Supply Chain Networks Shrink Your Effective Sample Size

Key findings

• The supplied network contains repeated economic clusters such as Micron and SK Hynix around Nvidia and Shin-Etsu around several semiconductor manufacturers, so many stock rows can still reflect a smaller set of common shocks.
• Network econometrics provides inference methods for observations connected through an observed graph, supporting network-aware or clustered treatment of standard errors rather than assuming every company observation is independent.

Research question: How should a quant think about effective sample size, standard errors, and event counts when supply chain relationships make cross-sectional stock observations statistically dependent?

No. One thousand stocks can represent far fewer than one thousand independent observations when common customers, suppliers, industries, and bottlenecks make their returns and forecast errors move together. Effective sample size should reflect those clusters rather than raw row count.

The graph itself tells you why observations are dependent

The supplied Altsets network gives several concrete examples. Micron and SK Hynix both map to Nvidia as a customer, so the two suppliers share an obvious source of demand information. Shin-Etsu Chemical maps to Samsung Electronics, TSMC, and Intel, with displayed supplier revenue shares of 2.43%, 4.02%, and 1.79% respectively. Those are distinct customer relationships, but the customers also participate in the same semiconductor manufacturing cycle. A cross-sectional strategy that owns or studies all of these companies does not have a set of economically isolated bets.

This matters when a researcher reports significance from a factor regression or a long-short portfolio. If several stocks move because the same customer or industry shock reached them through the network, the sample contains clustered information. Adding more connected stocks can increase the row count without increasing the amount of independent evidence by the same amount. The issue is not unique to supply chains. The advantage of the graph is that it gives the researcher an observed structure for defining where some of that dependence may come from.

Network dependence can change the standard error even when the coefficient stays the same

Econometric research explicitly studies random variables whose dependence arises from an observed network. Kojevnikov, Marmer, and Song develop limit theory and network-HAC standard errors for settings where observations are connected and dependence decays through the network. The practical implication for a supply chain quant is straightforward: ordinary heteroskedasticity-robust errors can be too optimistic if residuals remain correlated among economically connected firms.

A first diagnostic can be much simpler than a full network-HAC implementation. After fitting a cross-sectional model, calculate whether residuals remain more correlated among direct customer-supplier pairs, companies sharing a customer, or companies inside the same network cluster than among random matched pairs. If the residual dependence is strong, the researcher should be skeptical of significance estimates that assume independent cross-sectional errors. Clustered errors by industry may help, but they can still miss cross-industry relationships such as HPE and Nvidia both connecting to Microsoft.

Effective sample size should be thought of in shocks as well as stocks

Suppose a strategy tests supplier reaction to customer earnings across 200 supplier observations. If 70 of those observations come from suppliers tied to the same ten customers, the economically independent event count can be much closer to ten customer shocks than to seventy separate experiments. The exact effective sample size depends on the correlation structure and cannot be read directly from the graph, but the network can reveal when a headline observation count is misleading.

This becomes especially important in event studies. A single Nvidia earnings report can generate observations for Micron, SK Hynix, and other connected companies. Those supplier responses are valuable cross-sectional information about exposure differences, but they do not create several independent Nvidia earnings events. Statistical inference should recognize the event cluster even if the portfolio contains several securities. Counting stocks instead of shocks can make a small event sample appear much larger than it is.

Train-test splits can inherit the same dependence problem

Network dependence affects validation as well as standard errors. If companies connected to Nvidia appear in both training and test sets, the model can benefit from economic similarities shared across the split. That can be intentional when the deployment universe contains the same cluster, but it should not be confused with broad generalization. Likewise, a test period containing hundreds of stock-month observations can still be dominated by a small number of common macro or network shocks.

A stronger research report can therefore state several sample sizes: number of security observations, number of unique companies, number of unique relationship pairs, number of major customer or supplier events, and number of independent time periods or network clusters. None of those is a perfect effective-sample-size formula, but together they provide a much more honest picture than one giant row count. The researcher can then use clustered, block, or network-aware inference appropriate to the hypothesis.

