Monthly Inter-Industry Payment Flows

• Monthly inter-industry payment flows are aggregated measures of firm-to-firm payments that form directed, weighted networks mapping real-time economic interdependence.
• They employ graph-theoretic statistics to uncover structural relationships, systemic hubs, and shock-transmission channels often hidden in aggregate data.
• Network-enhanced forecasting models using these flows significantly improve nowcasting of GDP growth and bilateral payment dynamics.

Monthly inter-industry payment flows are monthly aggregates of payments from firms in one industry to firms in another, typically represented as directed, weighted networks whose nodes are industries and whose edges encode transaction values or counts. In the UK evidence base, these flows are constructed from payment-system data and mapped to industry classifications such as SIC or CPA, yielding high-frequency measures of economic interdependence that complement conventional bilateral time-series views and annual input-output frameworks. Across recent studies, the central analytical claim is that the network representation reveals structural relationships, systemic hubs, and shock-transmission channels that are only weakly visible in aggregate statistics or pairwise flow series alone (Humnabadkar, 2 Apr 2026).

1. Definition and data construction

Monthly inter-industry payment flows begin with transaction-level payment records in which each payment is assigned a payer industry, a payee industry, a date, and an amount. In one UK network study covering January 2017 to November 2024, 532,346 payment records are observed across $n=89$ two-digit SIC sectors and approximately $T \approx 95$ monthly snapshots. For each month $t$, payments from industry $i$ to industry $j$ are aggregated into

$$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$

and a directed, weighted adjacency matrix is defined by

$$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$

To isolate structural patterns from sheer scale, the matrix is row-normalized as

$$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$

so that $\bar A_{ij}(t)$ measures the share of industry $i$’s outflows that go to $T \approx 95$0 (Humnabadkar, 2 Apr 2026).

At finer industrial resolution, another UK study constructs monthly industry-by-industry matrices from anonymized and aggregated Direct Debit and Direct Credit payments drawn from the Bacs system over August 2015 to December 2023. For each month $T \approx 95$1, it forms both a value matrix and a count matrix,

$T \approx 95$2

where $T \approx 95$3 denotes payments in month $T \approx 95$4 from industry $T \approx 95$5 to industry $T \approx 95$6. Industry mapping is obtained by linking anonymized Service User Numbers to Companies House records and extracting 5-digit SIC codes; after statistical disclosure control, roughly 612 industries survive at the granular level, and these are further rolled into 105 CPA classes for benchmarking to official input-output tables (Hötte, 2024).

The more recent public release extends this construction materially. For January 2017 to November 2024 at the full 5-digit SIC level, $T \approx 95$7 industries are indexed and the monthly gross value of flows is written as

$T \approx 95$8

A methodological change of particular importance is that, when a firm has multiple SIC codes on its Companies House record, each payment is attributed equally to each SIC code rather than being assigned only to the first-listed code. The raw data come from both Bacs and the Faster Payment System, and the public release distinguishes “raw” from “cleaned” data, where the latter excludes transactions whose payer or payee cannot be matched to CPA codes used in official input-output tables (Hötte, 25 Aug 2025).

2. Network representation and graph-theoretic observables

The network representation treats industries as nodes and inter-industry payments as directed weighted edges. This permits the use of graph-theoretic statistics that summarize local and system-wide structure. In the two-digit SIC analysis, undirected degree centrality for industry $T \approx 95$9 in month $t$0 is defined as

$t$1

with out-degree and in-degree obtainable analogously from directed links. Betweenness centrality is defined by

$t$2

where $t$3 is the number of shortest paths from node $t$4 to $t$5 and $t$6 is the number of those paths passing through $t$7. This quantifies how often an industry acts as an economic bridge between others. Local clustering for industry $t$8 is

$t$9

and network density is

$i$0

These observables are used as structural summaries of interdependence, integration, and intermediary importance (Humnabadkar, 2 Apr 2026).

