Purpose

Business PhD and DBA dissertations often combine repeated company records with financial, governance, or strategic measures. This workflow turns a synthetic unbalanced firm-year archive into an auditable analysis. The example relates a digital-capability index to return on assets (ROA), separating within-firm changes from persistent differences between firms.

Public preview: Outputs and guidance only. The paid version includes all editable R Markdown, reusable functions, synthetic data, analysis code, and exported results.

You will audit panel keys and sample construction, compare pooled, fixed-effect, random-effect, and correlated-random-effect specifications, calculate firm-clustered uncertainty, build calendar-aware lags, examine influence, and write results in substantive units. Prerequisites are regression, basic R, and knowledge of the data source. These are associational models unless a separate research design justifies causal identification.

Settings and synthetic archive

For your archive, switch use_synthetic to FALSE and provide the dictionary’s columns. Save the original extract unchanged. Document the vendor, download date, identifier mapping, fiscal-year conventions, currency conversion, deflators, restatements, delistings, and inclusion rules. Ratios require explicit denominator checks; do not silently map undefined ratios to zero. No proprietary database or access credentials are included.

Missingness in observed records; absent firm-year records are audited separately.
variable missing percent
firm 0 0.000
year 0 0.000
sector 0 0.000
digital 0 0.000
log_assets 0 0.000
leverage 98 3.785
roa 0 0.000

Audit before modeling

Coverage, entry, exit, and missingness

statistic value
Observed firm-years 2589
Distinct firms 240
Calendar years 12
Firms with internal gaps 65
Firms not observed in final archive year 43

A missing row may represent entry, exit, a delisting, a reporting gap, or a merge failure. These cannot be distinguished from row presence alone. This example has quality-related early exit, delayed entry, intermittent gaps, and modest missing leverage. In real data, consult the source’s status records. Restricting to balanced panels can introduce survivorship bias.

Common estimation sample

All primary models use the same complete-case sample and minimum-year rule. The rule is transparent, not a universal threshold. Missing-data assumptions still need justification. Multiple imputation must respect firm structure and substantive models; a generic single-level imputation is not implemented here.

Within SD uses deviations from firm means and N minus number-of-firms degrees of freedom.
stage rows firms
Observed archive 2589 240
Complete required fields 2491 240
Minimum complete years per firm 2491 240
variable overall_sd between_sd within_sd
roa 4.322 3.711 2.377
digital 1.323 0.956 0.971
log_assets 0.706 0.623 0.363
leverage 0.128 0.076 0.108

The main analysis uses 2491 firm-years from 240 firms. Within-firm variation in the digital index is 0.97; between-firm SD is 0.96. These are different sources of information. Time-invariant sector effects cannot be separately estimated alongside firm fixed effects.

Compare panel specifications

Digital-index slope; all models use a common sample and firm-clustered uncertainty.
Model What it combines or controls Key limitation
Pooled OLS + year + sector Within and between contrasts Persistent unobserved firm quality can confound slopes
Firm and year fixed effects Within-firm changes net of common year effects Does not remove time-varying confounding or reverse causality
Random intercept + year + sector Within and between information under an orthogonality assumption Firm effects must be uncorrelated with regressors
Mundlak correlated random effects Adds firm means of time-varying regressors Mean adjustment is a modeling assumption, especially with selection/unbalanced histories
model term estimate std_error p lower upper
Pooled OLS digital 1.845 0.049 p < .001 1.748 1.942
Firm + year FE digital 1.419 0.044 p < .001 1.332 1.506
Random effects digital 1.729 0.045 p < .001 1.640 1.819
Mundlak CRE digital 1.419 0.044 p < .001 1.332 1.506

Results text: With firm and year fixed effects, a one-point increase in the digital-capability index within a firm was associated with a 1.42-percentage-point difference in ROA, 95% CI [1.33, 1.51], p < .001, conditional on log assets and leverage. This is not the effect of assigning a firm to adopt a technology.

Correlated effects and inference

The Mundlak specification adds firm means of all time-varying regressors, including year indicators because observation histories are unbalanced. Its within slopes should agree closely with fixed effects in this linear setup. This agreement checks implementation; it does not prove causality. A cluster-robust joint test of the added means can inform the random-effect orthogonality assumption, but does not choose a model automatically.

test F df1 df2 p
Added means jointly zero 24.736 14 239 p < .001
check value
Absolute FE vs CRE digital-slope difference 0

The approximate robust joint test gives p < .001. Clustered errors allow heteroskedasticity and arbitrary dependence within firms while relying on sufficiently many independent firms. They do not fix omitted variables. The random-effect tables use an Arellano HC1 group-clustered covariance and a firms-minus-one t reference; the fixed-effect tables use fixest’s cluster small-sample adjustments. Small numerical differences in uncertainty are expected. The plain RE model uses Swamy–Arora variance components; CRE uses Wallace–Hussain because the additional means make a separate between-regression variance-component calculation rank deficient.

