Overview
Panel datasets are common in finance, economics, management and public policy theses, and the modeling choices have real consequences. Pooled OLS ignores unobserved heterogeneity; fixed effects remove it but cannot estimate time-invariant variables; random effects are efficient but only consistent if the unit effects are unrelated to your regressors. Add a lagged dependent variable and both standard estimators become biased, which is where difference and system GMM come in.
We start by understanding your panel's dimensions (many units over few years, or few units over many years), then agree an estimation strategy with appropriate tests: Breusch–Pagan LM for pooled versus random effects, F-tests for unit effects, and the Hausman or robust Mundlak test for fixed versus random effects. We then address heteroskedasticity, serial correlation and cross-sectional dependence with suitable standard errors.
You receive commented code, clean regression tables with the diagnostics that belong under them, and plain explanations — for example, what a within-firm coefficient actually says, and why it differs from a between-firm comparison.
Who it’s for and the problems it solves
This is for you if you are…
- Master's and doctoral students in finance, accounting, economics and management using firm or country panels
- Researchers building panels from databases such as World Bank indicators, company filings or household surveys
- Authors responding to reviewers about endogeneity, clustered standard errors or GMM instrument counts
- Policy analysts evaluating outcomes across regions or institutions over time
Common problems we help with
- The Hausman test rejects random effects, but your key variable does not vary over time
- Stata reports that the Hausman test statistic is negative or the variance matrix is not positive definite
- Your supervisor asks whether standard errors are clustered and at what level
- Your system GMM results show hundreds of instruments and a Hansen p-value of 1.000
- Your panel is unbalanced, with firms entering and leaving the sample
- You need to show robustness but are unsure which checks matter
What’s included — and what isn’t
Included
- Panel structure review: N and T, balance, gaps, entry and exit, and variable transformations (logs, ratios, winsorizing)
- Pooled OLS, fixed effects (within), random effects (GLS) and between estimators, with their assumptions explained
- Breusch–Pagan LM test, F-test for unit effects, Hausman test and the cluster-robust Mundlak (correlated random effects) alternative
- Two-way fixed effects for unit and time, and high-dimensional fixed effects where needed
- Diagnostics for heteroskedasticity (modified Wald), serial correlation (Wooldridge test) and cross-sectional dependence (Pesaran CD)
- Cluster-robust, Driscoll–Kraay or panel-corrected standard errors chosen to match the diagnosed problems
- Dynamic panels: Arellano–Bond difference GMM and Blundell–Bond system GMM with AR(1)/AR(2), Hansen and difference-in-Hansen tests
- Instrument count control (collapsing, lag limits) with the instrument count reported
- Panel unit-root tests (Im–Pesaran–Shin, Fisher-type, CIPS) for long-T panels
- Robustness checks: alternative measures, subsamples, lags, and excluding outliers
- Tables and code in Stata, R (plm, fixest), EViews or Python (linearmodels)
Not included
- Choosing the estimator or instrument set that gives the 'best' significance without justification
- Hiding failed diagnostic tests or unreported specifications
- Writing your empirical chapter for submission — we explain so you can write
- Sourcing proprietary data you are not licensed to use
What you receive
- Estimation strategy memo
- The model, estimators, tests and standard-error approach, with the reasoning, agreed before estimation.
- Regression tables
- Side-by-side pooled, FE, RE and (if needed) GMM results with coefficients, clustered standard errors or confidence intervals, and diagnostic statistics in the table notes.
- Diagnostics appendix
- Hausman or Mundlak results, serial-correlation and dependence tests, VIFs, and for GMM the AR(2), Hansen and instrument-count reporting.
- Code and data log
- Commented Stata do-file, R script or EViews program plus a log of every variable construction and sample restriction.
- Interpretation walkthrough
- A session explaining the coefficients, diagnostics and limitations so you can present and defend them.
How it works
Review the data and question
We look at your panel, hypotheses and variable definitions, and flag problems such as look-ahead bias or inconsistent units early.
Agree the strategy
We decide on static or dynamic models, fixed or random effects criteria, and standard errors, and record the plan.
Prepare and describe
Variables are constructed, outliers treated by a stated rule, and descriptive statistics and correlations produced.
Estimate and test
We run the models and diagnostics, then robustness checks.
Deliver and explain
Tables, code and a walkthrough, followed by a round of questions.
Estimators and tests
- Fixed effects (within)
- Removes time-invariant unit characteristics by using variation within each unit over time; consistent even when those characteristics correlate with regressors.
- Random effects (GLS)
- Treats unit effects as random draws uncorrelated with regressors; efficient and able to estimate time-invariant variables when that assumption holds.
- Hausman and Mundlak tests
- Hausman compares FE and RE estimates under classical assumptions; the Mundlak approach adds unit means of regressors and works with cluster-robust errors.
- Clustered standard errors
- Allow arbitrary correlation within units over time; two-way clustering (for example, firm and year) when shocks are shared across units.
