF UPGRADES*

By using a durable-goods monopolist model, this paper investigates the timing of upgrades. I consider a three-period model where the monopolist can upgrade the product in the second and third periods by investing in R&D. I analyse the non-commitment and commitment cases. In the latter case, the decision on the timing of upgrades is made in the first period in advance. It is shown that the time-inconsistency problem causes the monopolist in the non-commitment case to release a new version more rapidly than in the commitment case. Moreover, even in the non-commitment case, the release of a new version can still be later than the optimum from the social viewpoint.

A deterministic linear quadratic time-inconsistent optimal control problem

A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a time-consistent solution to the original time-inconsistent problem. Under certain conditions, we constructively prove the existence of such an equilibrium control which is represented via a forward ordinary differential equation coupled with a backward Riccati--Volterra integral equation. Our constructive approach is based on the introduction of a family of $N$-person non-cooperative differential games.

Contract Law and Development

We relate the design of contract law to the process of development. In this paper, contract law denes which types of private agreements are enforceable (i.e. are binding and enforced by courts) and which are not. More specically, we consider an economy where agents face a hold-up problem (moral hazard in teams). The resulting timeinconsistency problem leads to ineciently low levels of eort and trading among agents. The solution to this problem requires a social contract which meets two conditions: (i) an economy-wide delegate (judge) responsible for the enforcement of the social contract and (ii) a set of non-enforceable private contracts (regulation). However, because this mechanism is costly, its eectiveness depends on the aggregate production of the economy. To capture the interaction between contract enforcement and development, we introduce a multi-period economy and show that, in the early stages of development, the mechanism is infeasible. The appearance of enforcement institutions and regulation is delayed for the later stages. At this point of time, the hold-up problem is solved and this spurs economic growth further. Finally, the relationship between economic development and the evolution of contract law may be non-monotonic, which may explain why empirical studies fail to nd a robust relationship between the two.

A Tale of Two Cities: Bureaucratisation in Mayor-Council and Council-Manager Municipalities

This paper presents a theory that predicts under what circumstances self-interested politicians ‘bureaucratise’ their administrations, in the sense that they delegate the powers to hire, fire and promote public employees to autonomous bodies (like civil service commissions). The main testable proposition is that, in polities with a higher concentration of powers, politicians will bureaucratise their administrations to overcome time inconsistency problems in their relationships with public employees. This prediction is tested with data drawn from US municipalities, where two main types of local governments co-exist: mayor-council and council-manager. Results show that municipal governments with a higher concentration of powers (i.e. mayor-council) tend to have more bureaucratised administrations.

Competitive Markets without Commitment

In the presence of a time-inconsistency problem with agency contracts, we show that competitive markets can implement allocations that Pareto-dominate those achieved by a benevolent government, and they induce more effort. We analyze a model with moral hazard and a two-sided lack of commitment. After agents have chosen their work, firms can modify contracts and agents can switch firms. If the ex post market outcome satisfies a weak notion of competitiveness and sufficiently separates individuals, it is Pareto superior to a government’s allocation with a complete breakdown of incentives. Moreover, competitive markets without commitment implement more effort in equilibrium under general conditions.

A NOTE ON DURABLE GOODS MONOPOLISTS: COMMITMENT TO FORWARD COMPATIBILITY

This note re-examines the previous results on durable goods monopolists under the time inconsistency problem that the firm tends to make its goods less compatible as a “planned obsolescence” strategy in the presence of network effects. We find that the possibility of the commitment to forward compatibility is profitable to the monopolist, depending upon the degree of technological progress and network effects. Therefore, contractual commitments that are frequently feasible and observed in real-world markets make the society better off.

A General Theory of Markovian Time Inconsistent Stochastic Control Problems

We develop a theory for stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a Bellman optimality principle. We attach these problems by viewing them within a game theoretic framework, and we look for Nash subgame perfect equilibrium points. For a general controlled Markov process and a fairly general objective functional we derive an extension of the standard Hamilton-Jacobi-Bellman equation, in the form of a system of non-linear equations, for the determination for the equilibrium strategy as well as the equilibrium value function. All known examples of time inconsistency in the literature are easily seen to be special cases of the present theory. We also prove that for every time inconsistent problem, there exists an associated time consistent problem such that the optimal control and the optimal value function for the consistent problem coincides with the equilibrium control and value function respectively for the time inconsistent problem. We also study some concrete examples.

