Product Complementarity Research Articles

Aggregate Demand Externalities, Income Distribution, and Wealth Inequality

We study a two-class model of growth and the distribution of income and wealth at the intersection of contemporary work in classical political economy and post-Keynesian economics. The key insight is that aggregate demand is an externality for individual firms: this generates a strategic complementarity in production and results in equilibrium underutilization of the economy's productive capacity, as well as hysteresis in real output. Underutilization also affects the functional distribution of income and the distribution of wealth: both the wage share and the workers' wealth share would be higher at full capacity. Consequently, fiscal allocation policy that achieves full utilization also attains a higher labor share and a more equitable distribution of wealth; while demand shocks have permanent level effects. Extensions look at hysteresis in the employment rate and growth. These findings are useful as an organizing framework for thinking through the lackluster economic record of the so-called Neoliberal era, the sluggish recovery of most advanced economies following the Great Recession, and the importance of fiscal policy in countering large shocks such as the Covid-19 pandemic.

Nonlinear Taxation and International Mobility in General Equilibrium

We study the nonlinear taxation of internationally mobile workers in general equilibrium. Contrary to conventional wisdom, in general equilibrium, migration lowers the bottom tax rate but raises the top tax rate, making the optimal tax system more progressive and moving tax rates closer to those in an economy with fixed wages. The intuition is that governments attract high-skilled workers by amplifying pre-tax wage inequality and partly offsetting trickle-down forces from production complementarities. This finding raises doubts about the importance of trickle-down for optimal taxation and offers a novel explanation for why globalization may increase tax progressivity and wage inequality.

Complementarity of Information Products

In “Marketing Information: A Competitive Analysis,” Sarvary, M., and P. M. Parker. 1997. “Marketing Information: A Competitive Analysis.” Marketing Science 16 (1): 24–38 (SP (ii) if consumers choose not to purchase any information product, it is assumed that their initial prior variance is 1 (implied by the utility function specification). This internal inconsistency leads to the possibility that when information products are uncorrelated and their variances are close to 1, marginal utility is increasing in the number of products purchased, and hence information products can be complements in their model. We show that if we remove this internal inconsistency, in the parameter space considered by SP this space of parameters requires consumer’s initial prior to be relatively precise and information products to be highly correlated (either positively or negatively).

Marriage Market and Labor Market Sorting

We build a novel equilibrium model in which households' labor supply choices form the link between sorting on the marriage market and sorting on the labor market. We first show that in theory, the nature of home production – whether partners' hours are complements or substitutes – shapes marriage market sorting, labor market sorting and labor supply choices in equilibrium. We then estimate our model on German data to assess the nature of home production in the data, and find that spouses' home hours are complements. We investigate to what extent complementarity in home hours drives sorting and inequality. We find that the home production complementarity – by strengthening positive marriage sorting and reducing the gender gap in hours and labor sorting – puts significant downward pressure on the gender wage gap and within-household income inequality, but it fuels between-household inequality. Our estimated model sheds new light on the sources of inequality in today's Germany and – by identifying important shifts in home production technology towards more complementarity – on the evolution of inequality over time.

A signalling model of loss leader pricing strategy

AbstractThe traditional theory of loss leader pricing strategy generally relies on assumptions such as high consumer search cost, product complementarities, and short‐sighted consumer rationality. We argue that with the rise of e‐commerce, consumer search cost is substantially reduced, and in many cases, loss leader goods have no obvious complements but many substitutes. In this paper, we set up a model with both base product and advance product where the latter's quality is observable only to a fraction of the consumers. It is shown that a firm may use loss leader pricing strategy to signal the quality of its advance product to the uninformed consumers. Therefore, as a signalling device, loss leader pricing strategy is conducive to correct the lemons problem.

