Haavelmo theorem

The Haavelmo theorem (after the Norwegian economist Trygve Haavelmo ) relates to the income effects of budget-balance-neutral fiscal policy and states that an increase in government expenditure G, which is fully financed by additional taxes T, leads to an increase in equilibrium income / equilibrium domestic product Y, which is at least is as large as the increase in government spending or the tax increase necessary to finance it, i.e.: ${\displaystyle \Delta Y\geq \Delta G=\Delta T}$

Since, in contrast to private households, a state does not have a marginal savings rate , 100% of the tax revenue is reinvested, according to Haavelmo. Taking into account the multiplier effect, a higher national income can therefore be calculated.

As a result of this theorem it can be stated that the state can increase the macroeconomic income / domestic product by levying more taxes and immediately spending this income in full again (so-called budget extension ).

It can be concluded from the theorem that an infinite expansion of tax-financed government spending could increase the gross domestic product indefinitely . Basically, however, with economic laws, linear relationships cannot be assumed in any order of magnitude; rather, non-linearities would have to be taken into account for stronger impulses. Thus, in an econometric model, impulses of arbitrary strength (in this case, budget extension of the government account) cannot be entered if the results are not to be unrealistic.

Mathematical derivation

First, the multiplier of a greatly simplified economy on the goods market is derived. The investments are assumed to be constant. They neither react to a change in the interest rate (also because the money market is not taken into account in the model), nor to a change in income. The disposable income is as defined. ${\displaystyle Y_{v}=Y-T}$

${\displaystyle Y=c_{0}+c_{1}\cdot Y_{v}+I+G}$

${\displaystyle Y=c_{0}+c_{1}\cdot (Y-T)+I+G}$

${\displaystyle Y-c_{1}\cdot Y=c_{0}-c_{1}\cdot T+I+G}$

${\displaystyle Y(1-c_{1})=c_{0}-c_{1}\cdot T+I+G}$

${\displaystyle Y={\frac {1}{1-c_{1}}}\cdot (c_{0}-c_{1}\cdot T+I+G)}$

The Haavelmo theorem assumes that additional government expenditures are compensated by a corresponding tax increase. That is why it is set. It follows: ${\displaystyle G=T}$

${\displaystyle Y={\frac {1}{1-c_{1}}}\cdot (c_{0}-c_{1}\cdot G+I+G)}$

${\displaystyle Y={\frac {1}{1-c_{1}}}\cdot (c_{0}+(1-c_{1})\cdot G+I)}$

Forming the total differential shows the effect of such a tax refinanced increase in government spending:

${\displaystyle dY={\frac {1}{1-c_{1}}}\cdot (dc_{0}+(1-c_{1})\cdot dG+dI)}$

${\displaystyle {\frac {\partial Y}{\partial G}}={\frac {1}{1-c_{1}}}\cdot (0+(1-c_{1})\cdot 1+0)}$

${\displaystyle {\frac {\partial Y}{\partial G}}={\frac {1-c_{1}}{1-c_{1}}}=1}$

The multiplier for an increase in government spending is 1. In plain English, this means that for each additional unit G that is refinanced through taxes, income Y is again increased by one unit. The disposable income, which is defined as , remains constant. ${\displaystyle Y_{v}=Y-T}$

Alternative to derivation

Alternatively, one could justify the Haavelmo theorem using the following derivation:

The multiplier effect on government spending increases demand as follows: ${\displaystyle \Delta G}$

${\displaystyle \Delta Y={\frac {1}{1-c_{1}}}\Delta G}$

The multiplier effect in taxes lowers demand, but only by ${\displaystyle \Delta T}$

${\displaystyle \Delta Y=-{\frac {c_{1}}{1-c_{1}}}\Delta T}$

Taken together, tax-financed government spending ( ) increases demand ${\displaystyle \Delta G=\Delta T}$

${\displaystyle \Delta Y={\frac {1}{1-c_{1}}}\Delta G-{\frac {c_{1}}{1-c_{1}}}\Delta T=\Delta G\left({\frac {1}{1-c_{1}}}-{\frac {c_{1}}{1-c_{1}}}\right)=\Delta G}$

criticism

Various aspects are expressed as criticism of the multiplier approach:

• Neglect of the personal and functionally different consumption rates
• Flexibility of wages, prices and interest in the medium to long term
• Dependency of current consumer spending on current income with a marginal consumption rate between zero and one (absolute income hypothesis; opposite: permanent income hypothesis; life cycle hypothesis)
• Neglecting asset and capacity effects in the context of the short-term analysis

literature

• T. Haavelmo: Multiplier Effects of a Balanced Budget , in: Econometrica 13, 311-318, 1945.
• Hans G. Monissen: The Haavelmo Theorem for Endogenous Tax Revenue . In: The Haavelmo Theorem for Endogenous Tax Revenue . No. 1 , January 1991, pp. 25-28 ( ECOCHRON [accessed September 8, 2008]).
• P. Lang: Integration, Currency and Growth. Dimensions of international economic relations . Ed .: R. Ohr. Duncker and Humblot, Berlin 2002.

Web links

• Fifteen Fatal Fallacies of Financial Fundamentalism (Engl.)
• Economic Fallacy VI: The Divisive Multiplier (Engl.)
• "Multiplier Effects of a Balanced Budget." Econometrica (1945), 13: 311-318 by Trygve Haavelmo " (English; PDF; 411 kB)

Individual evidence

1. ↑ See Gabler Wirtschaftslexikon online on the subject