Calculate effective sample size for the estimator being reported

For an equal-weight mean of $N$ residual outcomes, with residual variances $\sigma_i^2$ and correlations $\rho_{ij}$, define effective sample size by matching the mean's variance to that of independent observations with the same average residual variance:

$$N_{\mathrm{eff}}= N\frac{\sum_i\sigma_i^2} {\sum_i\sigma_i^2+2\sum_{i<j}\sigma_i\sigma_j\rho_{ij}}.$$

Under equal residual variances, this becomes

$$N_{\mathrm{eff}}=\frac{N}{D_G},\qquad D_G=1+\frac{2}{N}\sum_{i<j}\rho_{ij}.$$

This is an estimator-specific variance comparison, rather than a universal number of independent firms in the graph. Equal clusters of size $m$ with within-cluster correlation $\rho$ give the familiar design effect $1+(m-1)\rho$. An average of $d$ correlated neighbors per firm with common residual correlation $\rho$ gives $D_G=1+d\rho$. For example, 500 firms, ten correlated neighbors per firm, and 2% residual correlation imply a design effect of 1.20 and about 417 independent-observation equivalents. Those are illustrative assumptions, not estimated correlations.

Economic weights can change a dependence calibration

A selected four-firm Altsets subgraph centered on Samsung illustrates why industry and network adjustment can differ. Intel, AMD, Qualcomm, and Broadcom have six possible pairs. In the September 2026 selected graph, five share a same-direction Samsung channel. An industry cluster treats all six as connected; the binary network treats five as connected; directional weights allow their intensities to differ.

Hold the strongest pair's assumed residual correlation at 5% and scale weaker pairs using their relationship kernels. The calibrated effective counts are 3.478 under industry clustering, 3.556 under the binary network, 3.697 under Relationship Size weighting, and 3.859 under directional-percentage weighting, compared with four under independence. The difference isolates covariance geometry while holding maximum correlation fixed. It does not establish that the directional estimate is the true effective sample size: the correlations are assumed for this exercise, not measured from returns.

For an empirical test, remove market, style, and leave-one-out industry effects before estimating pairwise residual dependence. Use lagged network snapshots to forecast subsequent residual covariance and compare industry, binary-distance, and economically weighted specifications out of sample. Supplier Revenue % is the natural demand-side exposure for suppliers sharing a customer; Customer Cost % is the corresponding supply-side exposure for customers sharing a supplier. The covariance model develops that distinction.

Challenge the result with degree-preserving rewired graphs and direction-swapped weights. If these placebos forecast covariance as well as the actual, correctly oriented graph, the commercial-transmission interpretation weakens. If network adjustment adds little after industry controls, the effective count can remain close to nominal. Report the covariance assumptions alongside the count, and retain event- or time-block inference where one common shock generates many firm observations.

Rows are not the same thing as independent evidence

Supply chain data can expand a quant dataset dramatically because one event can connect to many firms. That is analytically useful, but it can also create false confidence if every connected row is treated as a new independent experiment. The graph should be used not only to build features, but also to identify where the observations themselves are statistically dependent. A model supported by many companies, many distinct network clusters, and many independent events is much stronger than one whose impressive sample size comes mostly from repeating the same underlying shock across connected firms.

The graph-aware validation guide explains how connected firms can leak economic similarity across train and test sets. The event-study guide explains why several supplier reactions to one customer event should still be recognized as one event cluster.

Sources

• Altsets supply chain dataset
• Limit theorems for network dependent random variables
• Supply Chain and Correlation

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Methodology

Read the methodology for this research.

Cite this research

Altsets Research. "Supply Chain Networks Shrink Your Effective Sample Size." Published September 26, 2026. https://www.altsets.com/research/network-dependence-effective-sample-size

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