Industry Aware Firm Level Network Reconstruction

Abstract

A number of recent contributions have put forward the topological structure of production networks as a key determinant of macro-economic dynamics. However, firm-to-firm production networks data is generally not available. Against this background, reconstruction method based on firms' size have been developed. This paper enriches this set of reconstruction methods by integrating input-output sectoral flows in the reconstruction process. We derive analytical expressions for the maximum entropy solutions to the firm network reconstruction problem with sectoral input-output constraints, first for binary networks and then for weight reconstruction. We perform a numerical analysis comparing standard and input-output based reconstruction methods using Hungarian production network data. Our results show that adding input-output constraints substantially reduces deviations from the input-output structure compared with standard methods. Our augmented method provides an almost perfect fit to input-output data, though all methods have difficulties reproducing other structural characteristics.

Figures (4)

• Figure 1: Industry-pair input--output errors for one reconstructed network. Each cell $(S,B)$ shows the relative deviation $(\widehat{s}_{S,B}-s_{S,B})/s_{S,B}$ between reconstructed and target IO flows from sector $S$ to sector $B$. Cells with $s_{S,B}=0$ are omitted (or set to 0) by construction. Positive values indicate over-allocation of flow from $S$ to $B$; negative values indicate under-allocation.
• Figure 2: Comparison of Economic Systemic Risk Index (ESRI) values between the empirical network and reconstructed networks across four methods. Each panel shows a log-log scatter plot of empirical ESRI (x-axis) versus the mean over $10$ realizations of method ESRI (y-axis) for one reconstruction method. Points below $10^{-5}$ on either axis are omitted. The diagonal line ($y=x$) indicates equality between empirical and reconstructed ESRI.
• Figure 3: Comparison of Economic Systemic Risk Index (ESRI) values between the empirical network and reconstructed networks across four methods. Each panel shows a log-log scatter plot of empirical ESRI (x-axis) versus the maximum over $10$ realizations of method ESRI (y-axis) for one reconstruction method. Points below $10^{-5}$ on either axis are omitted. The diagonal line ($y=x$) indicates equality between empirical and reconstructed ESRI.
• Figure 4: Comparison of Economic Systemic Risk Index (ESRI) values between the empirical network and reconstructed networks across four methods. Each panel shows a log-log scatter plot of empirical ESRI (x-axis) versus method ESRI (y-axis) for a single realization for one reconstruction method. Points below $10^{-5}$ on either axis are omitted. The diagonal line ($y=x$) indicates equality between empirical and reconstructed ESRI.

Theorems & Definitions (7)

• Remark 1
• Lemma 2.1: dcGM solves the binary reconstruction problem
• Lemma 2.2: dcIAGM solves the binary reconstruction problem
• Remark 2
• Lemma 3.1: IPF-industry solves the weight reconstruction problem
• Lemma 3.2: MaxEnt baseline
• Lemma 3.3: MaxEnt with sector-pair targets