A Post Keynesian Perspective on the Rise of Central Bank Independence: A Dubious Success Story in Monetary Economics

This paper critically assesses the rise of central bank independence (CBI) as an apparent success story in modern monetary economics. As to the observed rise in CBI since the late 1980s, we single out the role of peculiar German traditions in spreading CBI across continental Europe, while its global spread may be largely attributable to the rise of neoliberalism. As to the empirical evidence alleged to support CBI, we are struck by the nonexistence of any compelling evidence for such a case. The theoretical support for CBI ostensibly provided by modeling exercises on the so-called time-inconsistency problem in monetary policy is found equally wanting. Ironically, New Classical modelers promoting the idea of maximum CBI unwittingly reinstalled a (New Classical) “benevolent dictator” fiction in disguise. Post Keynesian critiques of CBI focus on the money neutrality postulate as well as potential conflicts between CBI and fundamental democratic values. John Maynard Keynes’s own contributions on the issue of CBI are found worth revisiting.

Informational externalities, strategic delay, and optimal investment subsidies

Abstract This paper examines optimal government policy when private investment generates information, but investors cannot internalize the informational value their actions have to others. Equilibrium exhibits inefficient delay, as investors adopt a wait‐and‐see approach. The government can alter incentives via an investment subsidy, but complications arise, since future subsidies may induce investors to disregard current policy initiatives. The paper shows that the government achieves its desired outcome only when the the investment subsidy is financed by a non‐distortionary, lump‐sum tax. When taxation is distortionary, the government faces a time inconsistency problem that may prevent effective policy.

A Political Agency Theory of Central Bank Independence

We propose a theory to explain why, and under what circumstances, a politician endogenously gives up rent and delegates policy tasks to an independent agency. We apply this theory to mon- etary policy by extending a stochastic general equilibrium model. This model provides a theory of central bank independence that is unrelated to the standard time inconsistency problem which underlies all formalized theories of central bank independence. We derive five key predictions of the model and show that they are broadly consistent with the data. Finally, we show that while instrument independence of the central bank is desirable, goal independence is not.

Carbon Taxes and Innovation without Commitment

Abstract Climate mitigation policy should be imposed over a long period, and spur innovation of new technologies in order to make stabilization of green house gas concentration economically feasible. The government may announce current and future policy packages that stimulate current R&D in climate-friendly technologies. However, once climate-friendly technologies have been developed, the government may have no incentive to implement the pre-announced future policies, that is, there may be a time inconsistency problem. We show that if the government can optimally subsidize R&D today, there is no time inconsistency problem. Thus, lack of commitment is not an argument for higher current R&D subsidies than the first-best subsidy. If the offered R&D subsidy is lower than the optimal subsidy, the current (sub-game perfect) carbon tax rate exceeds the first-best carbon tax rate.

Transaction-cost efficiency and the democratic deficit

The extensive literature on the European Union's (EU) democratic deficit suffers from two serious limitations. First, it proposes to solve the problem by analogy with national practices instead of looking for its roots, and possible solutions, in the integration process itself. Second, this literature considers only the normative aspects of a condition that also has significant efficiency implications. Analogical reasoning has led to a continuous expansion of the powers of the European Parliament (EP) without any notable increase in democratic legitimacy. The origin of the democratic deficit is, quite simply, the failure to convert a majority of voters to the cause of political integration. This failure forced integrationist elites to sacrifice democracy on the altar of deeper integration in the hope of ‘making Europe without Europeans’. The strategy of pursuing political integration under the guise of economic integration backfired when it became evident that the EU kept falling behind its major international competitors in spite of ambitious projects like the Single European Market and Economic Monetary Union (EMU). One reason for this unsatisfactory performance is that in sacrificing democracy for the sake of deeper integration, EU leaders also sacrificed many formal and informal methods developed by democratic regimes in order to reduce various political transaction costs. Thus delegation of monetary policy to an independent central bank is a well-known method for solving the time inconsistency problem. In case of serious external shocks, however, a balance must be struck between commitment to monetary stability and flexibility. This is possible in a democracy, where elected policy-makers are able to provide the necessary political counterweight to the central bank's technocrats; this is impossible in the EU, where the European Central Bank (ECB) operates in a political vacuum. In turn, exclusive commitment to monetary stability further undermines the legitimacy of the Union. At present it seems that the only feasible way of reducing the democratic deficit is to reduce the mismatch between the extensive commitments of the EU and its limited normative and institutional resources.

