Consider hypothetical eligible expenditures in common currency units. Assume that the American-style formula applies without any special rules, reductions, basic-research components, or interactions with deductions. The volume formula below uses a flat 30 percent for an amount below the French threshold. These are simplified design comparisons, not complete tax-liability calculations or currency-converted claims for actual firms.
| Firm |
Each of three preceding years |
Current eligible spending |
Half of preceding average |
Simplified incremental credit |
Volume credit |
| Stable research program |
100 |
100 |
50 |
7.0 |
30 |
| Expanding research program |
100 |
120 |
50 |
9.8 |
36 |
| High historical base |
200 |
120 |
100 |
2.8 |
36 |
For the stable firm, the historical-base credit is 0.14 multiplied by the difference between 100 and 50, yielding 7. Its year-on-year increase in spending is zero. That observation does not show whether the credit preserved research that would otherwise have been cut, but it disproves the assumption that every credited unit above the base must represent current spending growth.
The expanding firm spends 20 more than the stable firm and receives 2.8 more under the simplified historical formula. Under the volume formula, the corresponding difference is 6. The third firm has the same current expenditure as the expanding firm but receives a smaller historical-base credit because of its preceding spending. An evaluator comparing claimants must therefore account for expenditure histories rather than infer policy intensity from current firm size alone.
Now suppose the expanding firm would have spent 110 without support, and actually spends 120. Additional expenditure is 10, even though observed spending is 120 and the increase from its prior annual level is 20. Using the simplified credit of 9.8, the illustrative additional-spending ratio is 10 divided by 9.8, or 1.02. Using the volume payment of 36 gives 0.28. These ratios share an assumed behavioral response only to expose the arithmetic. They do not estimate that firms would respond identically to two different incentive designs.
If the no-policy counterfactual were 125, the observed 120 would imply a decline of 5 relative to that forecast, despite a rise from the historical 100. Such an estimate would require careful examination of uncertainty and identification; it would not justify claiming that a positive tax payment mechanically reduced research. The counterfactual is an empirical proposition, not a residual chosen to make the program look effective.