Sources Of State Dependence Research Articles

Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems

<abstract><p>In this paper, we study the well-established quasi-boundary value methods for regularizing inverse state-dependent source problems, where the convergence analysis of three typical cases is presented in the framework of filtering regularization method under suitable source conditions. Interestingly, the quasi-boundary value methods can be interpreted as certain Lavrentiev-type regularization, which was not known in literature. As another major contribution, efficient numerical implementation based on matrix exponential in time is developed, which shows much improved computational efficiency than MATLAB's backslash solver based on the all-at-once space-time discretization scheme. Numerical examples are reported to illustrate the promising computational performance of our proposed algorithms based on matrix exponential techniques.</p></abstract>

The inverse problem of reconstructing reaction–diffusion systems

This paper considers the inverse problem of recovering state-dependent source terms in a reaction–diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a time trace of their values at a fixed point on the boundary of the spatial domain. We show both uniqueness results and the convergence of an iteration scheme designed to recover these sources. This leads to a reconstructive method and we shall demonstrate its effectiveness by several illustrative examples.

Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion

ABSTRACTIt is investigated the role of the state–dependent source–term for the localization by means of the kinetic energy of radially symmetric states for the stationary p–Laplace diffusion. It is shown that the oscillatory behavior of the source–term, with respect to the state amplitude, yields multiple possible states, located in disjoint energy bands. The mathematical analysis makes use of critical point theory in conical shells and of a version of Pucci–Serrin three–critical point theorem for the intersection of a cone with a ball. A key ingredient is a Harnack type inequality in terms of the energetic norm.

Persistence of innovation: Discriminating between types of innovation and sources of state dependence

This paper advances current research on the persistence of innovation drawing on a panel data set constructed from three waves of the German part of the Community Innovation Survey covering the time span from 2002 to 2008 (i.e., CIS IV, CIS 2007, and CIS 2009). We explore persistence patterns for various types of innovation (i.e., organizational, product and process innovation) and allowing for the moderating impact of firm-level characteristics. We use the ascertained patterns of persistence to comparatively evaluate various sources (and underlying theoretical accounts) of state dependence.

Unemployment persistence: not only stigma but discouragement too

This article shows how stigma effects and discouragement counterbalance as sources of state dependence in unemployment throughout the business cycle.

Life Cycle Employment and Fertility Across Institutional Environments

In this paper, we formulate a dynamic utility maximization model of female labor force participation and fertility choices and estimate approximate decision rules using data on married women in Italy, Spain and France. The pattern of estimated state dependence effects across countries is consistent with aggregate patterns in part-time employment and child care availability, suggesting that labor market rigidities and lack of child care options are important sources of state dependence. Simulations of the model reveal that Italian and Spanish women would substantially increase their participation rates were they to face the French institutional environment.

Modeling Multiple Sources of State Dependence in Random Utility Models: A Distributed Lag Approach

We propose a utility-theoretic brand-choice model that accounts for four different sources of state dependence: 1. effects of lagged choices (structural state dependence), 2. effects of serially correlated error terms in the random utility function (habit persistence type 1), 3. effects of serial correlations between utility-maximizing alternatives on successive purchase occasions of a household (habit persistence type 2), and 4. effects of lagged marketing variables (carryover effects). Our proposed model also allows habit persistence to be a function of lagged marketing variables, while accommodating the effects of unobserved heterogeneity in household choice parameters. This model is more flexible than existing state-dependence models in marketing and labor econometrics. Using scanner panel data, we find structural state dependence to be the most important source of state dependence. Marketing-mix elasticities are systematically understated if state-dependence effects are incompletely accounted for. The Seetharaman and Chintagunta (1998) model is shown to recover spurious variety-seeking effects while overstating habit-persistence effects. Ignoring habit persistence type 1 leads to an underestimation, while ignoring habit persistence type 2 leads to an overestimation of structural state-dependence effects. We find lagged promotions to have carryover effects on habit persistence. Ignoring one or more sources of state dependence underestimates the total incremental impact of a sales promotion. We draw implications for manufacturer pricing.

