How to Use VSTACK and LAMBDA to Author Dynamic Concentration Deficit Index Models in Microsoft Excel

In market structure analysis and regulatory economics, antitrust authorities often evaluate how far an industry’s market share distribution diverges from a completely egalitarian benchmark (where all firms hold an equal share 1/N). The Concentration Deficit Index (CDI) computes the cumulative deficit between an industry’s observed cumulative concentration curve and an ideal benchmark curve. By utilizing dynamic array functions—specifically VSTACK, HSTACK, LAMBDA, LET, and SCAN—analysts can construct dynamic CDI models in Microsoft Excel without legacy VBA macros.

Mathematical Formulation of the Concentration Deficit Index

Let an industry have N competitors sorted in descending order of market share: s₁ ≥ s₂ ≥ … ≥ s_N, where ∑ s_i = 1. The observed cumulative concentration of the top k firms is C_k = ∑_{i=1}^k s_i. In a perfectly equal market of N competitors, the expected cumulative share is E_k = k / N.

The Concentration Deficit Index (CDI) measures the normalized area between the observed Lorenz concentration curve and the egalitarian diagonal:

CDI = (1 / (N - 1)) * ∑_{k=1}^{N-1} (C_k - k / N)

CDI ranges between 0.0 (perfect equality where every firm holds exactly 1/N) and 1.0 (pure monopoly where one firm holds 100% and remaining competitors hold zero). Unlike the standard Gini coefficient, the CDI weights early concentration among the leading firms directly.

Creating the Reusable LAMBDA Function in Name Manager

In modern Excel (Microsoft 365 or Excel 2024), navigate to Formulas > Name Manager and define a defined name titled CONCENTRATION_DEFICIT with the following dynamic formula:

=LAMBDA(shares,
    LET(
        clean, FILTER(shares, (shares > 0) * ISNUMBER(shares)),
        sorted, SORT(clean, 1, -1),
        tot, SUM(sorted),
        norm_shares, sorted / tot,
        n, ROWS(norm_shares),
        IF(n <= 1, 1,
            LET(
                cum_c, SCAN(0, norm_shares, LAMBDA(acc, val, acc + val)),
                cum_c_cut, TAKE(cum_c, n - 1),
                k_seq, SEQUENCE(n - 1, 1, 1, 1),
                egal_seq, k_seq / n,
                diff_sum, SUM(cum_c_cut - egal_seq),
                cdi, diff_sum / (n - 1),
                cdi
            )
        )
    )
)

This dynamic formula dynamically calculates cumulative sums via SCAN, computes ideal egalitarian sequences, and resolves the deficit area.

Constructing the Full Dynamic Scorecard with VSTACK

Assume firm market revenues are recorded in cells A2:A12. In cell C2, input this self-contained reporting formula:

=LET(
    revs, A2:A12,
    cdi_val, CONCENTRATION_DEFICIT(revs),
    clean_revs, FILTER(revs, (revs > 0) * ISNUMBER(revs)),
    sorted_revs, SORT(clean_revs, 1, -1),
    tot_rev, SUM(sorted_revs),
    n, ROWS(sorted_revs),
    cr4, SUM(TAKE(sorted_revs, 4)) / tot_rev,
    hhi, SUM((sorted_revs / tot_rev)^2) * 10000,
    
    header, HSTACK("Antitrust Metric", "Computed Value", "Benchmark Interpretation"),
    r1, HSTACK("Concentration Deficit Index (CDI)", ROUND(cdi_val, 4), IF(cdi_val > 0.5, "Severe Oligopolistic Deficit", IF(cdi_val > 0.25, "Moderate Concentration", "Competitive"))),
    r2, HSTACK("Active Competitor Count (N)", n, "Total competing firms"),
    r3, HSTACK("CR4 Concentration Ratio", TEXT(cr4, "0.0%"), IF(cr4 > 0.6, "Dominant Top-4 Leadership", "Dispersed")),
    r4, HSTACK("Herfindahl Index (HHI)", ROUND(hhi, 1), IF(hhi > 1800, "Highly Concentrated", "Unconcentrated")),
    
    VSTACK(header, r1, r2, r3, r4)
)

Analytical Advantages in Merger Analysis

1. Continuous Area Metric: Measures the entire geometry of the concentration curve rather than relying on an arbitrary four-firm or eight-firm cutoff point.
2. Instant Spilled Updates: Modifying quarterly sales figures automatically updates the entire dashboard with zero manual recalculation.
3. Universal Portability: 100% macro-free formula architecture that functions flawlessly across desktop, web, and mobile Excel clients.