How to calculate the GDP multiplier

Income and expenditure multipliers of the German economy

Economic policy programs, which for pragmatic reasons operate under titles such as “protective shield for work” or “economic stimulus package”, often reflect party political interests and compromises and only in part represent economically sensible measures - provided such assessments are at all given the few empirical studies and their controversial results 1 In order to influence the macroeconomic control of politics, it would be important to assess the economic effects of economic policy measures and to be able to make scientifically sound proposals on this basis. While there is no shortage of more or less clever ideas about the right policy in the public discussion, the justification for them through empirically proven theories often remains in the dark. One of the few exceptions is the study by A. Truger et al. 2 On the basis of the Haavelmo theorem and our own calculations with the help of a model for Austria, the thesis is represented that the multipliers of government revenues are significantly below those of government expenditures. However, the economic policy recommendations derived from this cannot simply be transferred to Germany. This thesis was therefore checked in a comprehensive study, 3 the most important results of which are reported here. This is intended to contribute to closing the gap just outlined between economic research and practical economic policy.

The quantification of economic multipliers is currently explosive. Triggered by the economic and financial crisis of 2007 to 2009 and the resulting active stabilization policy, a controversial discussion has arisen in academia and beyond about the effects of state influence on the business cycle can realistically be expected.4 The answer to this question depends not only on the economic policy measures taken, but also on which effect (performance, employment, deficit ratio, etc.) is primarily to be achieved.

The problem of impact estimation

If the Federal Statistical Office estimates the macroeconomic effects of economic policy measures, such as the last increase in value added tax, it is limited to the closest, immediate effects.5 Here, exact data on the current state of the economy and the most concrete information about it are important how politicians want to finance their decisions. However, the question of whether - to stay with the example - VAT is shifted “to the front” (on the consumers) or “to the back” (to the companies) is unclear.6 Such an “estimate becomes even more problematic “When you consider the complexity of the subject. “Complexity” in this context means that, parallel to the deliberately brought about changes in the framework conditions of the economy or in the state's income and / or expenditure, there are always countless other changes that also affect the results of economic policy interventions, falsify them or even let them can thwart.

Furthermore, it has been known for centuries that economies are a cycle. These can strengthen or dampen impulses coming from outside (the rest of the world, the state) or inside (technology). The multiplier effect, according to which the increase in autonomous expenditure has a multiple impact on output and income, plays a role here. Whether and, above all, to what extent such multiplier effects actually exist is extremely controversial in the literature. The most important counter-argument is that - even if there should be such an effect - it fizzles out into the rest of the world in an open economy.

The most important counter-argument is empirical - and that closes the circle of argumentation: Because it is so difficult to estimate the economic impact of economic policy measures, the question can be asked whether the theoretically founded multipliers also work in an open economy like Germany's, does not seem to answer definitively. The fact that even econometricians share this economic policy skepticism is due to the trend towards ever more detailed models, partial analyzes, micro-econometric approaches, error correction models and other recent developments in time series analysis. This has led to a widespread neglect of medium-sized macroeconomic models. Instead of improving the latter and testing modern methods within the framework of a complex economic model, the research focuses primarily on the analysis of the residual information in the residuals of regression equations, the meaning of which depends on the existence of a long-term equilibrium.

Evaluation of economic policy using a model

We therefore assume that macroeconometric models in the field of business cycle, growth and crisis research represent an instrument that can only be replaced to a limited extent by modern trends in econometrics. To get to the point once again: The ceteris paribus condition can only be ensured with simulations based on a complex macroeconomic model, 7 whereas in today's usual analyzes one can often read: “It has not been possible to control for all other policy variables that might have influenced the evolution of GDP. "8

It is therefore necessary to have at least one econometric model of medium magnitude, which - albeit to a modest extent - depicts the complexity of the economy, its dependency on exogenous shocks and the most important cycles. The usual procedure for estimating the economic impact of economic policy measures is as follows: First, the economic policy measures are broken down into sub-measures, 9 which are then assigned to the instrument variables in the model and recombined, in order to finally see the reaction of the economy to an exogenously specified impulse in the Simulate the frame of the model. 10

Corresponding studies on specific economic policy measures must be drawn up, discussed and published before they reach the socio-political actors. A time delay could be avoided if the actors could make estimates of the effects without having to apply a macroeconomic model themselves. The bridge to this are quantified multipliers that can be calculated in advance regardless of political events, based on standardized sub-measures such as an increase in VAT by one percentage point or a reduction in income tax by 10 billion euros.

