Lakshman Krishnamurthi

Briesch, Richard A, Lakshman Krishnamurthi, Tridib Mazumdar and S. J. Raj. 1997. A Comparative Analysis of Reference Price Models. Journal of Consumer Research. 24(2): 202-214.

The effect of reference price on brand choice decisions has been well documented in the literature. Researchers, however, have differed in their conceptualizations and, therefore, in their modeling of reference price. In this article, we evaluate five alternative models of reference price of which two are stimulus based (i.e, based on information available at the point-of-purchase) and three that are memory based (i.e., based on price history and/or other contextual factors). We calibrate the models using scanner panel data for peanut butter, liquid detergent, ground coffee, and tissue. To account for heterogeneity in model parameters, we employ a latent class approach and select the best segmentation scheme for each model. The best model of reference price is then selected on the basis of fit and prediction, as well as on the basis of parsimony in cases where the fits of the models are not very different. In all four categories, we find that the best reference price model is a memory-based model, namely, one that is based on the brand's own price history. In the liquid detergent category, however, we find that one of the stimulus-based models, namely, the current price of a previously chosen brand, also performs fairly well. We discuss the implications of these findings.

Krishnamurthi, Lakshman, S. J. Raj and K. Sivakumar. 1995. Unique Inter-Brand Effects of Price on Brand Choice. Journal of Business Research. 34(1): 47-56.

How do price changes by one brand affect the choice of competing brands? Such inter-brand effects may depend on the specific strategy followed by a firm. For example, a firm may target a particular brand to exploit its vulnerability or to avoid direct competition with other brands. Or a firm may design its pricing strategy aimed at reducing cannibalization of its own brands. Previous studies have utilized standard logit models to investigate inter-brand ejects. However, these models impose constraints on price elasticities as a consequence of independence of irrelevant alternatives (HA) assumptions. As a result, estimated own- and cross-elasticities reflect the restrictive assumptions of the model and may not provide an accurate description of the hinds of asymmetric competition among brands noted previously. Though existing market share models at the aggregate level do capture such competitive asymmetries, most disaggregate level logit choice models do not capture such asymmetries in a satisfactory manner. In this article a generalized logit (or mother logit) model is used to estimate unique interbrand response parameters to capture asymmetry. This methodology, drawn from the econometrics literature, overcomes the necessity of making a priori assumptions of competitive patterns and instead can be used to identify competitive patterns as they exist in the market place. In analyzing brand choice data from three product classes, ILA is violated in all three cases to varying degrees. The cross-price elasticities are used to draw managerial implications for brand and product line management.

Papatla, Purushottam and Lakshman Krishnamurthi. 1992. A Probit Model of Choice Dynamics. Marketing Science. 11(2): 189-206.

There are many products which are repeatedly purchased by consumers. In such cases it is likely that choice history, that is the sequence of choices made in the past, as well as marketing variables affect subsequent choice decisions. Attempts to model the effects of choice history have been generally based on the inclusion of variables that represent brand loyalty and/or variety seeking behavior. In this paper we present a model of dynamic choice behavior which is more general and incorporates four characteristics. The first characteristic labeled preference reinforcement and preference reduction represents loyalty and variety seeking. The second is the short-term reluctance of a consumer to move from the current brand (inertia) or the willingness to move to another brand (mobility). The third characteristic captures the effect of repetitive consumption (the long term effect) on inertia and mobility. The fourth characteristic incorporates the similarity or dissimilarity of choice alternatives. This is important in a dynamic model because choice on the current purchase occasion can be affected by whether a similar or dissimilar alternative was chosen on the previous occasion. Similarities of alternatives are represented in terms of distances. The effect of price on choice behavior is also modeled. Individual-level purchase data from a consumer panel are used to estimate a covariance probit and an independent probit specification of the model. From a substantive perspective the model gives interesting insights into the dynamics of choice behavior. The model predicts switches better than a benchmark model which incorporates only loyalty. In addition, it is superior to three benchmark models in overall predictive ability.

Krishnamurthi, Lakshman, Tridib Mazumdar and S. J. Raj. 1992. Asymmetric Response to Price in Consumer Brand Choice and Purchase Quantity Decisions. Journal of Consumer Research. 19(3): 387-400.