The Asymmetric Information Model of State Dependence

Marketing researchers and practitioners are interested in consumer loyalty because of its managerial consequences. Previous empirical studies find that consumers are loyal not only to a brand, but also to a firm (umbrella brand). That is, even when firms offer new products, consumers tend to continue to purchase from the same firm. This repeat-purchase behavior might result from state dependence or from heterogeneity. The meaning of state dependence is that the current choice behaviorally depends on the previous one. The traditional model of state dependence assumes that the previous choice affects the current utility. This study suggests another source of state dependence: The previous choice affects the current information set. Specifically, the model assumes that the consumer (a) knows the attributes of the new product offered by the firm from which he/ she purchased in the previous period, (b) is uncertain about the attributes of the new products offered by the other firms, (c) can obtain full information about the attributes of all the products through a costly search, and (d) if the consumer decides not to search, he/she purchases the new product offered by the firm from which he/she purchases in the previous period. It is shown that state dependence can result either from the effect of previous choices on the current utility or from its effect on the current information set. This theoretical result raises the following question: What kind of data does a researcher need in order to distinguish between the two sources of state dependence? This study shows that the two sources can be distinguished with a standard panel data set. In other words, although the new source of state dependence is based on the search activity of consumers, there is an identifying factor that enables a researcher to detect such activity even without direct data on search. The empirical distinction is possible because the behavioral implications of the two sources of state dependence are different. They differ in the effect of product attributes on the repeat-purchase probability. The following example partially illustrates this result: There are two firms A and B; the consumer purchased a product from firm A in period t – 1; the only product attribute is x; and the utility is a linear function of x. One aspect of our findings is that in the traditional model of state dependence a change in both xA and xB that leaves the difference between them, (xA – xB), unchanged (neutral change, hereinafter) has no effect on the repeat-purchase probability. However, such a change does affect the repeat-purchase probability in the asymmetric information model of state dependence. This is only one aspect of the finding—the implications of the models differ in a more general fashion. The intuition of this result is the following. A neutral change has no effect on the repeat-purchase probability in the traditional model of state dependence, because it does not affect the difference between the utilities from both alternatives. In the asymmetric model of state dependence the consumer's decision process consists of two stages. First, he decides whether to search for information about the other alternative or not. Then, if he searches for information, he chooses the alternative that maximizes his utility. In the second stage, a neutral change has no effect on choices, since such a change does not affect the difference between the utilities from the two alternatives. In the first stage, the consumer knows xA, but does not know xB. It turns out that in this stage a neutral change does affect the search decision. When, for example, both x's decrease and the utility is a positive function of x, the probability of search increases, and thus the repeat-purchase probability decreases. The proposed source of state dependence is examined using structural estimation and panel data on television viewing choices in the United States. Controlling for both observed and unobserved heterogeneity, it is found that the suggested source is more important in creating repeat-purchase than the traditional one for most of the population (71%). This indicates that what was considered by previous studies to result from the dependence of consumer utility on their previous choices is at least partially due to the effect of the previous choices on consumers' information set. The distinction between the two sources of repeat-purchase is important because ignoring the informational explanation may lead to incorrect theoretical and empirical conclusions. For example, price discounts to induce trial are more important for consumers whose utility depends on previous choices, while advertising is more effective for those whose information set depends on previous choices.

Active Versus Passive Loyalty: A Structural Model of Consideration Set Formation

We offer an econometric framework that models a consumer's choice decision as a two-stage process: set formation followed by selection from the brands in the The proposed structural model of set is motivated by the fact that consumers have limited information-acquisition ability. In the context of frequently purchased products (FPPs), since these product categories are characterized by frequent price promotion of varying depths of discount, a faces significant uncertainty about the net utilities associated with the different brands. Thus, while a might know the range of potential prices, she is unaware of the actual posted price of a on any given purchase occasion unless she engages in pre-evaluation price search. Since information acquisition is costly, she needs to first decide how many and which brands to search the posted prices of. In the proposed framework, the process of pre-evaluation price search is conceptualized as brand and the set of sampled brands is referred to as the consumer's consideration set. A distinctive feature of the proposed specification is that it allows us to distinguish between two sources of state dependence - viz., passive and active loyalty. In this conceptualization, passive loyalty refers to state dependence arising out of consumer lock-in as a result of high search cost. Thus, a passively loyal repeatedly buys the same over successive purchase occasions because her cost of searching the posted prices of other brands is very high i.e. her optimal set does not include any other brand. In contrast, active loyalty refers to state dependence arising out of a high intrinsic preference for the selected brand. Thus, while an actively loyal considers more than the selected on any purchase occasion (because her search costs are low), she nonetheless buys the same because of her high intrinsic preference for the brand. Our key theoretical results are as follows: (i) relative to low price sensitive consumers, high price sensitive consumers have larger sets; (ii) the intensity of search is higher in product categories characterized by greater price variability. Thus, more frequent price promotions with deep discounts lead to large sets; and, (iii) a does not stay in the state of inertia for long. In the case of a passively loyal consumer, we will observe phases of inertia followed by a switching that in turn is followed by another spell of inertia. We use scanner panel data for liquid detergents to empirically validate the model. The key empirical results are as follows: (i) there are significant search costs that consumers incur in discovering the actual posted prices of the brands at the store. This implies that consumers do not consider (i.e. search the posted prices of) all the brands on a shopping trip; (ii) in-store display activities and feature ads reduce search costs for a thereby significantly increasing the probability of the being considered. Feature advertising reduces the search costs more than in-store displays; (iii) prior consumption influence quality perception of a for both liquid detergents and ketchup categories. However, consumption experience yield only limited additional quality information; and, (iv) estimates of price sensitivity critically depend on whether the specification explicitly models stage. In particular, a model that assumes that consumers search all the brands on all purchase occasions seriously underestimates the impact of price on choice decision. We also conduct a limited cross-category analysis using ketchup data set and find several interesting differences in price search behavior across the two product categories analyzed.

Robust estimation of discrete hidden Markov model parameters using the entropy-based feature-parameter weighting and source-quantization modeling

We propose a new variant of the discrete hidden Markov model (DHMM) in which the output distribution is estimated by state-dependent source quantizing modeling and the output probability is weighted by the entropy of each feature-parameter at a state. The state-dependent source is represented as a state-dependent quantized vector which is regarded as a variant of a representative vector at a state and its own codeword distribution, and the output distribution is derived by these state-dependent sources which will exist at a state. In addition, entropy-based feature-parameter weighting is proposed to reflect the different importance of each feature-parameter in a state, and the fuzzy function is applied to transform an entropy value into a feature-parameter weighting factor. From experiments, we found that proposed methods have shown an improvement of 5.6%, which indicates the effectiveness of proposed models in the robust estimation of output probabilities for DHMMs.

Structural identification of an unknown source term in a heat equation

The identification of an unknown state-dependent source term in a reaction-diffusion equation is considered. Integral identities are derived which relate changes in the source term to corresponding changes in the measured output. The identities are used to show that the measured boundary output determines the source term uniquely in an appropriate function class and to show that a source term that minimizes an output least squares functional based on this measured output must also solve the inverse problem. The set of outputs generated by polygonal source functions is shown to be dense in the set of all admissible outputs. Results from some numerical experiments are discussed.