It can be assumed that the economic effects can be represented as a first approximation by linear and additive functions. Therefore, even complex economic policy measures can be estimated with the help of standardized multipliers and focused on the largest expenditure items with regard to the expected effects. Furthermore, it must be taken into account that every macroeconomic model has peculiarities that distinguish it from others and that indicate that it is a model and not a macroeconomic reality. In order to get closer to the latter, several models are used by larger institutes, their results are compared and then checked for plausibility. Such a model comparison can also be carried out with the help of the standardized multipliers mentioned above. To a certain extent, this could revive the discussion among model makers even if the exchange of models - for whatever reasons - has become a little difficult. In any case, a correspondence between the results of different models that can be determined within certain limits can contribute to the objectification of the multiplier estimates.

Special features of the study

Concentrating on only one economic policy measure per impact assessment, the underlying study differs not only from its predecessors, which were carried out with the same model, but also from different analyzes that, for example, link the question of tax increases with the question of what for the additional revenue will be spent.11 However, focusing on the effects of individual measures will also make it possible to estimate structural changes within government spending, as Lane and Perotti12 do when one takes into account that the effects of different stimuli are overlapping. The prerequisite is that the models can serve a sufficiently broad spectrum of instrument variables. Concentrating on separate impulses is a prerequisite for obtaining clearly structured multiplier tables.

To increase the degree of objectivity, two models are used here. One of these is the RWI (KOMO) economic model. It has already been described in the literature.13 The authors have the two versions KM59 and KM61, both of which are still based on the old national accounts. Version 61 is used, which has a support range of ten years and extends to the end of 2004. In addition, a more recent version of the Econometric Model of the German Economy (EMGE), which has already been described in this journal, was used. 14

Selection of instrument variables

An instrument variable is understood here to be a model variable that records the impulse on which a simulation is based. In principle, all model variables can be disturbed by an impulse in order to then observe how this disturbance affects the overall system of the variables. So if one takes into account the reconstruction of the models, a wide range of variables would be available that could serve this purpose. In practice, however, only a few are usually of interest. In order to achieve maximum comparability with the aforementioned study by the Institute for Macroeconomics and Business Cycle Research, 15 whose central thesis is tested here, the variables listed in Table 1 were selected.

For technical reasons, only general changes in government consumption can be simulated in the KOMO. Although the EMGE allows a more differentiated approach, for reasons of comparability, an impulse was also simulated that generally affects government consumption (more precisely: the corresponding government expenditure). In terms of transfers to private households, no distinction could be made between pensions, unemployment benefit, child benefit, etc. Taxes on wages and salaries of employees can be simulated separately from taxes on income from entrepreneurship and assets with the two models used here. There is therefore no need to distribute the impulse to these two large income groups.

Table 1
Instrument variables
Direct employee taxesTanTxanBillion euros
Employees' social security contributionsSvanSvbanBillion euros
Employers' social security contributionsSvagSvbagBillion euros
Monetary transfers to householdsYtraAstsozBillion euros
Public construction investmentIbstAstibBillion euros
Government consumptionAcstAstyanBillion euros

Dimensioning of the impulses

Impetus was selected that consisted of increased or decreased expenditure or increased or decreased income for the state. When it comes to the corresponding political measures, the absolute values ​​play a role in the economic policy discussion, for example in order to keep an eye on the (absolute) new debt of the state - but also quotas that are calculated on this basis. Mind you, these are nominal (and not price-adjusted) variables that are discussed by politicians and the interested public, because it is these variables that burden the coffers. The size of the measures usually ranges from a few million euros to a double-digit figure in billions of euros. In relation to the gross domestic product, Heilemann and Wappler state for the Federal Republic of Germany: "Impetus of approx. 1% on the expenditure side and approx. 1.5% on the income side have so far in fact represented the upper limits of fiscal crisis intervention." 16

For the calculation of the multipliers, it is practically irrelevant how an impulse is dimensioned, provided that the reactions of the model are in the linear range. As a compromise between the different variants that can be found in the literature, it was decided to use impulses of 10 billion euros. That is a total of less than half a percent of the gross domestic product (as of 2012). Since the effects are linear and symmetrical, the effects of smaller or larger (but also reversed) impulses can easily be derived from the results reported here. Formally, the dimensioning of the expenditure and income impulses undertaken here corresponds to the amount of 10 billion euros that is simulated in the IMK study mentioned above. The impulses are given there, however, not with their nominal, but with the deflated values. 17

Direction of the impulses

The impulses can cause both a dampening and a stimulation of the economy. For some impulses, which effect occurs depends on which effect variable is being considered. The authors decided to evaluate the effect of an impulse using the real gross domestic product (GDP) as a yardstick and to proceed from the usual theoretical expectations. A positive (positive) impulse is therefore one that, as expected18, has a positive effect on gross domestic product - regardless of what the other effects are.