At 5-digit granularity, input-share and output-share matrices are central. In the 2025 public-release analysis, the input-share matrix and output-share matrix are

$i$1

These transforms express flows relative to industry input or output totals and are the basis for comparing payment networks to input-output tables and for computing centrality. Katz–Bonacich centrality is then written as

$i$2

with labour share parameter $i$3. The associated interpretation, stated in the source material, is that this centrality captures the propagation of shocks through inter-industry linkages (Hötte, 25 Aug 2025).

A related stylized-fact analysis defines shortest-path distance in the input-share graph and studies how correlations in industry growth decay with network distance. It also studies the complementary cumulative distribution function of Katz–Bonacich centrality and reports approximately linear upper tails on log-log plots. This suggests heavy-tailed influence distributions in the payment network, consistent with the idea that highly central industries can matter disproportionately for aggregate outcomes (Hötte, 2024).

3. Empirical regularities in monthly payment networks

Several empirical regularities recur across the UK studies. At the aggregate time-series level, monthly payment values and counts track broader macroeconomic and payment-system indicators closely. One study reports Pearson correlations, over 2016–2019 and excluding March 2020 to December 2022, of $i$4 between monthly value and Bacs total, $i$5 between monthly value and FPS, $i$6 between monthly value and non-seasonally adjusted GDP, $i$7 between monthly value growth and GDP, $i$8 between monthly count and GDP, and $i$9 between monthly count growth and GDP (Hötte, 2024).

In the expanded public release, monthly aggregates rise materially over the sample. Raw payments rose from approximately £150 bn per month in 2017 to approximately £300 bn per month by late 2024, while cleaned payments rose from approximately £60 bn per month to approximately £120 bn per month. During the Covid-19 episode, counts fell by approximately $j$0 in mid-2020 and values by approximately $j$1. The same study states that the series correlate very strongly with Bacs, CHAPS, FPS, M1, and GDP, with Pearson’s $j$2 on monthly values and $j$3–$j$4 on monthly growth rates for GDP (Hötte, 25 Aug 2025).

At the network level, the 89-sector study reports secular increases in integration. Density $j$5 rises from $j$6 in January 2017 to $j$7 in November 2024, a $j$8 increase. Local clustering averaged across industries grows from $j$9 to $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$0, or $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$1, and average path length shortens from $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$2 to $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$3, or $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$4. The temporary dip in density to $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$5 in 2020 marks the COVID disruption; by early 2022, integration not only recovered but exceeded previous highs (Humnabadkar, 2 Apr 2026).

Granular and benchmarked network summaries show that levels depend strongly on aggregation and truncation. For the 2022 snapshot aggregated to 104 CPA sectors, the value-weighted network in the new public-release analysis has density $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$6, average degree $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$7, reciprocity $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$8, transitivity $$w_{ij}(t)=\sum_{\substack{\text{payments } i\to j \text{ in month } t}} \text{value},$$9, and assortativity by degree $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$0. In the earlier benchmarking exercise for 2019 at 105 nodes, the payment-value network has density $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$1, average degree $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$2, reciprocity $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$3, transitivity $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$4, and assortativity $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$5. Both studies note that truncating low-share links brings payment-network density and clustering much closer to official input-output benchmarks, indicating that the largest linkages are comparatively stable across data constructions (Hötte, 25 Aug 2025).

Systemically important industries can also be identified from centrality rather than raw transaction volume alone. In the 89-sector study, the top three systemic industries by betweenness centrality and volume are Financial Services with $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$6, Wholesale Trade with $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$7, and Professional Services with $$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$8. The paper states that these sectors serve as critical intermediaries and that their network positions carry predictive power for systemic stress propagation (Humnabadkar, 2 Apr 2026).

