Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

The network origins of aggregate fluctuations

This paper argues that in the presence of intersectoral input-output linkages, microeconomicidiosyncratic shocks may lead to aggregate fluctuations. In particular, itshows that, as the economy becomes more disaggregated, the rate at which aggregatevolatility decays is determined by the structure of the network capturing such linkages.Our main results provide a characterization of this relationship in terms of the importanceof different sectors as suppliers to their immediate customers as well as theirrole as indirect suppliers to chains of downstream sectors. Such higher-order interconnectionscapture the possibility of "cascade effects" whereby productivity shocks to asector propagate not only to its immediate downstream customers, but also indirectlyto the rest of the economy. Our results highlight that sizable aggregate volatility isobtained from sectoral idiosyncratic shocks only if there exists significant asymmetryin the roles that sectors play as suppliers to others, and that the "sparseness" of theinput-output matrix is unrelated to the nature of aggregate fluctuations.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Market versus limit orders in an imperfectly competitive security

This paper analyzes the choice between limit and market orders in animperfectly competitive noisy rational expectations economy. There is a uniqueinsider, who takes into account the effect their trading has on prices. If theinsider behaves as a price taker, she will choose market orders if her privateinformation is very precise and she will choose limit orders otherwise. On thecontrary, if the insider recognizes and exploits her ability to affect themarket price, her optimal choice is to place limit orders whatever the precisionof her private information.

Aggregate fluctuations and the network structure of intersectoral trade

This paper analyzes the flow of intermediate inputs across sectors by adopting a network perspective on sectoral interactions. I apply these tools to show how fluctuationsin aggregate economic activity can be obtained from independent shocks to individualsectors. First, I characterize the network structure of input trade in the U.S. On thedemand side, a typical sector relies on a small number of key inputs and sectors arehomogeneous in this respect. However, in their role as input-suppliers sectors do differ:many specialized input suppliers coexist alongside general purpose sectors functioningas hubs to the economy. I then develop a model of intersectoral linkages that can reproduce these connectivity features. In a standard multisector setup, I use this modelto provide analytical expressions linking aggregate volatility to the network structureof input trade. I show that the presence of sectoral hubs - by coupling productiondecisions across sectors - leads to fluctuations in aggregates.

Social security, retirement, and the single-mindedness of the electorate

We propose a positive theory that is consistent with two important featuresof social security programs around the world: (1) they redistributeincome from young to old and (2) they induce retirement. We construct avoting model that includes a political campaign or debate prior to theelection. The model incorporates single-mindedness of the groups that donot work: while the workers divide their political capital between their age concerns and occupational concerns , the retired concentrate alltheir political capital to support their age group. In our model, theelderly end up getting transfers from the government (paid by the young)and distortionary labor income taxes induce the retirement of the elderly.In addition, our model predicts that occupational groups that work morewill tend to have more political power. The opposite is true fornon-occupational groups (such as the elderly). We provide some evidencethat supports these additional predictions.

Social security in theory and practice (II): Efficiency theories, narrative theories and implications for reform

166 countries have some kind of public old age pension. What economic forcescreate and sustain old age Social Security as a public program? Mulligan and Sala-i-Martin (1999b) document several of the internationally and historically common features of social security programs, and explore "political" theories of Social Security. This paper discusses the "efficiency theories", which view creation of the SS program as a full of partial solution to some market failure. Efficiency explanations of social security include the "SS as welfare for the elderly" the "retirement increases productivity to optimally manage human capital externalities", "optimal retirement insurance", the "prodigal father problem", the "misguided Keynesian", the "optimal longevity insurance", the "governmenteconomizing transaction costs", and the "return on human capital investment". We also analyze four "narrative" theories of social security: the "chain letter theory", the "lump of labor theory", the "monopoly capitalism theory", and the "Sub-but-Nearly-Optimal policy response to private pensions theory".The political and efficiency explanations are compared with the international and historical facts and used to derive implications for replacing the typical pay-as-you-go system with a forced savings plan. Most of the explanations suggest that forced savings does not increase welfare, and may decrease it.