The multipliers are according to the formula

m = Δq / Δp

calculated. With regard to the economic policy discussion, real variables such as the change in the number of persons in employment, the real gross domestic product or the real external contribution were used whenever possible for the measurement of the effects, i.e. for the quantity Δq in the numerator of the fraction. The value Δp in the denominator stands for the nominal value of the respective impulse, for example for a reduction in taxes or social security contributions by 10 billion euros. The signs are chosen so that they correspond to the (positive or negative) actual effect.

Duration of the impulse and observation of the effects

In principle, a one-off one-year impulse is simulated. To justify it, it must be remembered that the underlying philosophy is to break down complex economic policy measures into elementary impulses, the economic effects of which are to be examined individually and one after the other. The complex measures can then be reconstructed by using the additivity and linearity of the models used here and adding the effects of the individual impulses.

The same now applies to the time dimension. In this respect, the additivity hypothesis means that an impulse with a total volume of 20 billion euros, which extends over two years, can be viewed as a two-year one-year impulse of 10 billion euros. The effects of these two impulses can in turn be added, whereby the time allocation must be carefully observed.

Although it may not happen very often that economic policy measures such as the scrapping bonus are (can) be implemented for a limited period of time, the definition of the pulse duration made here for analytical reasons as one-time and limited to one year does not limit the applicability of the model results. On the contrary, it is to be expected that the possible combinations of the simulation results opened up in this way will broaden the range of applications. We see the advantage of one-off impulses in particular in the fact that in most cases a build-up or decay phase of the impulse effects can be observed and, as a rule, it is also possible to answer the question of whether negative post-termination effects occur after the impulse has faded.

All impulses are distributed evenly over the four quarters of the year with which the simulation begins (that is the year 2000 for KOMO and 2006 for EMGE). A seasonal spread of the impulses, which would be more realistic, but would considerably increase the simulation effort (above all, considerations on the implementation of the corresponding economic policy measure would be necessary), can be dispensed with, since the effects are reported both in absolute and relative terms with an annual frequency . The effects are shown in tabular form in the year of the impulse and the two following years (see Table 2).Both the KOMO and the EMGE are so-called short-term models, the accuracy limits of which should be reached within three simulation years.

Table 2
GDP multipliers for selected impulses
pulsemodel1 year2 years3rd yeartotal
Direct employee taxesKOMO0,520,09-0,030,58
Employee social security contributionsKOMO0,520,09-0,030,58
Employers' social security contributionsKOMO0,200,310,160,67
Monetary transfers to householdsKOMO0,520,09-0,030,58
Public construction investmentKOMO1,010,09-0,011,09
Government consumptionKOMO0,900,07-0,020,95

Selection of the effect variables and comparability of the model results

Apart from the exogenous variables that are not disturbed by an impulse, the effects of the simulated impulses are reflected in all model variables. It would be possible to show this, but it would lead to a very confusing presentation. Only the GDP multipliers are reported below. In relation to the multipliers, the results of simulations with the two models can be directly compared.

Economic policy consequences

The economically relevant thesis based on the Haavelmo theorem that the "multipliers on the income side [...] are almost consistently lower than those on the expenditure side" 19 has different consequences in different situations. If it is a matter of consolidating the state budget, the objective of doing as little “damage” to the economy as possible results in the recommendation of a priority increase in state income, for example through tax increases, because the negative effects to be expected on the economy are less than for Spending cuts. If, on the other hand, an economic upturn is important in an economic downturn, there should be a stronger concentration on government spending, as this will lead to a stronger economic upturn than government revenue with the same financial commitment.

Income multipliers

The above thesis can be confirmed by and large on the basis of the gross domestic product multipliers. However, a more differentiated view is necessary. In the case of a reduction in employee taxes and employee contributions to social security, the GDP multipliers of both models match almost perfectly - both in terms of the course of the effect and the aggregated (3-year) result, since all values ​​are in the first year and after three years are between 0.5 and 0.8. This means that these multipliers on the income side are roughly half as large as the multipliers on the expenditure side for government consumption and public construction investments, which are close to 1 (KOMO) or even higher (EMGE). Even if the KOMO produces a GDP multiplier slightly below 1 in the case of government consumption, it is still significantly larger than the four multipliers on the income side. In this sense, 2 x 4 confirmation cases of the above thesis can be registered. With regard to possible differences between the models, it is noticeable that in the EMGE positive effects still occur in the second year, so to speak as a "finish", but in the third year an echo effect can be observed that is more negative than that in the KOMO.

