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ABSTRACT
The difficulties economists have in conducting laboratory experiments necessitates much of their applied analysis being based on numerous quasi-experiments conducted under a variety of uncontrolled conditions. The result is the need to synthesis these results if any generally useful parameters are to be found for such things as value transfers or policy assessments in transportation. The paper reviews some of the issues involved in using meta-analysis to conduct statistical analysis of such previous quantitative work in transportation economics, examines the success that more recent meta studies have had in overcoming earlier criticisms of the methodology, and sets this in the contexts of on-going developments in meta-analysis more generally. The paper suggests ways that meta-analytics can address some remaining issues.
Acknowledgement
I would like to thank Yi-Ting Chiu, participants at the 58th Transportation Research Forum Annual Conference, held in Chicago, 2017, and especially my discussant, Jack Wells, and three referees of this journal for their comments on earlier versions of this paper. Their views have improved the paper considerably, although agreement with the referees is not always possible.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 The terms “prior studies”, “prior works” or “priors” are used interchangeably throughout to denote the original studies upon which any meta-analyses are based.
2 Strictly, since most of the elasticities calculated are set in a multivariate context, they are, as Moore (Citation1926) defines them, “partial elasticities” with other effects being held constant. The factors held constant generally provide one of the categories of moderator variables.
3 The meta-regression should itself be the subject of appropriate statistical assessment. I am grateful to one referee for asking whether the “Z’s” in such regressions have been assessed for multicollinearity. To my knowledge, excepting Wardman (Citation2014), this has seldom been done in transportation work, which is a clear limitation.
4 Software for modelling in this way includes; Comprehensive Meta-Analysis – A computer programme for meta-analysis, http://www.Meta-Analysis.com.
5 Some medical journals require that the authors provide the test of heterogeneity, along with a fixed-effects analysis and a random-effects analysis. This is not the case with transportation journals.
6 Fixed effect models, that are used to assist in controlling for unobserved heterogeneity in panel data, assuming this heterogeneity is constant over time, suffer from similar problems.
7 In terms of the gray literature, Wachs (Citation1989) highlighted the factors that can lead to “political” parameters, rather than objective ones, determining the values recorded in transportation reports. Anyone engaged in editing journals knows of publishers’ pressures to increase citations.
8 The situation was put even more starkly by the Nobel Prize winner, Ronald Coase (cited in Tullock, Citation2001) when he joked, “If you torture the data long enough, Nature will confess”.
9 Albeit not a complete assessment of power, Wardman (Citation2014, p. 380) does find “We have already pointed out that sample size was not found to impact on the reliability of the input elasticity data, and that the number of observations per study does not have an effect”.
10 Just focusing on meta-analysis of elasticities, similar issues arise regarding price elasticities of complementary goods, (Dahl and Sterner,Citation1991), on fuel (Espey, Citation1998; Brons, Nijkamp, Pels, & Rietveld, Citation2008), on final demands for transportation such as tourism (Crouch, Citation1996), and on travel time elasticities (Wardman, Citation2012).
11 Similar problems can apply to meta regressions of priors of technical efficiency using data-envelope analysis; e.g. Odeck and Bråthen (Citation2012) study of seaports and Brons et al. (Citation2005) of airports. In this case, indices are relative to the most efficient observed facility and this point of reference varies by study.
12 Moher, Liberati, Tetzlaff, and Altman (Citation2009) consider the extent and nature of standard reporting in medical research.
13 The adequate power for most economic work is usually taken as 80%, but this is an “accepted judgement” with no objective backing. As is the oft used 95% confidence intervals for individual parameters.
14 Long-run elasticities are based on cross-section data, and short-run on times series. The issue is not one of any lag structure modelling, which is often a component of time series work and could be included in a meta-analysis, but rather on the potential flexibility of individuals’ behaviours.
15 As Holmgren (Citation2007, p. 1027) observes regarding priors, “It is interesting to note that in most cases the choice of functional form is not discussed; instead a specific functional form is assumed”. More flexible forms, for example, like the transcendental logarithmic are seldom explored.
16 Put another way, if the set of linear demand curves priors all have prices above the mid-point of their associated demand curves, then these points on their respective curves will have elasticities exceeding unity; if prices are below the mid-point then the elasticities will be less than unity. All that higher values from arc, as opposed to point, elasticities may be telling us is that the latter studies involve low priced travel. Resolution requires more careful consideration of the actual information on the prices.
17 In his annotated survey of previous studies, Wardman does mention the importance of income levels on price elasticities of transportation but this is not followed up in the meta-regression.
18 The authors’ trouble in explaining some of the parameters in their OLS estimation may be not as so much due to the heteroscedasticity they suggest as to omitted variable bias with their regional dummy being a poor proxy for income variations across the primary cases.