4. Forecasting payment flows and nowcasting output

A major use of monthly inter-industry payment flows is forecasting. In the 89-sector study, the target variable is quarter-on-quarter growth in bilateral payments, adapted to a monthly context as

$$A(t)=\bigl[A_{ij}(t)\bigr]_{i,j=1}^{n}, \qquad A_{ij}(t)= \begin{cases} w_{ij}(t), & \text{if } w_{ij}(t)>0,\ 0, & \text{otherwise.} \end{cases}$$9

The baseline forecasting model is a univariate AR(2) with seasonality and industry-pair fixed effects,

$$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$0

while the network-enhanced specification augments this with contemporaneous network features such as degree, betweenness, clustering, and density,

$$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$1

Using an expanding-window scheme, traditional features alone yield out-of-sample $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$2, whereas adding network features raises $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$3 to approximately $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$4, an improvement of $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$5 percentage points. During the COVID-19 shock from March 2020 to December 2021, traditional $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$6 falls to $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$7, while the network-enhanced model achieves $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$8, for a gain of $$\bar A_{ij}(t)=\frac{A_{ij}(t)}{\sum_{k=1}^n A_{ik}(t)}, \qquad \sum_j \bar A_{ij}(t)=1,$$9 percentage points. These gains are reported as highly significant by Diebold–Mariano tests with $\bar A_{ij}(t)$0 and $\bar A_{ij}(t)$1 (Humnabadkar, 2 Apr 2026).

A complementary nowcasting framework is provided by the extended generalised network autoregressive model, GNAR-ex, designed for networks with time-varying edge weights and nodal time series. In this setup, nodal series are industry-level GVA growth,

$\bar A_{ij}(t)$2

and edge series are payment growth,

$\bar A_{ij}(t)$3

The model exploits node-neighbour and edge-neighbour relations on a fixed topology and estimates autoregressive, network-autoregressive, and cross-series coupling parameters jointly by ordinary least squares after stacking node and edge equations into a restricted VAR($\bar A_{ij}(t)$4). To guard against GDP-revision bias, the model is fit separately on each of nine quarterly ONS vintages from December 2021 to December 2023, and model selection over lag and neighbourhood order is based on out-of-sample nowcast error on earlier vintages (Mantziou et al., 2024).

The empirical role of payment flows in GNAR-ex is explicit. GDP growth $\bar A_{ij}(t)$5 depends on lagged payment growth from the industry’s immediate suppliers and customers through edge-coupling parameters and on higher-order neighbours through additional network effects. The study states that including payment flows reduces quarterly nowcast RMSE of aggregate GDP by $\bar A_{ij}(t)$6–$\bar A_{ij}(t)$7 relative to best ARIMA benchmarks, and that at the industry level the gain can exceed $\bar A_{ij}(t)$8 for sectors with volatile inter-industry linkages such as Construction and Transport. It also notes that the network parameters admit direct economic interpretation: a positive first-stage neighbour coefficient indicates that lagged GDP shocks in direct neighbours accelerate GVA growth in the focal industry, whereas a negative coefficient would indicate competition effects (Mantziou et al., 2024).

5. Relation to official statistics and input-output accounting

Monthly inter-industry payment flows are often evaluated against official input-output tables, GDP, and payment-system aggregates rather than treated as direct replacements for them. The benchmarking exercise using 5-digit SIC data aggregated to CPA classes compares annual payment matrices to the ONS “Combined Use” table and to analytical Industry$\bar A_{ij}(t)$9Industry and Product$i$0Product symmetric tables. Edge-level Pearson correlations of input shares between payments and ONS tables for 2018–2019 range from $i$1 to $i$2, while output-share correlations are weaker at $i$3 to $i$4. By contrast, industry-level correlations of total inputs or outputs exceed $i$5 in most cases. This indicates that alignment is stronger for node totals than for fine-grained bilateral structure (Hötte, 2024).

The later public-release analysis reports stronger correspondence. For 2018–2022, link-level Pearson correlations between log-flows in the payment-value network and PxP or IxI edges are approximately $i$6–$i$7, compared with approximately $i$8–$i$9 in the earlier dataset. Output-share correlations exceed input-share correlations at approximately $T \approx 95$00 versus $T \approx 95$01. Industry-level row and column sum correlations are reported at approximately $T \approx 95$02–$T \approx 95$03 for inputs and $T \approx 95$04–$T \approx 95$05 for outputs, while growth-rate correlations remain strong for inputs in 2021–2022 but weak for output during Covid years (Hötte, 25 Aug 2025).