With regard to the social security contributions to be paid by the company, both models agree well. The level and course of the GDP multipliers for an impulse on the employers 'social security contributions are almost identical in both models and well below 1.If one compares the multipliers with those of the employees' direct taxes and social security contributions, they appear to have been halved again in the first year of the simulation , but then reach roughly the same level after three years. In other words: In both models there is a stretching of the effect, which overall corresponds to the above thesis. That gives two more confirmatory cases.

The German economy is currently reacting about half as much to the relief of employers as to the workforce in terms of the social security contributions to be paid in the first year. This result is plausible if one assumes that entrepreneurs (can and must) plan their income and expenditure over the long term compared to that of employees.

As an interim result, it can be stated that the income-side GDP multipliers with an impulse affecting income from entrepreneurship and assets, here the employers' social security contributions, achieve overall effects that are well below 1, even after three years. This means that the corresponding multipliers differ greatly from those on the expenditure side. Furthermore, in terms of their effect on GDP, these impulses do not differ in their overall effect from those of relief for employees, but in terms of their course, which extends over a longer period of time.

Expenditure-side multipliers

On superficial examination, the expenditure multipliers are very similar in both models with one exception. On closer inspection, however, there are differences. In terms of transfers to private households, the multipliers of the KOMO are consistently lower than those of the EMGE, and indeed so low that they cannot support the thesis examined. In contrast, the multipliers of the EMGE are not higher than, but very close to 1. In the case of the KOMO, it is already zero in the second year EMGE - due to the circulatory effects - almost the same effect in the second year as in the first. For this reason, the aggregated multiplier is also much larger and therefore more suitable to support the above thesis.

The public construction investments have already been identified as a confirmation case of the more precise Haavelmo theorem. Here, too, the KOMO shows a weaker reaction than the EMGE. However, this concerns not only the positive effects in the first year, but also the negative echo in the third: The EMGE in turn produces a slow decay of the effect in the second year with a negative gross domestic product multiplier in the third year. In the case of government consumption, the multipliers of both models show a time course as in the case of transfers: in the case of the KOMO, the effect is essentially limited to the first year, while in the case of the EMGE it is extended over two years and a negative response in the third year generated. However, the level of the multipliers in the EMGE is roughly twice as high as in the KOMO. The aggregated multipliers are close to and well above 1, so that this result is very compatible with the above thesis that multipliers on the expenditure side are larger than those on the income side.

Overall, in the underlying study, 20 of 18 relevant cases 13 could be rated as confirmation of the thesis, whereby one of the remaining five cases (monetary transfers, KOMO) must be interpreted as a refutation. Four results are either based on an incorrect specification by the KOMO or do not allow a clear assessment. However, only the comparatively clear and probably indisputable results were reported here (see Table 3).

Table 3
Status of the specified Haavelmo theorem: Confirmation and refutation cases
Direct employee taxesKOMOApproved
Employee social security contributionsKOMOApproved
Employers' social security contributionsKOMOApproved
Monetary transfers to householdsKOMONot confirmed
Public construction investmentKOMOApproved
Government consumptionKOMOApproved


The controversy that regularly flares up about the right course in terms of economic policy to revive the economy in times of recession or depression could be made more objective if the actors had a clearer idea of ​​the expected effects of economic policy measures. The thesis, largely confirmed here, that the multipliers of government revenues are significantly below those of government expenditures, can serve as a rough guideline.

Depending on the situation, this thesis has different practical consequences. If it is a question of consolidating the national budget, the recommendation is to increase government revenues as a matter of priority, because the negative effects to be expected on the economy are less than those of spending cuts. If, on the other hand, an economic recovery is important when the economy is down, there should be a stronger focus on increasing government spending, as this would have a greater effect than an equally large reduction in government revenue with the same financial commitment. When putting together an “economic stimulus package”, however, government revenues and expenditures will always play a role for political reasons; detailed multiplier tables can help to find out the expected overall economic effect and, if necessary, to optimize it.