The study investigates whether consumers exhibit asymmetry (i.e., different sensitivity) to negative ("loss") and positive ("gain") differences between the reference price and the purchase price in brand choice and purchase quantity decisions. Using panel data for two frequently purchased products with three brands in each product category, we find that consumers loyal to a brand ("loyals") respond to gain and loss with the same sensitivity in brand choice decisions. However, consumers not loyal to any brand ("switchers") respond more strongly to gains than to losses. In purchase quantity decisions, brand-loyal consumers are found to respond asymmetrically to gains and losses, but the direction of the asymmetry depends on whether the decision is made before or after the household inventory reaches a stock-out level (i.e., the level at which the household inventory needs to be replenished). When the decision is made after a stock-out, brand-loyal consumers are more responsive to a gain in the price of their favorite brand than to a loss. In contrast, when the quantity decision is made before a stock-out, loyals are more sensitive to a loss than to a gain. In only two of the six brands examined do we find evidence of asymmetry in switchers' quantity decisions. In both cases, switchers respond more strongly to a price loss than to a gain, regardless of whether the purchase decision is made before or after a stock-out.

Krishnamurthi, Lakshman, Jack Narayan and S. J. Raj. 1989. Intervention Analysis Using Control Series and Exogenous Variables in a Transfer Function Model: A Case Study. International Journal of Forecasting. 5(1): 21-27.

This paper presents a case study to show how a control group can be used to obtain more accurate estimates of the impact of interventions. Intervention analysis using the ARIMA time series method is applied in an experimental design context using multiple input transfer function analysis. The study combines the analytic rigor of time series analysis with the careful controls provided by an experiment involving a test and control series. The data are from a field experiment with test and control panels connected to a split-cable TV system.

Krishnamurthi, Lakshman and S. J. Raj. 1988. A Model of Brand Choice and Purchase Quantity Price Sensitivities. Marketing Science. 7(1): 1-21.

Many consumer decisions involve a discrete choice and a continuous outcome. Examples of such decisions are whether to own a home or rent one and how much to spend, which brand of orange juice to buy and how many ounces to buy. In cases like these, the choice decision is typically modeled separately, say, using a logit model and the continuous outcomes modeled separately using regression analysis. However, the continuous outcomes may not be independent of the discrete choice and vice versa, and modeling the two decisions independently can lead to inefficient choice parameter estimates and biased and inconsistent regression parameter estimates. In this paper, we present a methodology from the limited-dependent variable literature to model the dependence between the choice and quantity decisions. Our substantive interest is in the role of price in the choice and quantity decisions. When choosing among alternatives, we argue that consumers consider prices of all the competitive brands. In the quantity decision on the other hand, only the price of the chosen alternative is expected to impact how much of the alternative is purchased. The analysis of three brands, using disaggregate level panel data, strongly supports our hypothesis about the role of competitive prices in the choice and quantity decisions.

Briesch, Richard A, Lakshman Krishnamurthi, Tridib Mazumdar and S. J. Raj. 1997. A Comparative Analysis of Reference Price Models. Journal of Consumer Research. 24(2): 202-214.

The effect of reference price on brand choice decisions has been well documented in the literature. Researchers, however, have differed in their conceptualizations and, therefore, in their modeling of reference price. In this article, we evaluate five alternative models of reference price of which two are stimulus based (i.e, based on information available at the point-of-purchase) and three that are memory based (i.e., based on price history and/or other contextual factors). We calibrate the models using scanner panel data for peanut butter, liquid detergent, ground coffee, and tissue. To account for heterogeneity in model parameters, we employ a latent class approach and select the best segmentation scheme for each model. The best model of reference price is then selected on the basis of fit and prediction, as well as on the basis of parsimony in cases where the fits of the models are not very different. In all four categories, we find that the best reference price model is a memory-based model, namely, one that is based on the brand's own price history. In the liquid detergent category, however, we find that one of the stimulus-based models, namely, the current price of a previously chosen brand, also performs fairly well. We discuss the implications of these findings.

Krishnamurthi, Lakshman, S. J. Raj and K. Sivakumar. 1995. Unique Inter-Brand Effects of Price on Brand Choice. Journal of Business Research. 34(1): 47-56.

How do price changes by one brand affect the choice of competing brands? Such inter-brand effects may depend on the specific strategy followed by a firm. For example, a firm may target a particular brand to exploit its vulnerability or to avoid direct competition with other brands. Or a firm may design its pricing strategy aimed at reducing cannibalization of its own brands. Previous studies have utilized standard logit models to investigate inter-brand ejects. However, these models impose constraints on price elasticities as a consequence of independence of irrelevant alternatives (HA) assumptions. As a result, estimated own- and cross-elasticities reflect the restrictive assumptions of the model and may not provide an accurate description of the hinds of asymmetric competition among brands noted previously. Though existing market share models at the aggregate level do capture such competitive asymmetries, most disaggregate level logit choice models do not capture such asymmetries in a satisfactory manner. In this article a generalized logit (or mother logit) model is used to estimate unique interbrand response parameters to capture asymmetry. This methodology, drawn from the econometrics literature, overcomes the necessity of making a priori assumptions of competitive patterns and instead can be used to identify competitive patterns as they exist in the market place. In analyzing brand choice data from three product classes, ILA is violated in all three cases to varying degrees. The cross-price elasticities are used to draw managerial implications for brand and product line management.

