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We revisit granular models that represent the size of a firm as the sum of the sizes of multiple constituents or sub-units. Originally developed to address the unexpectedly slow reduction in volatility as firm size increases, these models also explain the shape of the distribution of firm growth rates. We introduce new theoretical insights regarding the relationship between firm size and growth rate statistics within this framework, directly linking the growth statistics of a firm to how diversified it is. The non-intuitive nature of our results arises from the fat-tailed distributions of the size and the number of sub-units, which suggest the categorization of firms into three distinct diversification types: well-diversified firms with sizes evenly distributed across many sub-units, firms with many sub-units but concentrated size in just a few, and poorly diversified firms consisting of only a small number of sub-units. Inspired by our theoretical findings, we identify new empirical patterns in firm growth. Our findings show that growth volatility, when adjusted by average size-conditioned volatility, has a size-independent distribution, but with a tail that is much too thin to be

Intra-firm trade describes the trade between affiliated firms and is increasingly important as global production is fragmented. However, statistics and data on global intra-firm trade patterns are widely unavailable. This study proposes a novel multilevel approach combining firm and country level data to construct a set of country intra-firm trade networks for various segments of the automotive production chain. A multilevel network is constructed with a network of international trade at the macro level, a firm ownership network at the micro level and a firm-country affiliation network linking the two, at the meso level. A motif detection approach is used to filter these networks to extract potential intra-firm trade ties between countries, where the motif (or substructure) is two countries linked by trade, each affiliated with a firm, and these two firms linked by ownership. The motif detection is used to extract potential country level intra-firm trade ties. An Exponential Random Graph Model (ERGM) is applied to the country level intra-firm trade networks, one for each segment of the automotive production chain, to inform on the determinants of intra-firm trade at the country lev

Instruction-tuned Large Language Models (LLMs) are increasingly deployed as AI Assistants in firms for support in cognitive tasks. These AI assistants carry embedded perspectives which influence factors across the firm including decision-making, collaboration, and organizational culture. This paper argues that firms must align the perspectives of these AI Assistants intentionally with their objectives and values, framing alignment as a strategic and ethical imperative crucial for maintaining control over firm culture and intra-firm moral norms. The paper highlights how AI perspectives arise from biases in training data and the fine-tuning objectives of developers, and discusses their impact and ethical significance, foregrounding ethical concerns like automation bias and reduced critical thinking. Drawing on normative business ethics, particularly non-reductionist views of professional relationships, three distinct alignment strategies are proposed: supportive (reinforcing the firm's mission), adversarial (stress-testing ideas), and diverse (broadening moral horizons by incorporating multiple stakeholder views). The ethical trade-offs of each strategy and their implications for man

Strong local clusters help firms compete on global markets. One explanation for this is that firms benefit from locating close to their suppliers and customers. However, the emergence of global supply chains shows that physical proximity is not necessarily a prerequisite to successfully manage customer-supplier relations anymore. This raises the question when firms need to colocate in value chains and when they can coordinate over longer distances. We hypothesize that one important aspect is the extent to which supply chain partners exchange not just goods but also know-how. To test this, we build on an expanding literature that studies the drivers of industrial coagglomeration to analyze when supply chain connections lead firms to colocation. We exploit detailed micro-data for the Hungarian economy between 2015 and 2017, linking firm registries, employer-employee matched data and firm-to-firm transaction data from value-added tax records. This allows us to observe colocation, labor flows and value chain connections at the level of firms, as well as construct aggregated coagglomeration patterns, skill relatedness and input-output connections between pairs of industries. We show tha

Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years before a new firm emerges and rapidly obtains a large market share. We seek the simplest realistic model giving rise to such diverse market structures and dynamics. We focus on markets in which every client adopts a single firm, and can, from time to time, switch to a different firm. Examples include markets of cell phone and Internet service providers, and of consumer products with strong brand identification. In the model, the size of a particular firm, labelled $i$, is equal to its current number of clients, $n_i$. In every step of the simulation, a client is chosen at random, and then selects a firm from among the full set of firms with probability $p_i = (n_i^α+ β)/K$, where $K$ is the normalization factor. Our model thus has two parameters: $α$ represents the degree to which firm size is an advantage ($α$ > 1) or disadvantage ($α$ < 1), relative to strict proportionality to size ($α$ = 1), and $β$ represents the degree to which small

We propose a novel measure to investigate firms' product specialisation: product coreness, that captures the centrality of exported products within the firm's export basket. We study product coreness using firm-product level data between 2018 and 2020 for Colombia, Ecuador, and Peru. Three main findings emerge from our analysis. First, the composition of firms' export baskets changes relatively little from one year to the other, and products far from the firm's core competencies, with low coreness, are more likely to be dropped. Second, higher coreness is associated with larger export flows at the firm level. Third, such firm-level patterns also have implications at the aggregate level: products that are, on average, exported with higher coreness have higher export flows at the country level, which holds across all levels of product complexity. Therefore, the paper shows that how closely a product fits within a firm's capabilities is important for economic performance at both the firm and country level. We explore these issues within an econometric framework, finding robust evidence both across our three countries and for each country separately.