  • 1 Cf. A. Belke: Fiscal Stimulus Packages and Uncertainty in Times of Crisis: Economic Policy for Open Economies, in: Economic Analysis and Policy, Vol. 39 (2009), no. 1, p. 28 f.
  • 2 A. Truger, K. Rietzler, H. Will, R. Zwiener: Alternative strategies of budget consolidation in Austria after the recession, report by the Institute for Macroeconomics and Business Cycle Research (IMK) in the Hans Böckler Foundation on behalf of the Vienna Chamber of Labor, Düsseldorf 2010.
  • 3 G. Quaas, M. Klein: Simulation of economic effects of standardized economic policy measures with the help of the macro-econometric models KOMO 61 (old national accounts) and EMGE (new national accounts). The study was funded by the Hans Böckler Foundation and was published in Berlin in 2012 under the title “Multipliers of the German Economy”.
  • 4 See E. Ilzetzki, E. G. Mendoza, C. A. Végh: How Big (Small?) Are Fiscal Multipliers, IMF Working Paper, WP / 11/52, 2011.
  • 5 Cf. Federal Statistical Office: Effects of a possible VAT increase on the consumer price index, press release, Wiesbaden, July 12, 2005.
  • 6 Cf. W. Kitterer: Impact of sales tax, expert opinion on behalf of the Federal Minister of Economics, Tübingen 1981; see B. Fritzsche, H. Gebhardt, U. Heilemann, H. von Loeffelholz: Perspectives and Options of German Financial Policy 1991 to 1994, in: Wirtschaftsdienst, 71st year (1991), H. 1, pp. 19-32 .
  • 7 Cf. G. Quaas: On the role of theory in macroeconometric forecasting models, in: WiSt - Wirtschaftswwissenschaftliches Studium, 35th year (2006), no. 9, pp. 515-518.
  • 8 See JM Arnold, B. Brys, C. Heady, A. Johansson, C. Schwellnus, L. Vartia: Tax Policy for Economic Recovery and Growth, in: The Economic Journal, Volume 121 (2011), H. 1, pp. F59-F80.
  • 9 K. Deuverden provides a good example: The coalition agreement from a financial perspective, in: Wirtschaft im Wandel, 11th year (2005), no. 12, p. 372 f.
  • 10 Cf. U. Heilemann, G. Quaas, J. Ulrich: Overall economic impact of the budgetary policy of the coalition agreement, in: Wirtschaftsdienst, 86th year (2006), no. 1, pp. 27-36.
  • 11 Cf. M. Bleany, N. Gemmell, R. Kneller: Testing the endogenous growth model: public expenditure, taxation and growth over the long-run, in: Canadian Journal of Economics, 34th vol. (2001), H. 1, pp. 36-57.
  • 12 Cf. P. Lane, R. Perotti: The Trade Balance and Fiscal Policy in the OECD, in: European Economic Review, 42nd vol. (1998), no. 3, pp. 887-895.
  • 13 Cf. U. Heilemann: The RWI economic model - an overview, in: W. Gaab, U. Heilemann, J. Wolters (eds.): Working with econometric models, Berlin 2004, pp. 161-212; see U. Heilemann, S. Wappler, G. Quaas, H. Findeis: Agony of choice? Financial policy between consolidation and economic stabilization, in: Wirtschaftsdienst, 88th year (2008), no. 9, pp. 586-593.
  • 14 Further information at The authors would like to thank the members and guests of the research seminar “Politics and Economy” for the helpful comments and criticisms on the underlying study.
  • 15 A. Truger, et al., Op. Cit.
  • 16 Cf. e.g. U. Heilemann, S. Wappler: “Budget goes before economy” - efficiency and effectiveness of fiscal economic policy 1967 to 2010, will appear soon, p. 145.
  • 17 See A. Truger et al., Loc. Cit., P. 23.
  • 18 The basis of the expectations are the theories of neoclassical synthesis, in particular the AS-AD model.
  • 19 See A. Truger et al., Loc. Cit., Pp. 4, 18 and 23.
  • 20 Cf. G. Quaas, M. Klein: Multipliers of the German Economy, loc.

Title: Public Income and Public Spending Multipliers of the German Economy

Abstract: Theoretically based on the Haavelmo theorem, this study analyzes the economic effects that increasing public expenditure or reducing public income have on the gross domestic product of Germany, with the help of two medium-sized macro-econometric models, the RWI business cycle model and the Econometric Model of the German Economy. The major finding is that most of the public revenue multipliers are considerably lower than most of the public spending multipliers. However, both the dimension and the time course of the effects are a function of the specific kind of politico-economic measures taken by the government.

JEL classification: E17, E61, H12