Micro units → macro volatility
How do heterogeneous firm shocks become aggregate fluctuations?
Weights, marginal volatility, dependence, and population paths jointly determine diversification.
Explore aggregation and volatility →Current research front
Concentration Is Not Scaling
Two systems can have the same concentration path and different rates of diversification.
Direct economic weights describe concentration. Aggregate-variance scaling depends on the complete population-indexed stochastic exposure: marginal variances, dependence, composition, and the path along which the population changes. The current manuscript turns that distinction into an exact finite-interval accounting result.
Direct concentrationH(N) = w(N)ᵀw(N)
≠
Aggregate varianceV(N) = w(N)ᵀΣ(N)w(N)
A level property of weights is not, by itself, an elasticity of a variance–covariance system.
One programme, three transformations
Aggregation does not merely summarize the economy
It helps create the quantities we later interpret as volatility, specialization, and economic relatedness.
Economic table → specialization index
When does normalization change the meaning of revealed advantage?
Observation size can distort a familiar index and motivate a probability-based alternative.
Explore location quotients and pLQ →Locations → areas → networks
How do geographic support and representation shape measured relatedness?
Boundaries, distance, normalization, and transformations help define the network being measured.
Explore correlation structures →Published foundation
The same location quotient can mean different things
An identical LQ value can represent a different distance from specialization for observations of different sizes.
The location-quotient programme shows how row, column, observation, and table size shape the distribution and persistence of a familiar economic index. The probabilistic location quotient then replaces a brittle threshold with a size-conditional transition probability.
From a thresholdLQ > 1to a transition objectpLQ = P(LQₜ₊₁ > 1 | current size conditions)
Spatial antecedent
The map is part of the measurement
Administrative areas are not passive containers: their scale and geometry help determine the relationship represented by a co-location measure.
The geography programme treats similarity matrices as locational correlation structures. It then asks how discrete areas, continuous distance, normalization, and input transformation change the industry network we claim to observe.
Ideas recovered from the thesis
Research propositions with deeper evidence trails
These are antecedents and options, not six simultaneous active projects. The current publication sequence remains anchored in the aggregation programme.
Firms are not sectors
Aggregation can make fluctuations approximately linear even when firm-level dynamics remain strongly nonlinear.
Follow the micro-to-macro trail →Population is not effective diversification
The number of firms, their weights, marginal volatility, and dependence are distinct economic objects.
See what controls diversification →The same LQ can mean different things
Observation size changes the economic meaning of an identical location-quotient value.
Read the location-quotient result →Thresholds can become probabilities
The probabilistic location quotient reframes specialization as a size-conditional transition probability.
Understand pLQ →Relatedness depends on representation
Counts, logs, normalizations, and binary specialization can generate different economic networks.
Inspect the similarity framework →Boundaries can act like kernels
Administrative areas are not passive containers: their geometry helps define measured spatial overlap.
Trace areas into continuous space →Research status
A programme with explicit provenance
The portal distinguishes current manuscripts, published work, working papers, thesis results, and research directions.
Concentration Is Not ScalingCurrent manuscriptFormal foundation for the aggregation programme
Size distortions of location quotients and pLQPeer-reviewed publicationPublished foundation on normalization and observation size
Correlation structures in economic geographyWorking paperSpatial co-occurrence, normalization, and industry networks
Thesis essays and technical trailsResearch archiveDerivations, figures, experiments, and future options
Research archive, not a frozen thesis
Follow the idea, then inspect the evidence
Start with the present programme, choose a curated reading trail, and move from a research proposition into the original derivations, figures, data arguments, and technical material.