An analysis of the accounting principles applied by the European Farm Accountancy Data Network

In spite of its relative importance in the economy of many countriesand its growing interrelationships with other sectors, agriculture has traditionally been excluded from accounting standards. Nevertheless, to support its Common Agricultural Policy, for years the European Commission has been making an effort to obtain standardized information on the financial performance and condition of farms. Through the Farm Accountancy Data Network (FADN), every year data are gathered from a rotating sample of 60.000 professional farms across all member states. FADN data collection is not structured as an accounting cycle but as an extensive questionnaire. This questionnaire refers to assets, liabilities, revenues and expenses, and seems to try to obtain a "true and fair view" of the financial performance and condition of the farms it surveys. However, the definitions used in the questionnaire and the way data is aggregated often appear flawed from an accounting perspective. The objective of this paper is to contrast the accounting principles implicit in the FADN questionnaire with generally accepted accounting principles, particularly those found in the IVth Directive of the European Union, on the one hand, and those recently proposed by the International Accounting Standards Committee’s Steering Committeeon Agriculture in its Draft Statement of Principles, on the other hand. There are two reasons why this is useful. First, it allows to make suggestions how the information provided by FADN could be more in accordance with the accepted accounting framework, and become a more valuable tool for policy makers, farmers, and other stakeholders. Second, it helps assessing the suitability of FADN to become the starting point for a European accounting standard on agriculture.

Social security and democracy

Many political economic theories use and emphasize the process of votingin their explanation of the growth of Social Security, governmentspending, and other public policies. But is there an empirical connectionbetween democracy and Social Security program size or design? Using somenew international data sets to produce both country-panel econometricestimates as well as case studies of South American and southern Europeancountries, we find that Social Security policy varies according toeconomic and demographic factors, but that very different politicalhistories can result in the same Social Security policy. We find littlepartial effect of democracy on the size of Social Security budgets, onhow those budgets are allocated, or how economic and demographic factorsaffect Social Security. If there is any observed difference, democraciesspend a little less of their GDP on Social Security, grow their budgetsa bit more slowly, and cap their payroll tax more often, than doeconomically and demographically similar nondemocracies. Democracies andnondemocracies are equally likely to have benefit formulas inducingretirement and, conditional on GDP per capita, equally likely to induceretirement with a retirement test vs. an earnings test.

What social security: Beveridgean or Bismarckian?

Why are Bismarckian social security systems associated with largerpublic pension expenditures, a smaller fraction of private pension andlower income in-equality than Beveridgean systems? These facts arepuzzling for political economy theories of social security whichpredict that Beveridgean systems, involving intra-generationalredistribution, should enjoy larger support among low-income people andthus be larger. This paper explains these features in a bidimensionalpolitical economy model. In an economy with three income groups,low-income support a large, redistributive system; middle-income favoran earning-related system, while high-income oppose any public system,since they have access to a superior saving technology, a privatesystem. We show that, if income inequality is large, the voting majorityof high-income and low-income supports a (small) Beveridgean system,and a large private pillar arises; the opposite occurs with lowinequality. Additionally, when the capital market provides higherreturns, a Beveridgean system is more likely to emerge.

The P-median problem in a changing network: The case of Barcelona

In this paper a p--median--like model is formulated to address theissue of locating new facilities when there is uncertainty. Severalpossible future scenarios with respect to demand and/or the travel times/distanceparameters are presented. The planner will want a strategy of positioning thatwill do as ``well as possible'' over the future scenarios. This paper presents a discrete location model formulation to address this P--Medianproblem under uncertainty. The model is applied to the location of firestations in Barcelona.

Is altruism important for understanding the long-run effects of social security?

This paper quantifies the effects of social security on capital accumulation and wealth distribution in a life cycle framework with altruistic individuals. The main findings of this paper are that the current U.S. social security system has a significant impact on capital accumulation and wealth distribution. I find that social security crowds out 8\% of the capital stock of an economy without social security. This effect is driven by the distortions of labor supply due to the taxation of labor income rather than by the intergenerational redistribution of income imposed by the social security system. In contrast to previous analysis of social security, I found that social security does not affect the savings rate of the economy. Another interesting finding is that even though the current U.S. social security system is progressive in its benefits, it may lead to a more disperse distribution of wealth.

Assessing an intuitive condition for stability under a range of traffic conditions via a generalised Lu-Kumar network

We argue the importance both of developing simple sufficientconditions for the stability of general multiclass queueing networks and also of assessing such conditions under a range of assumptions on the weight of the traffic flowing between service stations. To achieve the former, we review a peak-rate stability condition and extend its range of application and for the latter, we introduce a generalisation of the Lu-Kumar network on which the stability condition may be tested for a range of traffic configurations. The peak-rate condition is close to exact when the between-station traffic is light, but degrades as this traffic increases.