customer base analysis partial defection of behaviourally loyal clients in a non contractual fmcg retail setting customer relationship management crm enjoys increasing attention as a countermeasure to switching behaviour of customers because foregone profits of partially defected customers can be significant an increase of the retention rate can be very profitable in this paper we focus on the treatment of a company s most behaviourally loyal customers in a non contractual setting we build a model in order to predict partial defection by behaviourally loyal clients using three classification techniques logistic regression automatic relevance determination ard neural networks and random forests focusing on partial attrition of high frequency shoppers who exhibit a regular visit pattern may overcome the problem of unidentifiability of total defection in non contractual settings classification accuracy pcc and area under the receiver operating characteristic curve auc are used to evaluate classifier performance on a test hold out sample using real life data from an fmcg retailer we show that future partial defection can be successfully predicted i e exceeding the benchmark hurdle of the null model there are no significant differences in terms of performance among alternative classification techniques similar to direct marketing applications we find that past behavioural variables more specifically rfm variables recency frequency and monetary value are the best predictors of partial customer defection this set of variables complements demographic variables confirming findings by other authors about its importance in predicting churn behaviour moreover additional variables listed in decreasing order of importance such as the length of customer relationship mode of payment buying behaviour across categories usage of promotions and brand purchase behaviour are shown to be moderately useful to incorporate in attrition models

uniqueness of steady states in models with overlapping generations in this paper we examine the likelihood of multiple real steady states in deterministic exchange economies with overlapping generations there is a single good and a single agent per generation with constant relative risk aversion expected utility in order to test for multiple equilibria we employ methods from computational algebraic geometry in our examples we find that multiplicity becomes less likely as the life span of agents increases but becomes more likely as the coefficient of risk aversion increases for moderate values of risk aversion multiplicity is very unlikely when agents live for five or more periods jel c61 c63 d50 d58

earnings instability and earnings inequality of males in the united states 1967 1991 although much research has focused on recent increases in annual earnings inequality in the united states the increases could have come from either of two sources the distribution of lifetime earnings could have become more unequal or the receipt of lifetime earnings could have become more unstable based on an analysis of the 1968 92 panel study of income dynamics we find that lifetime earnings inequality increased during the early 1980s and that earnings instability increased during the 1970s we also examine how these trends are related to changes in the distribution of wages and hours and the returns to education

tax reform and automatic stabilization an income tax provides implicit insurance by dampening the variability of disposable income and consumption using an empirical framework derived from the consumption insurance literature and data from the panel study of income dynamics we examine the effect of federal income tax reforms of the 1980 s on automatic stabilization of consumption overall erta and tra86 reduced consumption stability by about 50 percent recently increased eitc generosity restored or enhanced consumption insurance the welfare cost of moving to the post tra86 system is sizable for relatively risk averse households facing large income risk but is much more modest for the typical household jel h21

verifying competitive equilibria in dynamic economies in this paper i examine e equilibria of stationary dynamic economies with heterogeneous agents and possibly incomplete financial markets i give a simple example to show that even for arbitrarily small e 0 allocation and prices can be far away from exact equilibrium allocations and prices that is errors in market clearing or individuals optimality conditions do not provide enough information to assess the quality of an approximation i derive a sufficient condition for an e equilibrium to be close to an exact equilibrium if the economic fundamentals are semi algebraic one can verify computationally whether this condition holds the condition can be interpreted economically as a robustness requirement on the set of e equilibria which form a neighbourhood of the computed approximation i illustrate the main result and the computational method using an infinite horizon economy with overlapping generations and incomplete financial markets copyright 2011 oxford university press

approximate versus exact equilibria in dynamic economies this paper develops theoretical foundations for an error analysis of approximate equilibria in dynamic stochastic general equilibrium models with heterogeneous agents and incomplete financial markets while there are several algorithms that compute prices and allocations for which agents first order conditions are approximately satisfied approximate equilibria there are few results on h interpret the errors in these candidate solutions and how to relate the computed allocations and prices to exact equilibrium allocations and prices we give a simple example to illustrate that approximate equilibria might be very far from exact equilibria we then interpret approximate equilibria as equilibria for close by economies that is for economies with close by individual endowments and preferences

