Reading Guide to the Aggregation Section
This page is a navigation map for the Aggregation section.
The section can be read in different ways depending on what you are looking for. Some readers may want a short conceptual overview. Others may want the data first, or the main theoretical mechanism, or the technical appendices.
Start here
If you are new to this section, begin with these pages:
- Aggregation of Firm-Level Exports and Imports
- Introduction to Aggregate Volatility
- Overview of Sections and Core Contributions
- Conclusion on Volatility Aggregation
Reading routes
Route A. New reader in 20 minutes
A short path for broad audiences.
- Aggregation of Firm-Level Exports and Imports
- Introduction to Aggregate Volatility
- Overview of Sections and Core Contributions
- Data and Methods
- Conclusion on Volatility Aggregation
Route B. Economist route
A path for readers interested in aggregate volatility, diversification, trade concentration, and firm heterogeneity.
- Introduction to Aggregate Volatility
- Related Works
- The Quest for Volatility
- Reviewing the Diversification Issues
- Firms are not Sectors
- Origin of Departure from LLN
- Conclusion on Volatility Aggregation
Route C. Empirics-first route
A path for readers who want the data, empirical patterns, and measured components first.
- Data and Methods
- Key Empirical Features: Distribution of Firm Sizes and Fluctuations
- Size Distribution of Firms
- Firm Level Fluctuations
- Acknowledging Entry and Exit Events
- Estimated Dependence of Components
Route D. Full theory route
A path for readers who want the conceptual and mathematical backbone.
- Mathematical Framework: Aggregate Volatility in Log Scale
- Non-Linearities
- Micro to Macro Fluctuations
- Firms are not Sectors
- Dependence of Variance with Population Size
- Variance of Parts' Time Series Mean (The Law of Large Numbers)
- Understanding Comovements and Variance in Large Numbers
- Origin of Departure from LLN
- Conclusion on Volatility Aggregation
Section clusters
1. Motivation and orientation
- Aggregation of Firm-Level Exports and Imports
- Introduction to Aggregate Volatility
- Overview of Sections and Core Contributions
2. Literature and economic motivation
- Related Works
- The Quest for Volatility
- Network Effects
- Further Literature Comments
- Reviewing the Diversification Issues
3. Data and empirical foundations
- Data and Methods
- Key Empirical Features: Distribution of Firm Sizes and Fluctuations
- Size Distribution of Firms
- Firm Level Fluctuations
4. Core framework
- Mathematical Framework: Aggregate Volatility in Log Scale
- More about Partitions
- Simple Structure of Sectoral Sales
- Non-Linearities
- Mean and Variance of Transformed Random Variables
- Micro to Macro Fluctuations
- Firms are not Sectors
- Log Aggregate Deviations and Sectoral Contributions
5. Diversification, population size, and covariance structure
- Reviewing the Diversification Issues
- Dependence of Variance with Population Size
- Aggregating a Group of Agents: Sum of Powers
- Mandelbrot and Sensitivity in Size Distributions
- Expected Level of Parts' Time Series
- Micro Fluctuations and Moments
- Analysis of Log Quantile Levels
- Variance of Parts' Time Series Mean (The Law of Large Numbers)
- Understanding Comovements and Variance in Large Numbers
- Variance as a Function of Micro Moments
- Origin of Departure from LLN
- Moments of Log Quantile Levels
6. Extensions and realism checks
- Acknowledging Size Distribution
- Acknowledging Entry and Exit Events
- Estimated Dependence of Components
- Classification of Matrix Elements and Their Impact on Variance
7. Appendices and technical support
- Appendix II. Gibrat and Appendix III. The Problems of Percentual Growth Rates
- Appendix I: Uncertainty Introduced by Off-Diagonal Elements
- Appendix II: Accounting Variance by Frequency
- Appendix V: Persistence of Firm Size
- Appendix III: Log-Normal and Log-Laplace
- Moment of a Log-Normal in the Context of Size Distribution
- Moments of a Log-Laplace
- Appendix IV: Computational Experiments
- Experiment 2: Power Sums
If you want only the main line
If you want the shortest route that still captures the main argument, read these pages in order:
- Introduction to Aggregate Volatility
- Data and Methods
- Firm Level Fluctuations
- Mathematical Framework: Aggregate Volatility in Log Scale
- Firms are not Sectors
- Reviewing the Diversification Issues
- Understanding Comovements and Variance in Large Numbers
- Origin of Departure from LLN
- Conclusion on Volatility Aggregation
If you want the technical backup
These pages provide supporting derivations, robustness arguments, and simulation details:
- Moments of Log Quantile Levels
- Appendix I: Uncertainty Introduced by Off-Diagonal Elements
- Appendix II: Accounting Variance by Frequency
- Appendix V: Persistence of Firm Size
- Appendix III: Log-Normal and Log-Laplace
- Moment of a Log-Normal in the Context of Size Distribution
- Moments of a Log-Laplace
- Appendix IV: Computational Experiments
- Experiment 2: Power Sums