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Under estimate refers to the approximate determination of numerical values , variables or parameters by appearances , experience or statistically - mathematical methods. The result of an estimate usually deviates from the true value . The true value can actually only be determined with countable quantities . On the other hand, every measurement - in whatever accuracy range - is fraught with unavoidable measurement uncertainties , so that one never gets true values, only probable (most) e values.

Colloquial meaning

In everyday life , one speaks of an estimate when the result is determined quickly on the basis of visual inspection, intuition or experience . To put it more precisely, an estimate is the intuitive number or evaluation of measurable (mostly physical) or countable quantities. It is usually preferred to a more precise determination because it would be too costly or the estimation error is meaningless in practice.

Some examples:

  • "I guess a teaspoon of salt is too much."
  • "I guess we ran 2 km."
  • "The altimeter has halfway confirmed my rough estimate."
  • "I guess it's been 10 minutes."
  • "The police estimated the participation at 5000 demonstrators."

A common colloquial synonym for a rough, intuitive estimate is “pi times the thumb” or “ aiming over the thumb ”. So-called rules of thumb are available for many areas to quickly improve such procedures .

Estimates in Statistics

An approximate determination ( approximation ) of numerical values, parameters or results based on given values is considered an estimate . In the case of measured values, their accuracy is determined and specified as their measurement uncertainty or selected on the basis of the available resources or conditions - which then depends on the estimation method and effort.

Appreciation in business and technology

Here, too, is valued more often than is commonly assumed. While it can be for larger buildings statics relatively accurately calculate the strength of some components or the superposition of manufacturing - tolerances but less well. High safety factors are therefore used for particularly important sub-aspects . Whether these are set at 2.5 or 3, for example, is partly a matter of opinion.

Another example is complicated or networked measurements . As a rule, what matters to the client is a result that guarantees a certain level of accuracy and reliability . Most economical would be to determine the necessary detailed work with methods of strict statistics . However, experienced engineers plan more series of measurements in order to be able to deal with certain eventualities. How much additional effort is built in "for safety" is partly colored personally.

Many decisions in companies and in projects are made less on the basis of precisely calculable key figures ( business or economic key figures ) than on the basis of experience , forecasts , rough estimates or surveys of only a few people. In banking, this includes valuation or collateral valuation or the labor market forecast . Nevertheless, the Delphi method (refereed survey of experts) , for example, is a generally recognized means of assessing future developments.

Estimation in tax law

The estimate made in accordance with § 162 AO is of elementary importance in tax law. It is permissible if no tax return has been submitted or if the tax authorities have considerable doubts about the correctness of the declared tax bases. Estimates are only allowed if the tax bases cannot be determined. The lack of formal or material correctness of the bookkeeping i. S. d. § 158 AO. Only the tax bases are estimated, never the tax to be assessed. Legitimate estimates therefore always require objective connecting facts and must not be arbitrary; they never serve as a punishment, but rather for the uniform enforcement of tax laws against everyone and thus for tax justice. An estimate is often carried out as part of an external tax audit (so-called tax audit) if formally incorrect bookkeeping or materially incorrect bookkeeping has been established. Inadequate checkouts (for example missing Z-receipts at electronic cash registers in the catering industry) are a standard case for additions. The same applies to missing shift slips for taxis. If the operator of a taxi company violates his duty to record the shift slips, the tax office is entitled to make an estimate. In addition, this leads to the revocation of the license according to Section 25 Passenger Transport Act. When determining the sales tax, so-called input tax amounts may not be estimated, since input tax may only be deducted according to § 15 UStG if a proper original invoice is available. The tax courts can and must, if necessary, estimate themselves according to § 96 FGO. To relieve the judges, some tax courts have so-called in-house auditors to investigate the facts and review estimates. Another application is the checking of values ​​in the context of an estimate, e.g. B. the estimate of the withdrawal value.

Appraisal in civil proceedings

In civil proceedings , too, the court's appraisal is permissible in accordance with Section 287 of the German Code of Civil Procedure (ZPO) if the parties are in dispute as to whether damage has occurred and how high the damage is or an interest to be replaced. In doing so, the court must decide freely, taking into account all the circumstances, and, if necessary, collect evidence. The same applies if the amount of a claim is in dispute between the parties and the full clarification of all relevant circumstances is associated with difficulties that are out of proportion to the importance of the disputed part of the claim. The law accepts that the result of the estimate not infrequently does not agree with reality, on the other hand, the estimate should be as close as possible to this. In any case, an estimate must be omitted if it were completely in the air due to a lack of concrete evidence and would therefore be arbitrary. If the court is not sufficiently convinced to make an estimate, the result is non liquet .

Individual evidence

  1. Michael Brinkmann: Estimates in Tax Law . 2nd Edition. Erich Schmidt, Berlin 2012, ISBN 978-3-503-13851-7 .
  2. cf. BFH of February 16, 2004, XI R 25/02, BStBl. II 2004, 599
  3. cf. BGH June 24, 2009, VIII ZR 332/07, NJW-RR 2009, 1404