Nonbinding Goals in Teams: A Real Effort Coordination Experiment

Problem definition: We investigate the impact of nonbinding (wage-irrelevant) goals, set by a manager, on a team of workers with “weak-link” production technology. Can nonbinding goals improve team production when team members face production complementarity? Academic/practical relevance: Nonbinding goals are easy to implement and ubiquitous in practice. These goals have been shown to improve individual performance, but it remains to be seen if such goals are effective in team production when there is production complementarity among workers. Methodology: We first develop a theoretical model where goals act as reference points for workers’ intrinsic motivation to complete the task. We then test our hypotheses in a controlled, human-subjects experiment. In our experiment, participants act as managers or workers, and we examine the impact of nonbinding goals on team outcomes. Results: Consistent with our model, we find evidence that team production does increase when managers are able to set goals. This effect is strongest when goals are challenging but attainable for weak-link workers. However, we also find evidence that many managers assign goals that are too challenging for weak-link workers, resulting in suboptimal team production, lower profits, and higher wasted performance (performance above the weak-link level). Managerial implications: Our analysis indicates that goals are effective motivators in teams, but some managers may have difficulty overcoming personal biases when setting goals. The task of setting team goals is more complex than setting individual goals, and many managers can benefit from training on how to set good goals for the team. Moreover, our finding that suboptimal goals also increase wasted performance suggests that improving goal-setting strategies is especially important in production settings where overperformance is costly for the firm (scrap, energy use, inventory costs, lower prices as a result of oversupply, etc.).

The superstar and the followers: Intra-firm product complementarity in international trade

Export sales of multi-product firms are known to be skewed towards their best performing core products. Less is known about the large number of products outside the core that still account for a considerable share of the export value. I use high-quality Swedish firm-registry data to investigate if the exports of core and non-core products are systematically interconnected. Using a novel instrumental variable approach, I find evidence that the exports of non-core products respond to trade of the core. Conversely, the same complementarity is not found using non-core products as placebo-cores. Decomposing the response, I find that over a quarter of the effect can be attributed to price changes of non-core products, suggestive of demand-side explanations. The main contribution of this paper is identifying a new, sizeable, and systematic within-firm one-way complementarity between products that can explain non-core product trade flows. Ignoring this pattern of cross-product dependence may lead to an under-emphasis on the core and over-emphasis on individual trade flows as products should not be viewed in isolation, since the ‘superstar’ core has (contemporaneous) followers.

Minimum wage, trade and unemployment in general equilibrium

AbstractThe path‐breaking work of Card and Krueger, showing that a higher minimum wage can increase employment, turned the age‐old conventional wisdom on its head. This paper demonstrates that this apparently paradoxical result is perfectly plausible in a competitive general equilibrium production structure of a small open economy with a non‐traded good, without recourse to monopsony, spatial heterogeneity, heterogeneity of consumers and so on, the usual theoretical drivers behind the result. Following Jones and Marjit, we build a simple general equilibrium model with production complementarity and we show that a higher minimum wage can raise aggregate employment. Expansion in the non‐traded sector following a wage hike may be consistent with the overall expansion of the export sector in a multi‐good framework, an unlikely outcome in a conventional two‐good model which cannot accommodate with production complementarity.

COMPLEMENTARY PRODUCT CATEGORIZATION AND ITS INFLUENCE ON THE MAKE, BUY, AND ALLY DECISION: AN EXPLORATORY STUDY

The role of complementary products is becoming increasingly important in facilitating innovation and has become a pivotal aspect of an organisation’s technology strategy. To address the lack of a useful framework that captures the different dimensions of product complementarity, this paper proposes a categorization for complementary products centered on user engagement. Based on a sample of 305 make, buy, and ally decisions for 32 primary product firms in the Personal Computing industry, this paper explores the influence of the proposed categorization on its strategy decision for developing complementary products. Results suggest a nuanced categorization of product complementarity adds value to explaining the decision, with the firm’s knowledge capital having a non-trivial influence on it. This paper endeavors to contribute to the literature on platform innovation by examining significance of inter-product relationships on strategy.

The impact of glacier shrinkage on energy production from hydropower-solar complementarity in alpine river basins

Variable energy sources such as solar and runoff sources are intermittent in time and space, following their driving hydro-meteorological processes. Recent research has shown that in mountainous areas the combination of solar and hydropower has large potential (termed complementarity) to cover the temporal variability of the energy load and, by this mean, to facilitate integration of renewables into the electricity network. Climate change is causing widespread glacier retreat, and much attention is devoted to negative impacts such as diminishing water resources and shifts in runoff seasonality. However, the effects of glacier shrinkage on complementarity between hydropower and solar energy sources have been disregarded so far. This research aims at filling this gap. Data from the Eastern Italian Alps are used for the analysis. The Decision Scaling approach is used to analyze the electric energy system sensitivity and vulnerability to change in precipitation, temperature and glacier coverage. With this method, the electric energy system is first subject to a scenario-independent climate stress test, while projections from Regional Climate Models (RCMs) are then used to infer the likelihood of the future climate states and subsequently changes in complementarity of energy production. Results show that glacier shrinkage and increasing temperatures induced by climate change lead to a marked shift of seasonal hydropower production. As a consequence, the complementarity between hydropower and solar photovoltaic increases in a marked way in the basin with the largest original glacier coverage. Changes in complementarity are less significant in larger basins characterized by less glacier contribution.

