Multipliers and Supermultipliers in a Multisectoral Framework: Macroeconomic Tools After All?

ABSTRACTThe paper starts showing that the common mistake of considering Keynesian income and/or employment multipliers as sector-specific, in a multisectoral framework, is taking its way back into economics. The phenomenon coincides with the recent debate about the macroeconomic Sraffian supermultiplier and generates some new miscommunication by using similar terminology to sectoral multipliers. Thus, the aim of bringing forward the understanding that Keynesian multipliers and Sraffian supermultipliers constitute macroeconomic relations even in multisectoral models is pursued by emphasising the differences between the traditional input–output multipliers and their Keynesian counterparts and by showing the required adaptations for supermultiplier representations. Once aggregate multipliers and supermultipliers are obtained, there is no need for further multisectoral operations and all the differences in impact between economic activities must be attributed to the simple input–output multipliers. Some estimates are presented using data from the World Input-Output Database (WIOD).KEYWORDS: Input–output analysismacroeconomicsKeynesian multiplierSraffian supermultiplierJEL CODES: B51C67E11E12 AcknowledgmentsI would like to thank Gabriel Brondino, José Bruno Fevereiro, Marcelo Tonon and Michael Lahr for the comments and suggestions made at the 26th Input-Output Association Conference in Juiz de Fora, and, again, to Marcelo Tonon, for a later discussion about the paper. Also to Óscar Dejuán, who sent me by e-mail his detailed notes on a previous version, to Nuno Teles, for his careful reading and accurate remarks, and to the two anonymous reviewers for the suggestions, which certainly improved this final version.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 See the appendix for the step-by-step derivation.2 See the appendix.3 See the appendix for intermediate steps.4 As discussed later, separate multipliers leading us to matrix representations could arise from different propensities to consume attributed to different income groups, not from different economic activities.5 Boosted by the ‘increased expenditure of wages and profits that is associated with the primary employment’ (Kahn Citation1931, p. 173).6 A similar procedure can be found in Trigg and Lee (Citation2005) for employment and ten Raa (Citation2005, p. 28) for income. See the appendix for intermediate steps.7 Interestingly enough, the results concerning the division between total income multipliers and simple income multipliers first appear in economics as an empirical curiosity (Moore and Petersen Citation1955; Hirsch Citation1959; Sandoval Citation1967). From there, Sandoval (Citation1967), Bradley and Gander (Citation1969) and ten Raa and Chakraborty (Citation1983) have started to seek an explanation through different mathematical approaches. Notwithstanding, none of these studies mention the Keynesian multiplier, including the second edition of Miller and Blair (Citation2009), which also acknowledges the fact that the ratio of total to simple ‘income multipliers can be shown to be a constant across all sectors’ (Miller and Blair Citation2009, p. 254) — in that case, provided that the ‘parallel between this measure [the type II] and the type I effect […] is the same as that between the total and simple household income multipliers’ (Miller and Blair Citation2009, p. 253). Still, the link with the Keynesian multiplier is explicitly recognised in Miyazawa (Citation1960, Citation1968, Citation1976) and, more recently, Trigg and Lee (Citation2005) and ten Raa (Citation2005).8 ‘It would be extremely unfortunate if the multiplicity of multipliers were to be regarded as a defect of the analysis, when in fact it is rather a tribute to the flexibility of the concept’ (Samuelson Citation1942, p. 586).9 ‘For in given circumstances a definite ratio, to be called the multiplier, can be established between income and investment and, subjected to certain simplifications, between the total employment and the employment directly employed on investment (which we shall call the primary employment)’ (Keynes Citation1936[1973], p. 113, original emphasis).10 Neither for the ratio of secondary to primary employment, as in Kurz (Citation1985, p. 130), nor for the multiplier relating total to primary employment.11 In this case, one could talk about a matrix multiplier, as the results are the same for multipliers as matrices or as scalars.12 Regardless of whether the induction process comes from the income or from the employment. The description of an income being spent was adopted here because it seems to be more appealing.13 The associated right eigenvectors now presenting the same proportions of the sum of consumption and investment coefficients, respectively a+b and c+d.14 Acknowledging that the ‘key concept behind hyper-integration is the induced character of (fixed and circulating) investment expenditures’ (Garbellini and Wirkierman Citation2014, p. 163).15 Actually, Dejuán (Citation2014) has presented two types of matrices converting autonomous demand to gross output, a Keynesian one with induced consumption and a Sraffian with induced investment. Portella-Carbó (Citation2016) has presented matrices converting autonomous demand to gross output and employment, with induced consumption and investment.16 See Timmer et al. (Citation2015) for a guide to the database. For income, the special definition in (Equation16(16) v=xˆ−1[x−(i′Axˆ)′](16) ) for the value added was adopted, and, for employment, the chosen variable in the Socio-Economic Accounts was the number of persons engaged in economic activities.17 Ramey (Citation2011) reviews the empirical evidence about government spending multipliers and Spilimbergo et al. (Citation2009, p. 2) offer accessible ‘background information for policymakers on fiscal multipliers’.18 Since consumption and investment were assumed to be completely induced for all countries, the results for the United States should be considered distorted only if there is plausible evidence that the autonomous portions of consumption and investment, via institutional channels for finance, for instance, are above the average of the other countries.