Incorporating rigidity and commitment in the timing structure of macroeconomic games

This paper proposes a novel framework that generalizes the timing structure of games. Building on alternating move games and models of rational inattention, the players' actions may be rigid, i.e., infrequent. This rigidity in the timing of moves makes the game more dynamic and asynchronous, acting as a commitment mechanism. Therefore, it can enhance cooperation and often eliminate inefficient equilibrium outcomes present in the static (normal form) game. Interestingly, (i) this can happen even in a finite game (possibly as short as two periods) and (ii) without reputation building. Furthermore, (iii) the required degree of commitment may be under some circumstances arbitrarily low and under others infinitely high. Our main example comes from macroeconomics in which various rigidities have played a central role. Investigating the Kydland–Prescott–Barro–Gordon monetary policy game, we derive the necessary and sufficient degree of long-term policy commitment to low inflation under which the influential time-inconsistency problem is eliminated.

Why Stare Decisis?

All Courts rule ex-post, after most economic decisions are sunk. This might generate a time-inconsistency problem. From an ex-ante perspective, Courts will have the (ex-post) temptation to be excessively lenient. This observation is at the root of the principle of stare decisis. Stare decisis forces Courts to weigh the benefits of leniency towards the current parties against the beneficial effects that tougher decisions have on future ones. We study these dynamics and find that stare decisis guarantees that precedents evolve towards ex-ante efficient decisions, thus alleviating the Courts’ time-inconsistency problem. However, the dynamics do not converge to full efficiency.

Currency Substitution and Central Bank Independence in the Central and Eastern European Economies

This paper examines the extent to which the confrontation between the authorities implementing the monetary policy and the private agents asking for foreign currencies can influence the global process of currency substitution. The choice of an appropriate monetary policy depends on an original time-inconsistency problem where a partly-independent and conservative central bank is faced with a type of monetary targeting. The motives of the private agents in asking for foreign currencies are precautionary and/or speculative. We obtain the optimal growth of the aggregate in foreign currencies, which negatively depends on transparency, central bank credibility and inflation instability of the economy linked with the currency, and positively on inflation instability of the domestic economy. Then, we propose different measures of these determinants and we econometrically test this optimum in the economies of Central and Eastern Europe. The results are consistent with empirical literature on the macroeconomic determinants of dollarization. However, in this paper, the complexity of currency substitution is better illustrated and an empirical approach in relation to the institutional determinants of currency substitution is provided.

PRICE‐LEVEL TARGETING AND STABILISATION POLICY: A SURVEY

Abstract This paper surveys recent articles on the costs and benefits of price‐level targeting, focusing its use as a tool for stabilisation policy. It discusses how price‐level targeting can affect the short‐run trade‐off between output and inflation variability by influencing inflation expectations. It reviews how assigning an explicit price‐level target to a central bank that is unable to commit to its future policies can improve economic performance. It surveys other potential benefits and costs. Among the costs, it underlines the importance of perfectly rational expectations for the optimality of price‐level targeting, and an exacerbation of the time inconsistency problem.

Divestment, Entrepreneurial Incentives, and the Life Cycle of the Firm

An entrepreneur who wants to divest his firm suffers a time-inconsistency problem: divesting a stake creates an incentive to divest further since he does not internalize the arising agency costs for the stake already sold. This paper shows that this leads to excessive divestment in equilibrium and entails efficiency losses which can offset any potential divestment gains. As a result, firms may stay private even if there are large gains from going public. We show that venture capitalists can reduce these inefficiencies. This is because they have influence over a firm's divestment decisions and can distinguish between an excessive and a desirable dilution of equity (such as in response to liquidity shocks). We also show that the divestment inefficiency gives rise to an optimal time of going public, which trades off the gains from going public early (higher divestment gains) with its costs (higher divestment inefficiency).