a note on an integrated model of customer buying behavior abstract we propose a simple benchmark model for the integrated stochastic model of buying behavior developed in the article counting your customers compounding customer s in store decisions interpurchase time and repurchasing behavior eur j oper res 127 1 2000 109 119 re examining the previously analyzed data covering the purchasing of tea we find that the new benchmark model which involves merely three parameters and can be estimated entirely within a standard spreadsheet environment outperforms the original integrated model and provides clearer more complete answers to the managerial questions posed at the outset of the earlier paper

trends in the transitory variance of male earnings methods and evidence we estimate the trend in the transitory variance of male earnings in the united states using the michigan panel study of income dynamics from 1970 to 2004 using an error components model and simpler but only approximate methods we find that the transitory variance started to increase in the early 1970s continued to increase through the mid 1980s and then remained at this new higher level through the 1990s and beyond thus the increase mostly occurred about 30 years ago its increase accounts for between 31 and 49 percent of the total rise in cross sectional variance depending on the time period

stationary sunspot equilibria in a finance constrained economy abstract stationary sunspot equilibria are shown to exist in a production economy with infinite lived agents when it is not possible to borrow against future wage income equilibrium fluctuations exhibit persistence over time scales of the same order of magnitude as observed business cycles an active fiscal policy that stabilizes aggregate money expenditures can prevent such fluctuations

determinacy of equilibrium in stationary economies with both finite and infinite lived consumers abstract we consider the determinacy of perfect foresight equilibrium near steady state equilibria of stationary infinite horizon economies the work of t j kehoe and d k levine econometrica 53 1985 433 453 is generalized by the inclusion of both infinite lived agents and overlapping generations of finite lived agents and the inclusion of production and non depreciating pure rents we show that indeterminacy is possible in robust examples and that the dimension of the indeterminacy can be as large as the number of goods per period we also discuss extreme cases in which determinacy is guaranteed

decision making under uncertainty capturing dynamic brand choice processes in turbulent consumer goods markets we construct two models of the behavior of consumers in an environment where there is uncertainty about brand attributes in our models both usage experience and advertising exposure give consumers noisy signals about brand attributes consumers use these signals to update their expectations of brand attributes in a bayesian manner the two models are 1 a dynamic model with immediate utility maximization and 2 a dynamic forward looking model in which consumers maximize the expected present value of utility over a planning horizon given this theoretical framework we derive from the bayesian learning framework how brand choice probabilities depend on past usage experience and advertising exposures we then form likelihood functions for the models and estimate them on nielsen scanner data for detergent we find that the functional forms for experience and advertising effects that we derive from the bayesian learning framework fit the data very well relative to flexible ad hoc functional forms such as exponential smoothing and also perform better at out of sample prediction another finding is that in the context of consumer learning of product attributes although the forward looking model fits the data statistically better at conventional significance levels both models produce similar parameter estimates and policy implications our estimates indicate that consumers are risk averse with respect to variation in brand attributes which discourages them from buying unfamiliar brands using the estimated behavioral models we perform various scenario evaluations to find how changes in marketing strategy affect brand choice both in the short and long run a key finding obtained from the policy experiments is that advertising intensity has only weak short run effects but a strong cumulative effect in the long run the substantive content of the paper is potentially of interest to academics in marketing economics and decision sciences as well as product managers marketing research managers and analysts interested in studying the effectiveness of marketing mix strategies our paper will be of particular interest to those interested in the long run effects of advertising note that our estimation strategy requires us to specify explicit behavioral models of consumer choice behavior derive the implied relationships among choice probabilities past purchases and marketing mix variables and then estimate the behavioral parameters of each model such an estimation strategy is referred to as structural estimation and econometric models that are based explicitly on the consumer s maximization problem and whose parameters are parameters of the consumers utility functions or of their constraints are referred to as structural models a key benefit of the structural approach is its potential usefulness for policy evaluation the parameters of structural models are invariant to policy that is they do not change due to a change in the policy in contrast the parameters of reduced form brand choice models are in general functions of marketing strategy variables e g consumer response to price may depend on pricing policy as a result the predictions of reduced form models for the outcomes of policy experiments may be unreliable because in making the prediction one must assume that the model parameters are unaffected by the policy change since the agents in our models choose among many alternative brands their choice probabilities take the form of higher order integrals we employ monte carlo methods to approximate these integrals and estimate our models using simulated maximum likelihood estimation of the dynamic forward looking model also requires that a dynamic programming problem be solved in order to form the likelihood function for this we use a new approximation method based on simulation and interpolation techniques these estimation techniques may be of interest to researchers and policy makers in many fields where dynamic choice among discrete alternatives is important such as marketing decision sciences labor and health economics and industrial organization

