Abstract
Conventional estimates of purchasing power parities (PPP) rely on cross-country price data. Using Engel curves, Almås (Am Econ Rev 102:1093–1117, 2012) was, however, able to show that PPPs contain substantial bias. Since constructing conventional estimates is expensive and time consuming, Almås’ idea of employing Engel curves is welcome. This article examines the viability of the Engel curve approach to PPP and its sensitivity to differences in relative prices and preferences by estimating Engel curves not only between countries but also for regions within a given country. My empirical evidence from the United States and Norway suggests that the differences can be problematic, but not sufficiently to discredit the new methodology. A pragmatic approach to PPP estimation between countries that are different is to compute a PPP band, rather than a point estimate. I present a practical example of this using expenditure data from 2001, which yields a band for NOK and US dollar.
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Notes
By preferences I mean consumer preferences. However, in the “Section 5” below I explain why institutions may matter and how the definition of preferences could be broadened to include cultural and institutional factors and characteristics.
Moreover, as Beatty and Crossley (2012) point out, the Engel curve methodology requires downward-sloping curves, i.e. non-homothetic preferences. At the same time, a single price index for all households implies homothetic preferences. This can, however, occur if households are distributed in finite mixtures of preferences where preferences are homothetic within groups, but non-homothetic between them. This preference structure allows for both Engel curve estimation and index computation for types.
In fact, building on Beatty and Crossley (2012), constructing different PPP-estimates for different household groups may be a preferable approach when preferences are homothetic within-group but not homothetic between groups.
Notice that my PPP estimates for households of different material standards of living may serve several purposes. First, they capture possible differences in institutions and relative prices between countries. Second, they allow for non-homothetic preferences within-countries; see Beatty and Crossley (2012). I do not, however, estimate the number of groups in the finite mixture of preferences.
The coefficients c and f are typically negative since Engel-curves for food slope downward.
Thus, I report classical t values. I have computed, but do not report, heteroskedasticity-consistent t values. The differences between the two are small.
Again, the idea of a PPP-band is supported by the findings in Beatty and Crossley (2012) since a band allows for different estimates for households at different income levels.
This fraction is controlled by the smoothing parameter, which is set by the analyst. I use a smoothing parameter of 0.6. in the procedure PROC LOESS of the software package SAS. For technical details on and examples of code for such non-parametric regressions, see SAS/STAT\(\circledR \) 9.2 User’s Guide, 2nd Edn. Online: http://support.sas.com/documentation/.
Statistics Norway has constructed a special internet site in English on CES, sampling, weights, and latest developments. Use: http://www.ssb.no/english/subjects/05/02/forbruk_en/.
The producer and distributor of the US data files are: US Dept. of Labor, Bureau of Labor Statistics. Consumer expenditure survey, 2001: Interview survey and detailed expenditure file [Computer file]. Washington, DC: US Dept. of Labor, Bureau of Labor Statistics [producer], 2002. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2003.
The last digit in the ID represents the interview-quarter, the other the unique household.
I use fmly-files from diary data (da3675.fmly011-da3675.fmly014) and detailed expenditure files (da3675.expn011-da3675.expn014).
The result of 0.0809ln(7); see Theory.
The t values of the intercept estimates are 18.6 and 63.3 indicate small estimated standard deviations (0.0588 and 0.0150, respectively). The estimated standard deviation of the intercept difference becomes 0.060674. Thus, the t value of testing the intercept difference is 0.16.
See e.g. Rice (1995, p. 515). The estimated standard variation of the estimated intercept difference is \((0.010102^{2} + 0.00275^{2})^{0.5} = 0.010467.\)
I employ different specifications as part of a broader model selection process. If the QUAIDS-specification is true to the underlying structure, then the linear AIDS-specification is an approximation. In that case, the latter may still be quite accurate in the most interesting income interval.
Moreover, it allows smaller segments to have within-group homothetic preferences even if there are between-group differences.
The sums of squared errors were 3.54985 for the unconstrained and 3.56906 for the constrained. There were 999 observations, 8 parameters in the unconstrained regression and 3 linear restrictions in the constrained.
Table 6 Estimating Engel curves for food for regions: food’s share of income before tax on determinants Blundell et al. (1993) also study quadratic curves.
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Acknowledgments
I am grateful to comments and suggestions from Hilde C. Bjørnland, Terje Skjerpen, Knut Reidar Wangen, and anonymous referees. I also benefitted from discussions with Timothy Beatty and Ingvild Almås.
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Røed Larsen, E. Is the Engel curve approach viable in the estimation of alternative PPPs?. Empir Econ 47, 881–904 (2014). https://doi.org/10.1007/s00181-013-0766-6
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DOI: https://doi.org/10.1007/s00181-013-0766-6