Measuring productive performance using binary and ordinal output variables: the case of the Swedish fire and rescue services

Abstract

Fire protection is an example of a complex production process. This study measures efficiency by constructing binary and ordinal output variables from information on residential fires in Sweden about how a fire spreads from when the fire and rescue brigade arrives to when a fire is suppressed. The motivations behind this study are that there are only a few studies trying to estimate production efficiency for fire and rescue services, that data on a more detailed level is interesting for some public services, and there is a need to be able to measure efficiency differences even if only a binary or ordinal output variable is available. Using a logit random parameter model, the random effects are interpreted as efficiency differences. The conclusions are that fire and rescue services with a more flexible fire organisation with first response persons, working in collaboration with other municipalities and with larger populations are more efficient.

Keywords:

• qualitative output
• efficiency
• productivity
• logit parameter model
• fire departments

Acknowledgement

The funding body had no role in study design, in the collection, analysis and interpretation of data, in the writing of the report, or in the decision to submit the article for publication.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. The character ≻ means ‘preferred to’.

2. This measure was presented in a report by The Swedish Association of Local Authorities and Regions (SKL 2015) and is inspired by Jaldell (2005).

3. One reason for the estimated differences could be that different fire and rescue services fill out their report differently. However, a study found that that the only problem that could be quantified was geographical place (not considered in this paper) (Tykesson and Nilsson 2016).

4. Probit models were tested, but only resulted in similar output as the logit models.

5. A multinomial model was also tested and that model showed an ordinal ranking of the three outcomes.

6. If output and input are logarithms, then technical efficiency is defined as exp(–u_i). If u_i= 0, then the firm is said to be technical efficient and exp(–u_i) = 1. Technical inefficiency is thus measured on a scale between 0 and 1, the lower the more inefficient.

7. Coelli et al. (2005) discuss problems of using a two-stage method for continuous output measures. However, it is still used here in the binary output case to more clearly separate the two stages.

8. There are fewer observations since only turn-outs with less than 16 firefighters are included. The reason for not including more firefighters is the risk of outliers affecting the results and the reasonable assumption that the marginal product of additional firefighters over 16 is low.

Additional information

Funding

This work was supported by the Swedish Civil Contingencies Agency (grant number 2014-5283).