What was Robert Barro smoking when he came up with ‘Ricardian equivalence’?

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Lars Pålsson Syll
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Ricardian equivalence basically means that financing government expenditures through taxes or debts is equivalent, since debt financing must be repaid with interest, and agents — equipped with rational expectations — would only increase savings in order to be able to pay the higher taxes in the future, thus leaving total expenditures unchanged.

Why?

In the standard neoclassical consumption model — used in DSGE macroeconomic modeling — people are basically portrayed as treating time as a dichotomous phenomenon – today and the future — when contemplating making decisions and acting. How much should one consume today and how much in the future? Facing an intertemporal budget constraint of the form

c_t + c_f/(1+r) = f_t + y_t + y_f/(1+r),

where c_t is consumption today, c_f is consumption in the future, f_t is holdings of financial assets today, y_t is labour incomes today, y_f is labour incomes in the future, and r is the real interest rate, and having a lifetime utility function of the form

U = u(c_t) + au(c_f),

where a is the time discounting parameter, the representative agent (consumer) maximizes his utility when

u'(c_t) = a(1+r)u'(c_f).

This expression – the Euler equation – implies that the representative agent (consumer) is indifferent between consuming one more unit today or instead consuming it tomorrow. Typically using a logarithmic function form – u(c) = log c – which gives u'(c) = 1/c, the Euler equation can be rewritten as

1/c_t = a(1+r)(1/c_f),

or

c_f/c_t = a(1+r).

This importantly implies that according to the neoclassical consumption model changes in the (real) interest rate and consumption move in the same direction. And — it also follows that consumption is invariant to the timing of taxes, since wealth — f_t + y_t + y_f/(1+r) — has to be interpreted as present discounted value net of taxes. And so, according to the assumption of Ricardian equivalence, the timing of taxes does not affect consumption, simply because the maximization problem as specified in the model is unchanged.

That the theory doesn’t fit the facts we already knew.

And a couple of months ago, on Voxeu, Jonathan A. Parker summarized a series of studies empirically testing the theory, reconfirming how out of line with reality is Ricardian equivalence.

This only, again, underlines that there is, of course, no reason for us to believe in that fairy-tale. Ricardo himself — mirabile dictu — didn’t believe in Ricardian equivalence. In Essay on the Funding System (1820) he wrote:

But the people who paid the taxes never so estimate them, and therefore do not manage their private affairs accordingly. We are too apt to think that the war is burdensome only in proportion to what we are at the moment called to pay for it in taxes, without reflecting on the probable duration of such taxes. It would be difficult to convince a man possessed of £20,000, or any other sum, that a perpetual payment of £50 per annum was equally burdensome with a single tax of £1000.

And as one Nobel laureate had it:

Ricardian equivalence is taught in every graduate school in the country. It is also sheer nonsense.

Joseph E. Stiglitz, twitter