Dynamic Complementarity in Skill Production: Evidence From Genetic Endowments and Birth Order

The birth order literature emphasizes the role of parental investments in explaining why firstborns have higher human capital outcomes than their laterborn siblings. We use birth order as a proxy for investments and interact it with genetic endowments. Exploiting only within-family variation in both ensures they are exogenous as well as orthogonal to each other. As such, our setting is informative about the existence of dynamic complementarity in skill production. Our empirical analysis exploits data from 15,019 full siblings in the UK Biobank. We adopt a family-fixed effects strategy combined with instrumental variables to deal with endogeneity issues arising from omitted variables and measurement error. We find that birth order and genetic endowments interact: those with above-average genetic endowments benefit disproportionally more from being firstborn compared to those with below-average genetic endowments. This finding is a clean example of how genetic endowments ('nature’) and the environment ('nurture’) interact in producing educational attainment. Moreover, our results are consistent with the existence of dynamic complementarity in skill formation: additional parental investments associated with being firstborn are more ‘effective’ for those siblings who randomly inherited higher genetic endowments for educational attainment.

The Last Will Be First, and the First Last: Segregation in Societies With Relative Payoff Concerns

This paper studies coalition formation among individuals who differ in productivity. The output of a coalition is determined by the sum of the productivities and the size of the coalition. We consider egalitarian societies in which coalitions split their surplus equally and individualistic societies in which the surplus of a coalition is split according to productivity. Preferences of coalition members depend on their material payoffs, but are also influenced by relative payoff concerns, which relate their material payoffs to the average material payoff in the coalition. Our analysis uses two stability notions, the Core and the Myopic Stable Set. The stable partitions in both egalitarian and individualistic societies are segregated, i.e., individuals with adjacent productivities form coalitions. If some individuals are not part of a productive coalition, then these are the least productive ones for egalitarian societies and the most productive ones for individualistic societies. If all individuals have different productivity levels and there are sufficient complementarities in production, egalitarian societies induce more efficiency than individualistic societies.

Redistributive Capital Taxation Revisited

This paper shows that capital-skill complementarity provides a quantitatively significant rationale to tax capital for redistributive governments. The optimal capital income tax rate is 60%, which is significantly higher than the optimal rate of 48% in an identically calibrated model without capital-skill complementarity. The skill premium falls from 1.9 to 1.67 along the transition following the optimal reform in the capital-skill complementarity model, implying substantial indirect redistribution from skilled to unskilled workers. These results show that a government that cares about redistribution should take into account capital-skill complementarity in production when setting the tax rate on capital income.

Redistributive Capital Taxation Revisited

This paper shows that capital-skill complementarity provides a quantitatively significant rationale to tax capital for redistributive governments. The optimal capital income tax rate is 60%, which is significantly higher than the optimal rate of 48% in an identically calibrated model without capital-skill complementarity. The skill premium falls from 1.9 to 1.67 along the transition following the optimal reform in the capital-skill complementarity model, implying substantial indirect redistribution from skilled to unskilled workers. These results show that a government that cares about redistribution should take into account capital-skill complementarity in production when setting the tax rate on capital income.

Nonlinear Production Networks with an Application to the COVID-19 Crisis

We study the effects of negative supply shocks and shocks to the composition of final demand on aggregate output in a disaggregated neoclassical model with multiple sectors, factors, and input-output linkages. We show how nonlinearities associated with complementarities in consumption and production amplify the effect of negative supply shocks by creating supply bottlenecks and disrupting supply chain networks. These nonlinearities are particularly potent when the shocks are more heterogeneous as the worst-affected sectors drag down the other sectors. Nonlinearities are strengthened when changes in preferences lead households to tilt the composition of their demand towards the crippled sectors directly and indirectly through their supply chains. And nonlinearities are further intensified when factors cannot easily be reallocated across sectors to reinforce weak links. A quantitative investigation suggests that nonlinearities may amplify the impact of the Covid-19 shock by between 10\%-100\%, depending on the horizon of analysis and the exact size of the shocks.