technical note aggregating individual purchases to the household level household level panel data are the input for many types of marketing studies an interesting but until now unaddressed question is what is the effect of aggregating individual members purchases to the household level under standard assumptions the answer is unambiguous the household brand switching pattern looks more zero order than the typical individual family member s behavior when the standard assumptions are relaxed the overall spirit of the results do not change these conclusions give comfort to those who use brand switching data to partition product categories those looking for variety seeking behavior from household data are given some cause for concern as well as reasons for reinterpreting previous studies

dynamic competitive economies with complete markets and collateral constraints in this article we examine the competitive equilibria of a dynamic stochastic economy with complete markets and collateral constraints we show that provided the sets of asset pay offs and of collateral levels are sufficiently rich the equilibrium allocations with sequential trades and collateral constraints are equivalent to those obtained in arrow debreu markets subject to a series of limited pledgeability constraints we provide both necessary and sufficient conditions for equilibria to be pareto efficient and show that when collateral is scarce equilibria are not only pareto inefficient but also often constrained inefficient in the sense that imposing tighter borrowing restrictions can make everybody in the economy better off we derive sufficient conditions for the existence of markov equilibria and for the case of two agents for the existence of equilibria that have finite support these equilibria can be computed with arbitrary accuracy and the model is very tractable

an investigation into the order of the brand choice process this paper investigates the order of the brand choice process at the individual family level using a variety of tests t likelihood ratio binomial runs and multinomial runs tests the test of stationarity developed permits separate analyses for stationary and nonstationary purchase sequences our analyses indicate that the purchase sequences of a majority of stationary consumers are consistent with the zero order assumption this result is observed for all the nine frequently bought packaged goods studied with the use of panel data and for a product category soft drinks using experimental data

a multivariate polya model of brand choice and purchase incidence in this paper we develop an integrated stochastic model of purchase timing and brand selection which incorporates the influence of marketing mix variables seasonality and trend and also allows for various individual choice mechanisms our approach rests on the assumptions of a zero order choice process a poisson timing process and purchase rates following a multivariate gamma distribution over the population the scale parameters of which vary according to marketing activities and time the resulting model is a multivariate polya process and the distribution of brand choice probabilities turns out to be a generalized dirichlet distribution thus most currently used zero order models can be considered to be special cases of this approach furthermore we derive a number of market diagnostics which provide insights into market structure and demonstrate the model s use for marketing strategy simulation based on extensive testing of the underlying hypotheses we finally validate the model using empirical data and show that it fits the market in question

income instability and fiscal progression we construct the ratio of the post fisc transitory income variance to the pre fisc transitory income variance of family incomes as a measure of fiscal progressivity in canada between 1993 and 2008 this ratio can be interpreted as measuring the extent to which the fiscal system attenuates personal income instability we find that the tax and transfer system has been less eective in stabilizing market incomes after 1998 compared to the previous years this is attributable to the provincial and federal tax reforms from 1999 2001 which particularly aected families headed by individuals with less than high school education while the reforms reduced the eective marginal tax rates faced across all educational groups the reduction is relatively larger among families with highly educated main earners moreover the group with less than high school education is distinct in that the average eective tax burden in this group increased changes to social assistance also appear to have played a role