Violations of laws and regulations about food safety, production safety, quality standard and environmental protection, or negative consequences from loan, guarantee and pledge contracts, may result in operating and credit risks of firms. The above illegal or trust-breaking activities are collectively called discreditable activities, and firms with discreditable activities are named as discreditable firms. Identification of discreditable firms is of great significance for investment attraction, bank lending, equity investment, supplier selection, job seeking, and so on. In this paper, we collect registration records of about 113 million Chinese firms and construct an ownership network with about 6 million nodes, where each node is a firm who has invested at least one firm or has been invested by at least one firm. Analysis of publicly available records of discreditable activities show strong network effect, namely the probability of a firm to be discreditable is remarkably higher than the average probability given the fact that one of its investors or investees is discreditable. In comparison, for the risk of being a discreditable firm, an investee has higher impact than an investo

Understanding firm conduct is crucial for industrial organization and antitrust policy. In this article, we develop a testing procedure based on the Rivers and Vuong non-nested model selection framework. Unlike existing methods that require estimating the demand and supply system, our approach compares the model fit of two first-stage price regressions. Through an extensive Monte Carlo study, we demonstrate that our test performs comparably to, or outperforms, existing methods in detecting collusion across various collusive scenarios. The results are robust to model misspecification, alternative functional forms for instruments, and data limitations. By simplifying the diagnosis of firm behavior, our method offers researchers and regulators an efficient tool for assessing industry conduct under a Bertrand oligopoly framework. Additionally, our approach offers a practical guideline for enhancing the strength of BLP-style instruments in demand estimation: once collusion is detected, researchers are advised to incorporate the product characteristics of colluding partners into own-firm instruments while excluding them from other-firm instruments.

We present an open-source Python framework for modelling cascading physical climate risk in a spatial supply-chain economy. The framework integrates geospatial flood hazards with an agent-based model of firms and households, enabling simulation of both direct asset losses and indirect disruptions propagated through economic networks. Firms adapt endogenously through two channels: capital hardening, which reduces direct damage, and backup-supplier search, which mitigates input disruptions. In an illustrative global network, capital hardening reduces direct losses by 26%, while backup-supplier search reduces supplier disruption by 48%, with both partially stabilizing production and consumption. Notably, firms that are never directly flooded still bear a substantial share of disruption, highlighting the importance of indirect cascade effects. The framework provides a reproducible platform for analyzing systemic physical climate risk and adaptation in economic networks.

This paper investigates how institutional wage-setting constraints, such as a national minimum wage or collectively bargained wages, affect firm responses to demand shocks. We develop a framework to interpret heterogeneous shock responses that depend on the constraints firms face, and provide empirical evidence on the relevance of these constraints in shaping firm behavior across three countries with different institutional settings: Portugal, Norway, and Colombia. We discuss the implications of our findings for conventional estimates of rent-sharing and employer wage-setting power.

Social employment, which is mostly carried by firms of different types, determines the prosperity and stability of a country. As time passing, the fluctuations of firm employment can reflect the process of creating or destroying jobs. Therefore, it is instructive to investigate the firm employment (size) dynamics. Drawing on the firm-level panel data extracted from the Chinese Industrial Enterprises Database 1998-2013, this paper proposes a Markov-chain-based descriptive approach to clearly demonstrate the firm size transfer dynamics between different size categories. With this method, any firm size transition path in a short time period can be intuitively demonstrated. Furthermore, by utilizing the properties of Markov transfer matrices, the definition of transition trend and the transition entropy are introduced and estimated. As a result, the tendency of firm size transfer between small, medium and large can be exactly revealed, and the uncertainty of size change can be quantified. Generally from the evidence of this paper, it can be inferred that small and medium manufacturing firms in China have greater job creation potentials compared to large firms over this time period.