- Difference and system GMM
- Arellano–Bond and Blundell–Bond estimators for dynamic panels with lagged dependent variables and endogenous regressors, typically for large N and small T.
- GMM diagnostics
- AR(2) test for serial correlation in differenced errors, Hansen J test of overidentifying restrictions, difference-in-Hansen for subsets of instruments, and a check that instruments do not exceed the number of groups.
Fixed or random effects: more than one test
The Hausman test is often treated as the whole decision, but it relies on assumptions that are rarely met — in particular, that random effects are fully efficient, which fails under heteroskedasticity or clustering. It can also produce negative statistics. The Mundlak or correlated random effects approach gives a cluster-robust alternative and shows directly how unit means relate to the outcome.
Theory matters too. If your key variable barely changes over time (for example, board composition or legal origin), fixed effects will estimate it poorly or not at all. We explain your options, including hybrid within–between models, and help you justify the final choice.
Dynamic panels without instrument proliferation
System GMM is powerful and easy to misuse. By default, programs such as xtabond2 create instruments for every available lag, so the instrument count can grow faster than the number of firms. Too many instruments overfit the endogenous variables and weaken the Hansen test, which can report implausibly perfect p-values near 1.000. This problem is well documented in the methodological literature, notably Roodman's 'note on the theme of too many instruments'.
We limit lags, collapse the instrument matrix where appropriate, report the instrument count against the number of groups, and show that key results are stable across reasonable instrument sets. We also check that the lagged dependent variable's coefficient lies between the pooled OLS and fixed-effects estimates, a simple plausibility check.
- AR(1) in differences is expected; AR(2) should not be significant
- Hansen p-values that are very high are a warning, not reassurance
- Difference-in-Hansen tests check the extra system-GMM level instruments
What panel estimates can and cannot claim
Fixed effects deal with unobserved characteristics that do not change, but not with time-varying confounders or reverse causality. We help you describe coefficients as within-unit associations unless your design supports a causal reading, and suggest causal inference designs such as difference-in-differences or instrumental variables when the question is explicitly causal.
Many specifications and robustness checks also create a multiple-testing problem. We keep a record of all models estimated so the reported ones are a fair picture of the evidence.
What the work can look like
Illustrative example — fictional data
Sample excerpt: leverage and firm profitability
A master's student used an unbalanced panel of 312 listed manufacturing firms over 2012–2023 to study whether leverage affects return on assets. Numbers are invented for illustration.
Static models
The robust Mundlak test rejected random effects, χ²(6) = 41.3, p < .001. With firm and year fixed effects and firm-clustered errors, a 10-percentage-point increase in leverage was associated with ROA 0.9 points lower, 95% CI [−1.4, −0.4].
Dynamic model
Two-step system GMM with collapsed instruments (41 instruments, 312 groups): lagged ROA = 0.46, between pooled OLS (0.71) and FE (0.28). AR(2) p = .38; Hansen p = .27; difference-in-Hansen p = .44.
Limitation noted
Leverage choices may respond to expected profitability; results are therefore described as conditional associations with a GMM robustness check, not as a clean causal estimate.
Illustrative example with invented numbers, not a real client project.
What you’ll need to provide
- Research questions, hypotheses and the variables you want to test
- The panel dataset or the list of sources and variable definitions if we help assemble it
- The papers your model is based on, if you are extending an existing specification
- Software preference and any university template for tables
- Supervisor or reviewer comments to address
You don’t need everything ready to ask for a quote — tell us what you have and we’ll say what’s missing.
What affects price and turnaround
Price depends on
- Panel size and how much data assembly or cleaning is required
- Number of dependent variables, hypotheses and model specifications
- Whether dynamic GMM, two-way clustering or cross-sectional dependence corrections are needed
- Scope of robustness checks
- Delivered analysis or guided learning sessions
Turnaround depends on
- Whether the data are already merged and consistently identified
- Number of specifications and robustness checks
- Time for you to confirm variable definitions and sample restrictions
Every project is quoted individually. How we price our work.
Questions people ask before starting
Stata says my Hausman test is not valid. What should I do?
This usually happens when the variance difference is not positive definite, often because of heteroskedasticity or clustering. We use the robust Mundlak or an auxiliary-regression version instead and explain it in your methods.
At what level should I cluster standard errors?
Generally at the level where errors are likely to be correlated and where treatment or key variation occurs, often the firm or country. With few clusters (for example, fewer than about 30–50), we consider wild cluster bootstrap inference.
Is system GMM always better than fixed effects?
No. It is designed for dynamic models with large N and small T. With long panels or few units it can perform badly, and a well-specified fixed-effects model may be more credible.
Can you help me build the dataset?
We can help merge, clean and document data you have legitimate access to, and advise on public sources. Our secondary data sourcing service covers finding datasets in more depth.
Which software do you use?
Stata (xtreg, reghdfe, xtabond2), R (plm, fixest), EViews or Python (linearmodels). We match your institution's software where possible.
Will you write my empirical chapter?
No. You receive tables, code and detailed explanations, and we can review your draft for accuracy. The chapter is yours to write.