How to Use VSTACK and LAMBDA to Author Dynamic Comprehensive Concentration Index (CCI) Models in Microsoft Excel

Antitrust regulators and industrial economists evaluating market dominance frequently encounter situations where conventional measures provide incomplete insights. The Herfindahl-Hirschman Index (HHI) squares all market shares equally, while concentration ratios like CR4 ignore the distribution among the leading firms. Horvath’s Comprehensive Concentration Index (CCI) resolves this dilemma by explicitly separating the market share of the leading firm from the dispersion of remaining competitors. This guide demonstrates how to author dynamic CCI models in Microsoft Excel using VSTACK, LAMBDA, LET, and SORT.

Mathematical Formulation of Horvath’s CCI

Let an industry have N competitors sorted in descending order of market share: s₁ ≥ s₂ ≥ … ≥ s_N, where ∑ s_i = 1. Horvath defined the Comprehensive Concentration Index as:

CCI = s_1 + ∑_{i=2}^N (s_i)^2 * (2 - s_i)

In this formulation, the market leader’s share s₁ enters the index with full weight, reflecting immediate unilateral pricing power. Each subsequent competitor’s share s_i is weighted by (2 - s_i), ensuring that unequal distributions among the trailing rivals contribute proportionally to overall market power. CCI ranges between (3N – 2) / N² for perfectly equal competitors and 1.0 for a complete monopoly.

Creating the Reusable LAMBDA Function in Name Manager

In modern Excel (Microsoft 365 or Excel 2024), navigate to Formulas > Name Manager. Click New, enter the name HORVATH_CCI, and define the formula as follows:

=LAMBDA(shares,
    LET(
        clean, FILTER(shares, (shares > 0) * ISNUMBER(shares)),
        sorted, SORT(clean, 1, -1),
        total, SUM(sorted),
        norm_shares, sorted / total,
        n, ROWS(norm_shares),
        leader_share, INDEX(norm_shares, 1),
        IF(n = 1, 1,
            LET(
                rest_shares, DROP(norm_shares, 1),
                tail_sum, SUM((rest_shares ^ 2) * (2 - rest_shares)),
                cci, leader_share + tail_sum,
                cci
            )
        )
    )
)

This dynamic formula automatically cleans blanks and invalid characters, sorts competitors in descending order, extracts the leader’s share, and dynamically computes the trailing polynomial sum.

Building the Dynamic Anti-Trust Summary Table with VSTACK

Assume participant revenues are stored in cells A2:A12. In cell C2, insert this self-contained reporting formula:

=LET(
    revs, A2:A12,
    cci_val, HORVATH_CCI(revs),
    clean_revs, FILTER(revs, (revs > 0) * ISNUMBER(revs)),
    sorted_revs, SORT(clean_revs, 1, -1),
    tot_rev, SUM(sorted_revs),
    s1, INDEX(sorted_revs, 1) / tot_rev,
    hhi, SUM((sorted_revs / tot_rev)^2) * 10000,
    cr4, SUM(TAKE(sorted_revs, 4)) / tot_rev,
    
    header, HSTACK("Economic Metric", "Computed Value", "Market Classification"),
    r1, HSTACK("Horvath Comprehensive Index (CCI)", ROUND(cci_val, 4), IF(cci_val > 0.5, "Dominant Leader Market", IF(cci_val > 0.3, "Moderate Concentration", "Competitive"))),
    r2, HSTACK("Leader Share (s1)", TEXT(s1, "0.0%"), IF(s1 > 0.4, "Presumed Market Dominance", "Shared Leadership")),
    r3, HSTACK("Herfindahl Index (HHI)", ROUND(hhi, 1), IF(hhi > 1800, "Highly Concentrated", "Unconcentrated")),
    r4, HSTACK("CR4 Ratio", TEXT(cr4, "0.0%"), IF(cr4 > 0.7, "Tight Oligopoly", "Loose Oligopoly")),
    
    VSTACK(header, r1, r2, r3, r4)
)

Analytical Advantages of Horvath’s Model

1. Asymmetric Market Power: Directly accounts for the outsized competitive leverage of a dominant market leader while accurately reflecting the degree of rivalry among remaining participants.
2. Instant Spilled Recalculation: Adjusting competitor sales numbers dynamically updates the entire analysis dashboard without manual formula dragging.
3. Universal Office Compatibility: Functions seamlessly in browser-based Excel without requiring macro security exceptions or add-ins.