Hausman Test

Calculate the Hausman specification test comparing a Fixed Effects and a Random Effects fit of dependent_tickers (the panel of entities) on a regressor x.

Also known as: Hausman specification test, fixed versus random effects test.

Random Effects is more efficient than Fixed Effects but relies on entity effects being uncorrelated with the regressor(s) – if that assumption is violated, Random Effects is inconsistent while Fixed Effects remains consistent regardless. See panel_data_model.get_hausman_test for the full formula and references, and get_fixed_effects/get_random_effects for how the two models being compared are estimated (including how independent_tickers/independent_column shape the panel, and why independent_column is generally the more reliable choice here).

The formula is as follows:

\[H = (\text{betâ\_FE} - \text{betâ\_RE}) \text{'} \cdot \left[\operatorname{Var}(\text{betâ\_FE}) - \operatorname{Var}(\text{betâ\_RE})\right] \text{⁻¹} \cdot (\text{betâ\_FE} - \text{betâ\_RE}),\;\; \text{over the k slope coefficients the two models share (a pseudo-inverse when the difference is singular, and H floored at 0)}\]

H is chi-squared with k degrees of freedom; Random Effects is rejected when the p-value is below 0.05
β̂_FE comes from get_fixed_effects with entity effects only and β̂_RE from get_random_effects

Hausman Test in Python or via the MCP

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_hausman_test as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AAPL", "MSFT", "AMZN"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

toolkit.econometrics.get_hausman_test(independent_column="Volume", period="weekly")

Or, after setting up the Finance Toolkit MCP, ask:

Should a weekly panel of Apple, Microsoft and Amazon returns on trading volume from 2021 to 2025 use fixed or random effects, according to the Hausman test?

Which returns:

	Value
Hausman Statistic	0.5866
Degrees of Freedom	1
P-Value	0.4438
Prefer Fixed Effects (5%)	0

Using Your Own Data

get_hausman_test runs on any data, not only prices: ratios, economic indicators, yield curves or your own dataset. Pass a DataFrame, a Series or a dictionary of them to Econometrics as data, with the dates in the rows or the columns, and set changes to how its changes are calculated: "percentage", "log", "difference" for rates and ratios, or None when the data are changes already. For example, for the monthly unemployment rates of the United States and Germany, where each country is a column:

from financetoolkit import Economics, Econometrics

economics = Economics(start_date="2000-01-01")

unemployment = economics.get_unemployment_rate(
    countries=["United States", "Germany"], period="monthly"
)

econometrics = Econometrics(data=unemployment, changes="difference")

Then call econometrics.get_hausman_test with independent_tickers or independent_column, using the column names of the data as tickers.

Parameters

get_hausman_test accepts the following parameters.

Parameter	Type	Description	Example
`independent_tickers`	`str \| list[str] \| None`	The factor ticker(s), whose `column` values are broadcast identically to every entity at each date. Mutually exclusive with `independent_column`.	`"Benchmark"`
`independent_column`	`str \| None`	A different historical data column, taken per-entity from each of `dependent_tickers`’ own data, to use as the regressor. Mutually exclusive with `independent_tickers`.	`"Volume"`
`dependent_tickers`	`str \| list[str] \| None`	The panel of entity tickers to explain. Defaults to None, meaning every ticker in the `Toolkit` instance (other than `independent_tickers`, if given).	`["AAPL", "MSFT", "GOOGL"]`
`period`	`str`	The data frequency (daily, weekly, monthly, quarterly, or yearly). Defaults to “daily”.	`"weekly"`
`column`	`str`	The dependent variable’s historical data column. Defaults to “Return”.	`"Return"`
`include_benchmark`	`bool`	Whether to include “Benchmark” among the entities. Defaults to False.	`True`
`rounding`	`int \| None`	The number of decimals to round the results to. Defaults to None.	`2`

Hausman Test in Python or via the MCP

Using Your Own Data

Parameters

Related Panel Data