Conceptual mismatches between payment data and national accounts are central to interpretation. The documented issues include time of recording, because payments record cash clearing dates while supply-use tables are on an accrual basis; capital formation, because fixed-asset purchases and debt repayments appear in payments but are excluded from intermediate consumption; financial services, because payments record full credit flows whereas national accounts record only financial intermediation services indirectly measured; trade and transport margins, because supply-use tables reallocate margins while payments often move through intermediaries; distributive flows such as taxes, subsidies, and dividends, which appear in payments but are outside intermediate use; international trade, because only domestic sterling payments via Bacs are observed; and classification problems arising from multi-product firms or head-office coding (Hötte, 2024).

These constraints have motivated proposals for integration rather than substitution. Suggested uses include treating monthly payment matrices as experimental proxies for real-time intermediate demand, applying top-down balancing to adjust for FISIM, margins, gross fixed capital formation, and trade misalignments, combining value and count dimensions, extending classification to multi-SIC coding, and embedding payment flows as a monthly “nowcasted” input-output-table component in national accounts, cross-validated against surveys and VAT data. A plausible implication is that payment-flow systems are most informative when interpreted as high-frequency structural indicators that are mapped back to national-accounting concepts with explicit adjustment layers rather than as raw one-to-one measures of intermediate use (Hötte, 2024).

6. Interpretative issues, limitations, and research directions

The empirical promise of monthly inter-industry payment flows is accompanied by identifiable measurement and modeling limitations. Statistical disclosure control suppresses cells below minimal count or value thresholds, which removes small-volume links and firms with very few payments. Coverage bias remains industry-specific, with some sectors overrepresented and others underrepresented. In the public-release analysis, approximately $T \approx 95$06 of payments remain unclassified because of non-CPA-mappable Companies House codes or non-matched accounts, and high-value flows are disproportionately associated with non-matched accounts. Time-of-recording biases remain unquantified, and no direct deflators are applied to $T \approx 95$07, so price adjustments and inflation often require separate modeling (Hötte, 25 Aug 2025).

Methodological choices also matter substantively. One nowcasting study removes six sectors with known data-quality or conceptual mismatches to GDP, retains zero-flow edges in a static topology, and removes edges whose monthly payment series correlate with aggregate GDP growth above $T \approx 95$08 to avoid collinearity, leaving $T \approx 95$09 edges. Missing flows due to single-month pipeline delays are linearly interpolated in growth-rate form, whereas persistent zero-flow months remain coded as zero. The same study reports that no further penalization such as Lasso was needed in practice. These steps affect the effective network, the stability of coefficient estimates, and the interpretation of neighbour effects (Mantziou et al., 2024).

Despite these constraints, the research trajectory is converging on several directions. Official-statistics production may benefit from rolling monthly adjacency matrices, a compact set of stable network features such as degree, betweenness, clustering, and density, and automated pipelines that update within days of raw data arrival. Additional proposed extensions include combining rolling public releases to build a continuous time series back to 2015 and forward, investigating unclassified payments through partial matches, incorporating historical Companies House snapshots to correct firm entry and exit biases, developing seasonality filters directly for payment flows, exploring transaction counts as indicators of demand and price rigidities, and extending the framework to regional and cross-border payment flows (Humnabadkar, 2 Apr 2026).

A recurring misconception is that these datasets merely reproduce aggregate turnover or replicate input-output tables at higher frequency. The evidence does not support that view. The payment studies repeatedly show that network features carry incremental information beyond bilateral time-series behavior, that the strongest links are comparable to official structures while weak links differ materially by construction and disclosure rules, and that network-enhanced models perform particularly well when traditional temporal regularities break down. This suggests that the principal value of monthly inter-industry payment flows lies in their capacity to measure evolving economic topology in real time, especially during disruption, rather than in serving as a frictionless substitute for established macroeconomic accounts (Humnabadkar, 2 Apr 2026).