Papatla, Purushottam and Lakshman Krishnamurthi. 1992. A Probit Model of Choice Dynamics. Marketing Science. 11(2): 189-206.

There are many products which are repeatedly purchased by consumers. In such cases it is likely that choice history, that is the sequence of choices made in the past, as well as marketing variables affect subsequent choice decisions. Attempts to model the effects of choice history have been generally based on the inclusion of variables that represent brand loyalty and/or variety seeking behavior. In this paper we present a model of dynamic choice behavior which is more general and incorporates four characteristics. The first characteristic labeled preference reinforcement and preference reduction represents loyalty and variety seeking. The second is the short-term reluctance of a consumer to move from the current brand (inertia) or the willingness to move to another brand (mobility). The third characteristic captures the effect of repetitive consumption (the long term effect) on inertia and mobility. The fourth characteristic incorporates the similarity or dissimilarity of choice alternatives. This is important in a dynamic model because choice on the current purchase occasion can be affected by whether a similar or dissimilar alternative was chosen on the previous occasion. Similarities of alternatives are represented in terms of distances. The effect of price on choice behavior is also modeled. Individual-level purchase data from a consumer panel are used to estimate a covariance probit and an independent probit specification of the model. From a substantive perspective the model gives interesting insights into the dynamics of choice behavior. The model predicts switches better than a benchmark model which incorporates only loyalty. In addition, it is superior to three benchmark models in overall predictive ability.

Krishnamurthi, Lakshman, Tridib Mazumdar and S. J. Raj. 1992. Asymmetric Response to Price in Consumer Brand Choice and Purchase Quantity Decisions. Journal of Consumer Research. 19(3): 387-400.

The study investigates whether consumers exhibit asymmetry (i.e., different sensitivity) to negative ("loss") and positive ("gain") differences between the reference price and the purchase price in brand choice and purchase quantity decisions. Using panel data for two frequently purchased products with three brands in each product category, we find that consumers loyal to a brand ("loyals") respond to gain and loss with the same sensitivity in brand choice decisions. However, consumers not loyal to any brand ("switchers") respond more strongly to gains than to losses. In purchase quantity decisions, brand-loyal consumers are found to respond asymmetrically to gains and losses, but the direction of the asymmetry depends on whether the decision is made before or after the household inventory reaches a stock-out level (i.e., the level at which the household inventory needs to be replenished). When the decision is made after a stock-out, brand-loyal consumers are more responsive to a gain in the price of their favorite brand than to a loss. In contrast, when the quantity decision is made before a stock-out, loyals are more sensitive to a loss than to a gain. In only two of the six brands examined do we find evidence of asymmetry in switchers' quantity decisions. In both cases, switchers respond more strongly to a price loss than to a gain, regardless of whether the purchase decision is made before or after a stock-out.

Krishnamurthi, Lakshman, Jack Narayan and S. J. Raj. 1989. Intervention Analysis Using Control Series and Exogenous Variables in a Transfer Function Model: A Case Study. International Journal of Forecasting. 5(1): 21-27.

This paper presents a case study to show how a control group can be used to obtain more accurate estimates of the impact of interventions. Intervention analysis using the ARIMA time series method is applied in an experimental design context using multiple input transfer function analysis. The study combines the analytic rigor of time series analysis with the careful controls provided by an experiment involving a test and control series. The data are from a field experiment with test and control panels connected to a split-cable TV system.

Krishnamurthi, Lakshman and S. J. Raj. 1988. A Model of Brand Choice and Purchase Quantity Price Sensitivities. Marketing Science. 7(1): 1-21.

Many consumer decisions involve a discrete choice and a continuous outcome. Examples of such decisions are whether to own a home or rent one and how much to spend, which brand of orange juice to buy and how many ounces to buy. In cases like these, the choice decision is typically modeled separately, say, using a logit model and the continuous outcomes modeled separately using regression analysis. However, the continuous outcomes may not be independent of the discrete choice and vice versa, and modeling the two decisions independently can lead to inefficient choice parameter estimates and biased and inconsistent regression parameter estimates. In this paper, we present a methodology from the limited-dependent variable literature to model the dependence between the choice and quantity decisions. Our substantive interest is in the role of price in the choice and quantity decisions. When choosing among alternatives, we argue that consumers consider prices of all the competitive brands. In the quantity decision on the other hand, only the price of the chosen alternative is expected to impact how much of the alternative is purchased. The analysis of three brands, using disaggregate level panel data, strongly supports our hypothesis about the role of competitive prices in the choice and quantity decisions.