Dependence and residual diagnostics

test statistic p
Panel BG serial-correlation test, order 1 149.493 p < .001
Pesaran cross-sectional-dependence test -2.487 p = .013

Diagnostics are prompts to investigate design and model adequacy. They are not pass/fail certificates or a reason to switch uncertainty procedures until significance appears. Firm clustering does not cover dependence between firms. Year fixed effects absorb common mean shocks, not all residual cross-firm correlation. With only 12 years, two-way clustering by firm and year or long-T corrections can have weak small-sample behavior. Industry shocks may require clustering at a broader assignment/exposure level with enough independent clusters.

Calendar-aware lags

Using the previous row as a lag is wrong when years are missing. The helper requires the same firm and exactly one calendar year between records. A lagged digital measure can clarify timing, but does not make the exposure exogenous. Do not add a lagged dependent variable to a short-panel fixed-effect model without addressing dynamic-panel bias.

model term estimate std_error p lower upper
Current digital, lag-eligible sample digital 1.445 0.048 p < .001 1.35 1.539
Prior-year digital, lag-eligible sample lag_value -0.082 0.060 p = .171 -0.20 0.036

The lag comparison uses 2106 firm-years from 239 firms. Re-estimating the contemporaneous model on the same lag-eligible sample helps separate a timing change from a sample change. Covariate and outcome missingness may create additional lag gaps, so sample attrition must be reported.

Sensitivity and influence

Prespecified winsorization and balanced-history comparison

Winsorization changes values and may hide valid extreme firms. Here it is a transparent sensitivity check, not the default analysis. Cutoffs are computed across the common sample, not within year; record that decision. The balanced-history comparison changes the sampled population and is not inherently less biased.

Pooled-sample winsorization cutoffs.
model term estimate std_error p lower upper
Original common sample digital 1.419 0.044 p < .001 1.332 1.506
Winsorized sensitivity digital 1.418 0.046 p < .001 1.328 1.508
Complete full-history firms digital 1.511 0.086 p < .001 1.338 1.684
variable lower upper
roa 7.731 28.012
digital 2.921 8.995
log_assets 6.534 9.764
leverage 0.107 0.657

There are 49 full-history firms in the complete-case sample. The full-history estimate is included above, with a different sample composition. Select an outlier policy using the measurement process and a preregistered analysis plan, not the desired p-value.

Leave-one-firm-out estimates

Largest changes from omitting one firm; investigate, do not automatically remove.
omitted_firm estimate change
63 1.427 0.008
201 1.426 0.007
227 1.412 -0.007
10 1.413 -0.007
105 1.426 0.006
113 1.413 -0.006
27 1.413 -0.006
216 1.413 -0.006

The largest absolute slope change after removing one firm was 0.008 ROA percentage points per index point. Influential firms may be substantively important, erroneous, or differently measured. Document investigations rather than deleting them mechanically.

Reporting checklist

  • Identify the data vendor/source, extract date, permissions, fiscal-year alignment, units, and stable firm identifiers.
  • Record duplicate resolution, mergers, restatements, denominator checks, exclusions, and missingness handling.
  • Show sample flow, year coverage, firm counts, and within/between variation.
  • Explain the estimand, included fixed effects, time-varying controls, and identifying assumptions.
  • Distinguish percentage points from percent changes: ROA here is already on a percentage-point scale.
  • Specify the covariance estimator and clustering level; report coefficients, uncertainty, and substantive magnitude.
  • Report sensitivity to timing, sample composition, extreme values, and firm influence.
  • Keep associations separate from causal effects and retain reproducibility records.

When this workflow is not enough

Dynamic panels, endogenous regressors, selection into listing or survival, changing industry classification, nonrandom missing outcomes, rare binary outcomes, counts, and staggered treatment rollouts need specialized extensions. Arellano–Bond/system GMM requires attention to instrument proliferation, serial-correlation restrictions, and weak instruments; it is not supplied as a one-click remedy. Two-way clustering with few years and Driscoll–Kraay inference with short T can be unreliable. Multilevel models answer related but different questions about variance and random slopes. Use the companion causal-inference product when the research question is a treatment effect.

References and reproducibility

All firm records are synthetic. Known simulation coefficients are teaching references, not benchmarks that real-data results must match. The export files contain model comparisons, sample flow, diagnostics, sensitivity estimates, and figures.