📄️ Aggregation of Firm-Level Exports and Imports
Explore techniques for tracing the aggregation of firm-level exports and imports into national aggregates, with a focus on sectoral and aggregate fluctuations.
📄️ Introduction to Aggregate Volatility
Explore the dynamics of economic agents and aggregate characteristics, emphasizing the role of size distributions and micro fluctuations.
📄️ Overview of Sections and Core Contributions
A detailed overview of the sections covering literature review, data methods, mathematical definitions, and the core contributions related to aggregation of micro volatility.
📄️ Related Works
A review of approaches to explaining aggregate volatility in economics, contrasting regression-based methods with identity-based frameworks.
📄️ The Quest for Volatility
An exploration of the dynamics of aggregate sales fluctuations, challenging misconceptions in the aggregation of micro-level fluctuations to macro-level volatility.
📄️ Network Effects
A critical examination of uncritical trust in famous results and the implications of network effects on micro shock distribution.
📄️ Further Literature Comments
A detailed exploration of literature on eigenvector centrality, network cascades, and aggregate volatility, focusing on firm growth dynamics and distribution.
📄️ Data and Methods
An exploration of the data and methods used in analyzing French trade, focusing on the PHID dataset and formal relations in sales time series.
📄️ Key Empirical Features: Distribution of Firm Sizes and Fluctuations
Explore the distribution of firm sizes and their fluctuations, focusing on the logarithmic scale properties observed in economic agents.
📄️ Size Distribution of Firms
Analysis of the size distribution of firms in the French traders dataset, highlighting log-normal and Pareto distributions.
📄️ Firm Level Fluctuations
An analysis of firm-level fluctuations using log differences, exploring growth rates, autocorrelation, and aggregation methods.
📄️ Mathematical Framework: Aggregate Volatility in Log Scale
Explore the mathematical framework for understanding aggregate volatility in log scale, focusing on variance and covariance among agents.
📄️ More about Partitions
Explore the concept of partitions in aggregating firm sales, including equal weight and quantile partitions, and their implications for economic analysis.
📄️ Simple Structure of Sectoral Sales
Explore the decomposition of sectoral sales time series into components, focusing on aggregate variance and cross covariance matrices.
📄️ Non-Linearities
Explore the implications of logarithmic transformations in economic fluctuations, focusing on nonlinearities and their practical applications.
📄️ Mean and Variance of Transformed Random Variables
Explore the estimation of moments for logarithms of aggregate sales using Taylor expansion, focusing on expected value and variance.
📄️ Micro to Macro Fluctuations
An overview of the relationships between micro and macro fluctuations in linear and log terms, with a focus on differences and variances.
📄️ Firms are not Sectors
Explore the distinction between firms and sectors, focusing on how aggregate fluctuations can be expressed through firm and sector levels, and the implications of log deviations.
📄️ Log Aggregate Deviations and Sectoral Contributions
Explore how log aggregate deviations can be expressed as a linear combination of sectoral log deviations and the implications for aggregate variance.
📄️ Reviewing the Diversification Issues
An in-depth analysis of the diversification issues in aggregate time series, focusing on the volatility contributions from numerous agents and the implications of idiosyncratic and aggregate shocks.
📄️ Dependence of Variance with Population Size
Explore the relationship between variance and population size using a power law model, focusing on the implications for aggregate and part populations.
📄️ Aggregating a Group of Agents: Sum of Powers
Explore the aggregation of fluctuating agents, focusing on variance relations and quantile analysis.
📄️ Mandelbrot and Sensitivity in Size Distributions
Explore Mandelbrot's insights on the sensitivity of size distributions, particularly focusing on the lognormal distribution and its implications.
📄️ Expected Level of Parts' Time Series
Analyzing the expected level of parts' time series and its volatility, focusing on the narrow quantile condition and distribution assumptions.
📄️ Micro Fluctuations and Moments
An exploration of micro fluctuations in agents' characteristics, focusing on log-Laplace and log-normal distributions and their implications.
📄️ Analysis of Log Quantile Levels
Explore the expectations of log quantile levels under different micro shock distributions and their convergence properties.
📄️ Variance of Parts' Time Series Mean (The Law of Large Numbers)
Explore the variance of time series means in quantile levels, examining the law of large numbers and its implications on aggregate statistics.
📄️ Understanding Comovements and Variance in Large Numbers
Explore the impact of comovements and variance in large numbers, focusing on the balance between self-variance and covariance among agents.
📄️ Variance as a Function of Micro Moments
Explore the variance of quantile levels in relation to micro moments and the impact of log-normal and log-Laplace distributions.
📄️ Origin of Departure from LLN
Explore the origin of departure from the Law of Large Numbers in agent populations, examining firm comovement and self-variance.
📄️ Moments of Log Quantile Levels
Explore the moments of log quantile levels, focusing on variance calculations for log-normal and log-Laplace fluctuations.
📄️ Acknowledging Size Distribution
Explore the impact of size distribution on firm-level outcomes, examining log-normal and Pareto distributions in the context of French traders.
📄️ Acknowledging Entry and Exit Events
Explore the dynamics of entry and exit events in firms and their impact on sectoral sales time series through a detailed decomposition framework.
📄️ Estimated Dependence of Components
Examination of the estimated dependence of components B_{pt}, M_{pt}, and their counterparts, focusing on their time dependence and net comovements.
📄️ Classification of Matrix Elements and Their Impact on Variance
Analyzing the classification of matrix elements into blocks and their implications on variance, with insights from micro shocks and covariance structures.
📄️ Conclusion on Volatility Aggregation
A detailed exploration of how agent fluctuations determine aggregate volatility, challenging established misconceptions and offering new insights.
📄️ Appendix II. Gibrat and Appendix III. The Problems of Percentual Growth Rates
A detailed exploration of Gibrat's law and the issues with using percentual growth rates in firm sales time series analysis.
📄️ Appendix I: Uncertainty Introduced by Off-Diagonal Elements
Explore the uncertainty in aggregate variance estimation due to off-diagonal elements and cross covariance terms.
📄️ Appendix II: Accounting Variance by Frequency
Explore how measuring variables at different frequencies impacts the observed volatility in time series, using Fourier series for analysis.
📄️ Appendix V: Persistence of Firm Size
An exploration into the persistence of firm sizes and the meaningfulness of associating firms to a size value over their lifetime.
📄️ Appendix III: Log-Normal and Log-Laplace
Explore the technical details of log-normal and log-Laplace distributions, including moments and variance calculations.
📄️ Moment of a Log-Normal in the Context of Size Distribution
Explore the derivation of value distribution from population distribution using a log-normal model, emphasizing its application in size distribution analysis.
📄️ Moments of a Log-Laplace
Explore the mathematical derivation and properties of moments in a log-Laplace distribution, including detailed equations and theoretical insights.
📄️ Appendix IV: Computational Experiments
Detailed description of computational experiments for measuring dependence of aggregate idiosyncratic variance with population size.
📄️ Experiment 2: Power Sums
This section details the methodology and execution of Experiment 2, focusing on power sums derived from theoretical distributions, and their statistical analysis.