Social and biological collectives need to exchange information to persist and to function. This happens across internal networks, whose structure represents static channels through which information flows. Less studied is the quantity and variety of information transmitted. We characterize a part of the information flow, the information going into organizations, primarily business firms. We measure what firms read using a data set of hundreds of millions of records of news articles accessed by employees across millions of firms. We measure and relate quantitatively three essential aspects: reading volume, reading variety, and firm size. First we compare volume with firm size, showing that firms grow sublinearly with the volume of their reading. The scaling means that inequality in information volume exaggerates the classic Zipf's law inequality in firm size, pointing to an economy of scale in information consumption. Then, by connecting variety and volume, we show that the firms vary in their reading habits to a limited degree. Firms above a certain size become repetitive readers, consistent with the sudden onset of a coordination cost between teams, not individual employees. Final

We introduce a novel proxy for firm linkages, Characteristic Vector Linkages (CVLs). We use this concept to estimate firm linkages, first through Euclidean similarity, and then by applying Quantum Cognition Machine Learning (QCML) to similarity learning. We demonstrate that both methods can be used to construct profitable momentum spillover trading strategies, but QCML similarity outperforms the simpler Euclidean similarity.

This work analyzes data on all public US firms in the 50 year period 1970-2019, and presents 18 stylized facts of their scale, income, growth, return, investment, and dynamism. Special attention is given to (i) identifying distributional forms; and (ii) scale effects -- systematic difference between firms based on their scale of operations. Notable findings are that the Difference-of-Log-Normals (DLN) distribution has a central role in describing firm data, scale-dependent heteroskedasticity is rampant, and small firms are systematically different from large firms.

We study the correlation structure of firm growth rates. We show that most firms are correlated because of their exposure to a common factor but that firms linked through the supply chain exhibit a stronger correlation on average than firms that are not. Removing this common factor significantly reduces the average correlation between two firms with no relationship in the supply chain while maintaining a significant correlation between two firms that are linked. We then investigate if this observation can be used to reconstruct the topology of a supply chain network using Gaussian Markov Models.

We investigate a multi-agent model of firms in an R\&D network. Each firm is characterized by its knowledge stock $x_{i}(t)$, which follows a non-linear dynamics. It can grow with the input from other firms, i.e., by knowledge transfer, and decays otherwise. Maintaining interactions is costly. Firms can leave the network if their expected knowledge growth is not realized, which may cause other firms to also leave the network. The paper discusses two bottom-up intervention scenarios to prevent, reduce, or delay cascades of firms leaving. The first one is based on the formalism of network controllability, in which driver nodes are identified and subsequently incentivized, by reducing their costs. The second one combines node interventions and network interventions. It proposes the controlled removal of a single firm and the random replacement of firms leaving. This allows to generate small cascades, which prevents the occurrence of large cascades. We find that both approaches successfully mitigate cascades and thus improve the resilience of the R\&D network.

For a binary matrix X, the Boolean rank br(X) is the smallest integer k for which X equals the Boolean sum of k rank-1 binary matrices, and the isolation number i(X) is the maximum number of 1s no two of which are in a same row, column and a 2x2 submatrix of all 1s. In this paper, we continue Lubiw's study of firm matrices. X is said to be firm if i(X)=br(X) and this equality holds for all its submatrices. We show that the stronger concept of superfirmness of X is equivalent to having no odd holes in the rectangle cover graph of X, the graph in which br(X) and i(X) translate to the clique cover and the independence number, respectively. A binary matrix is minimally non-firm if it is not firm but all of its proper submatrices are. We introduce two matrix operations that lead to generalised binary matrices and use these operations to derive four infinite classes of minimally non-firm matrices. We hope that our work may pave the way towards a complete characterisation of firm matrices via forbidden submatrices.

We study how firm heterogeneity and market power affect macroeconomic fragility, defined as the probability of long slumps. We propose a theory in which the positive interaction between firm entry, competition and factor supply can give rise to multiple steady-states. We show that when firms are highly heterogeneous in terms of productivities, even small temporary shocks can trigger firm exit and make the economy spiral in a competition-driven poverty trap. We calibrate our model to incorporate the well-documented trends on rising firm heterogeneity in the US economy, and show that they significantly increase the likelihood and length of slow recoveries. We use our framework to study the 2008-09 recession and show that the model can rationalize the persistent deviation of output and most macroeconomic aggregates from trend, including the behavior of net entry, markups and the labor share. Post-crisis cross-industry data corroborates our proposed mechanism. We conclude by showing that firm subsidies can be powerful in preventing long slumps and can lead to welfare gains between 10% and 50%.

We develop a novel methodology for the proxy variable identification of firm productivity in the presence of productivity-modifying learning and spillovers which facilitates a unified "internally consistent" analysis of the spillover effects between firms. Contrary to the popular two-step empirical approach, ours does not postulate contradictory assumptions about firm productivity across the estimation steps. Instead, we explicitly accommodate cross-sectional dependence in productivity induced by spillovers which facilitates identification of both the productivity and spillover effects therein simultaneously. We apply our model to study cross-firm spillovers in China's electric machinery manufacturing, with a particular focus on productivity effects of inbound FDI.