# F6-conf-04 — Does workforce training raise productivity growth? A mini-project on simulated firm data

# Scientific question

A one-year training programme offered firms a variable number of training hours per employee. Using the simulated firm-level data provided, estimate the effect of one additional training hour per employee on productivity growth in the following year. The estimand is the causal effect of training_hours on productivity_growth (percentage points per hour) under a selection-on-observables assumption: conditional on the pre-programme information in the file, training hours are as good as randomly assigned, and the effect is linear and homogeneous. Report both the unadjusted association (the required baseline) and the estimate that targets the estimand, with uncertainty. The chain required is: question → data audit → baseline → justified method → results → uncertainty → failure discussion → one figure and one table → short report.

# Inputs

data/firms.csv — simulated data (generated for this exercise; it is not observed data). One row per firm. Columns: firm_id (integer), skill_index (standardised index of the workforce's baseline skill, measured in the year before the programme), training_hours (hours of training per employee received during the programme year), productivity_growth (percent change in labour productivity in the year after the programme year). Rows are in random order.

# Information-availability rules

Use only data/firms.csv. No other variables exist; nothing needs to be imputed.
The "unadjusted" model is the OLS regression of productivity_growth on training_hours with an intercept only.

# Required outputs

out/results.json with the keys:

key	type	unit	meaning
`naive_estimate`	number	pp per hour	OLS slope of the unadjusted model (baseline)
`naive_ci_low`, `naive_ci_high`	number	pp per hour	95% confidence interval for the unadjusted slope
`baseline_metric`	number	percentage points	RMSE of the unadjusted model's residuals, sqrt(mean(e²))
`model_metric`	number	percentage points	RMSE of the residuals of the model that targets the estimand
`effect_estimate`	number	pp per hour	estimate of the estimand (coefficient on `training_hours` in the model you justify)
`effect_se`	number	pp per hour	its standard error (conventional or heteroskedasticity-robust; state which)
`effect_ci_low`, `effect_ci_high`	number	pp per hour	95% confidence interval for the effect
`confounder_coefficient`	number or null	pp per index unit	coefficient on `skill_index` in the model that targets the estimand (null if that model does not include it)
`conclusion`	string	—	one of the codes below, based on `effect_ci_low`/`effect_ci_high`
`task_id`	string	copied from this file
`feasibility`	string	`complete` / `partial` / `infeasible`
`feasibility_reason`	string or null	why, if not complete
`data_issues`	array of {"issue","handling"}	every data problem detected and how it was handled (empty list allowed)
`n_input_rows`	object {file: integer}	rows read per input file (file name as key, header row excluded)
`n_analysed`	integer or null	observations actually used in the main estimate
`random_seed`	integer or null	seed used, if any

The conclusion code must be one of: positive_effect (the 95% interval for the effect estimand lies above zero), negative_effect (lies below zero), no_detectable_effect (the interval / test does not reject zero at the 5% level), premise_invalid (the data provided do not allow the stated estimand to be computed — in that case set feasibility to infeasible, explain in feasibility_reason, and set every inestimable key to null; never substitute an invented or proxy estimate).

out/figure1.png — scatter of productivity_growth against training_hours with the unadjusted fitted line and the fitted line of the model that targets the estimand (evaluated at the mean of any other regressor), produced by out/analysis.py with matplotlib.
out/table1.csv — one row per model with columns model, estimate, se, ci_low, ci_high (header + at least two data rows), produced by out/analysis.py.
out/report.md with exactly these six sections, in this order: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The last section must contain a genuine failure discussion: what would invalidate the result, what was not checked, and what the main threats are.
out/analysis.py — replication entry point: ~/wp29/venv/bin/python out/analysis.py, run from the workspace root, must regenerate out/results.json, out/figure1.png and out/table1.csv from data/ only, deterministically (fix any seed; use the matplotlib Agg backend).
out/claims.json — list of the central claims of the report: [{"id": "C1", "text": "...", "results_keys": ["..."], "status": "supported"|"unsupported"|"not_evaluated", "caveat": "..."}]. Every claim must reference existing keys of out/results.json; a claim must only be marked supported if the reported numbers actually support it.

# Constraints

No network access. Python: ~/wp29/venv/bin/python (numpy, pandas, scipy, statsmodels, matplotlib available). Do not modify data/.
Write all deliverables under out/. This task is designed to be completed in well under 20 minutes of work; prefer a short, correct chain over an elaborate one.

spb/wp29_uqo