Playing to the Crowd? Digital Visibility and the Social Dynamics of Purchase Disclosure

As people share more of their lives on social media, their consumption and purchase behaviors become increasingly visible to their peers, spawning a new form of digitally-enabled conspicuous consumption. We examine how the ensuing dynamics of social commerce affect these visibility choices. We use data from a platform dedicated exclusively to facilitating the display of verified online and offline purchases with optional product commentaries. We use fixed effects and matching techniques to control for endogeneity in commentary and consumer disclosure, while embedding a new text-based model of product similarity into our econometric analysis and capturing product complementarity using network-based measures of similarity. Our findings demonstrate that disclosed purchase patterns are shaped by other users, even those with whom the discloser has no previously stated relationship. We find that the source of attention shapes disclosure behavior, and we uncover a relationship between comments and purchase similarity of disclosed purchases, suggesting that consumers play to the crowd. The negative relationship between product reviews and purchase disclosure suggest that consumers may disclose a purchase because of a relationship with that particular item and not a desire to habitually reveal purchases. Our results shed new light on the distinction between digital visibility and social buzz, with managerial implications for retailers and social media platforms that support social consumption.

Aging in Place, Housing Maintenance, and Reverse Mortgages

AbstractWe study the role of housing wealth in financing retirement consumption. In our model retirees: 1. derive utility benefits from remaining in their home (aging in place); and 2. choose in each period whether to maintain their house. The evidence that we present shows that these features are important in explaining the saving decisions of the elderly. The costs and the maintenance requirement of reverse mortgages (RMs) reduce (or eliminate) the benefits of the loans for retirees who wish to do less maintenance. We evaluate the impact of different loan features on retirees’ utility, cash-flows to lenders, and to the government agency that provides mortgage insurance. We show that combining RMs with insurance against a forced home sale (e.g. due to a move to a nursing home) is Pareto improving and can lead to increased demand for the loans due to product complementarities.

Merger effects with product complementarity: Evidence from Colombia’s telecommunications

Mergers of firms producing complementary products entail two opposing effects: Lower prices, because they may internalize the impact of the complementarity, and higher prices, because the firms gain the ability to price discriminate. I use Colombian data to analyze mergers between firms providing complementary telecommunication services. I estimate a discrete choice model of demand for bundled fixed-line and mobile internet services, in which the degree of either substitutability or complementarity among products is a parameter of interest. Counterfactual experiments using the estimated model indicate pro-competitive effects of mergers with complements: despite a small increase in the price of standalone goods, consumer surplus increases.

P2V-MAP: Mapping Market Structures for Large Retail Assortments

The authors propose a new, exploratory approach for analyzing market structures that leverages two recent methodological advances in natural language processing and machine learning. They customize a neural network language model to derive latent product attributes by analyzing the co-occurrences of products in shopping baskets. Applying dimensionality reduction to the latent attributes yields a two-dimensional product map. This method is well-suited to retailers because it relies on data that are readily available from their checkout systems and facilitates their analyses of cross-category product complementarity, in addition to within-category substitution. The approach has high usability because it is automated, is scalable and does not require a priori assumptions. Its results are easy to interpret and update as new market basket data are collected. The authors validate their approach both by conducting an extensive simulation study and by comparing their results with those of state-of-the-art, econometric methods for modeling product relationships. The application of this approach using data collected at a leading German grocery retailer underlines its usefulness and provides novel findings that are relevant to assortment-related decisions.

Optimal Team Composition: Diversity to Foster Mutual Monitoring

We study optimal team design. In our model, a principal assigns either heterogeneous agents to a team (a diverse team) or homogenous agents to a team (a specialized team) to perform repeated team production. We assume that specialized teams exhibit a productive substitutability (e.g., interchangeable efforts with decreasing returns to total effort), whereas diverse teams exhibit a productive complementarity (e.g., cross-functional teams). Diverse teams have an inherent advantage in fostering desirable implicit/relational incentives that team members can provide to each other (tacit cooperation). In contrast, specialization both complicates the provision of cooperative incentives by altering the punishment agents can impose on each other for short expected career horizons and fosters undesirable implicit incentives (tacit collusion) for long expected horizons. As a result, expected compensation is first decreasing and then increasing in the discount factor for specialized teams, while expected compensation is always decreasing in the discount factor for diverse teams. We use our results to develop empirical implications about the association between team tenure and team composition, pay-for-performance sensitivity, and team culture.