the economics of indeterminacy in overlapping generations models abstract recent research indicates that there are robust examples of overlapping generations economies in which there are indeterminate equilibria without fiat money and equilibria with more than one dimension of indeterminacy this paper presents simple examples of a stationary pure exchange overlapping generations economy with one good in each period and a representative consumer who lives for three periods in each generation these examples exhibit every possible form of indeterminacy and instability furthermore the parameters of the principal example agree with empirical evidence we use our examples as case studies for analyzing the problems involved in computing the equilibria of such economies

trends in men s earnings volatility what does the panel study of income dynamics show abstract many recent studies have investigated trends in u s men s earnings volatility but the studies based on the panel study of income dynamics appear to conflict with each other and with studies based on other data we critique some of the existing methods of measuring earnings volatility and we advocate for transparent methods that focus on simple measures of dispersion in year to year earnings changes applying such measures in the psid we find that apart from the well known counter cyclicality of earnings volatility men s earnings volatility increased during the 1970s but did not show a clear trend afterwards until a new upward trend appeared after 1998

consumption savings decisions with quasi geometric discounting we study the consumption savings problem of an infinitely lived rational consumer who has time inconsistent preferences in the form of quasi geometric discounting the consumer operates a weakly concave production function and must simply divide current resources into current consumption and savings there is no uncertainty a solution to the consumer s problem is a subgame perfect equilibrium of a dynamic game between the consumer s successive selves we show that this game has a continuum of equilibria in stationary markov strategies not only is the stationary point of the consumer s asset holdings indeterminate but each stationary point has a continuum of dynamic paths converging to it the savings policy rules underlying these dynamic paths are step functions

labor income dynamics and the insurance from taxes transfers and the family article i nfo what do labor income dynamics look like over the life cycle what is the relative importance of persistent shocks transitoryshocksandheterogeneousprofiles to what extent dotaxes transfers and thefamilyattenuate these various factors in the evolution of life cycle inequality in this paper we use rich norwegian population panel data to answer these important questions we let individuals with different education levels have a sepa rate income process and within each skill group we allow for non stationarity in age and time heterogeneous experience profiles and shocksof varying persistence we findthattheincomeprocesses differ systematically by age skill level and their interaction to accurately describe labor income dynamics over the life cycle it is neces sary toallow for heterogeneity by education levelsand account for non stationarity inage and time our findings suggest that the redistributive nature of the norwegian tax transfer system plays a key role in attenuating the magnitude and persistence of income shocks especially among the low skilled by comparison spouse s income matters less for the dynamics of inequality over the life cycle

estimating the impact of consumer expectations of coupons on purchase behavior a dynamic structural model we examine the basic premise that consumers may anticipate future promotions and adjust their purchase behavior accordingly we develop a structural model of households who make purchase decisions to minimize their expenditure over a finite period the model allows for future expectations of promotions to enter the purchase decision households with adequate inventory of the product may face a trade off of buying in the current period with a coupon or defer the purchase until next period given their expectations of future promotions thus we provide a framework for examining the impact of consumer expectations on choice behavior the target audiences for our paper are a empirical researchers who intend to make structural models part of their applied research agenda and b managers who value and seek to understand the impact of consumers coupon expectations on current purchase behavior our research objective is to provide an empirical framework to examine whether and to what extent consumers anticipate future coupon promotions and adjust purchase behavior the central premise of our approach is that a rational consumer minimizes the present discounted value of the cost of a purchase where cost in a single period consists of purchase price inventory holding cost gains from coupons and potential stockout cost we aim to test whether our hypotheses regarding the various elements of the cost structure are supported and that whether consumers take into account future discounted cost when making current purchase decisions the research methodology we adopt is relatively new in econometrics and known as the estimable stochastic structural dynamic programming method the methodology amounts to incorporating a maximum likelihood routine embedded in a dynamic programming problem the dynamic programming problem is solved several times within a maximum likelihood iteration for each value of the state space elements and for each value of the parameters in the parameter set the state space in our model consists of purchase and nonpurchase alternatives in each time period coupon availability and no coupon availability in each time period level of inventory in each time period for each household and consumption rate of each household we use scanner panel data on purchases in the disposable diaper product category and promotions we estimate the inventory holding and stockout costs brand specific value of coupons and consumers expectations of future coupons the key insights and lessons learned can be summarized as follows 1 our results are consistent with the notion that consumers hold beliefs about future coupons and that such beliefs affect the purchase decision we find that the dynamic optimization model performs significantly better than a single period optimization model and a naive benchmark model 2 we find a high and significant stockout cost consistent with the essential nature of the product category our estimate of the holding cost yields a reasonable annualized percentage value when converted to the cost of capital we find that consumer valuation of coupons differ markedly across brands 3 our empirical evidence supports the notion that consumers hold beliefs about future coupon availability we also find that the expectations about future coupons estimated endogenously differ depending upon whether or not a coupon was available in the current period thus the proposed model structure yields rich managerial insights and facilitates several what if scenarios a possible limitation of our model and estimable structural models in general is the computational cost while it is possible to conceptually extend the state space to accommodate variations across households and add a richer parameter structure each addition multiplies the size of the state space and the computation time for this reason we have kept the state space as tight as possible and refrained from additions that would otherwise enable us to incorporate heterogeneity in consumer decisions for example we assumed that consumers are similar other than reflected by their purchase behavior we built a category purchase incidence model rather than a brand choice model we refrained from including unobserved heterogeneity in the parameters we chose to opt out of modeling autocorrelation and other time dependent error term patterns in the likelihood function thus we have made an effort to build a structural model that reasonably reflects consumer purchase behavior without requiring expensive computation currently there are developments in econometrics to approximate the computation of the valuation functions without sacrificing much accuracy when these methods are well developed we expect that structural models will become more commonplace in marketing

a theory of top income taxation and social insurance the development of the welfare state in the western economies between 1930 and 1990 coincided with a puzzling pattern in the taxation of top incomes eective tax rates at the top increased sharply but then gradually decreased even as social transfers continued rising we propose a new theory of the development of the welfare state to explain these facts our main insight is that social insurance and top income taxation are substitutes for averting social con ict we emphasize the role of the great depres sion as a source of aggregate risk and argue that the rise of the welfare state can be understood as a process of exploiting e ciency gains in response to gradual technolog ical improvements in the provision of social insurance our detailed arguments build on the policy histories of the united states great britain and sweden

earnings dynamics and inequality among canadian men 1976 1992 evidence from longitudinal income tax records using an extraordinary database drawn from longitudinal income tax records we decompose canada s growth in earnings inequality into its persistent and transitory components we find that the growth in earnings inequality reflects both an increase in long run inequality and an increase in earnings instability the canadian data strongly reject several restrictions commonly imposed in the u s literature and they also suggest that imposing these evidently false restrictions may lead to distorted inferences about earnings dynamics and inequality trends

recursive equilibrium in stochastic overlapping generations economies we prove the generic existence of a recursive equilibrium for overlapping generations economies with uncertainty generic here means in a residual set of utilities and endowments the result holds provided there is a sufficient number of potentially different individuals within each cohort

counting your customers compounding customer s in store decisions interpurchase time and repurchasing behavior abstract consumer buying decision is an important element of any company s efforts to count its customers stochastic models have been used extensively in previous studies of marketing and are usually constructed so as to easily fit the data and make predictions however the regularity of customer interpurchase time in store decisions and repeat buying behavior are not considered simultaneously in the literature since the empirical evidence suggests that all the above factors do indeed influence the firm s sales we here present a methodology which takes all these elements into account the methodology employed is illustrated by taking the customer purchase data for tea as an example by not eliminating light buyers the integrated model we developed achieves precise results and addresses the relative importance of each element while predicting firm sales

life cycle economies and aggregate fluctuations do the implications for business cycle issues change when we switch from studying infinitely lived representative agent models to more sophisticated demographic structures with finitely lived agents this article addresses that question by using a large overlapping generations model that is calibrated to u s demographic properties microeconomic evidence and national income and product accounts the finding is that the answers obtained are basically the same for the two kinds of models the article also explores the relative volatility of hours across age groups an issue that cannot be addressed by using the infinitely lived representative agent abstraction