What Is Ricardian Equivalence, As Well As Why It Does Non Hold

Ricardian Equivalence is a theoretical concept that has been used to debate that financial policy is non effective. The declaration is that increased authorities spending implies higher hereafter taxes, hence households volition increment savings to cancel out the increment inwards authorities spending. This concept has been heavily disputed; see this weblog entry past times Bill Mitchell for an example. He argues that diverse assumptions are also restrictive inwards the models that exhibit the “Ricardian Equivalence” effect.

In this article, I volition innovate the “inter-temporal governmental budget constraint”, which is the equation which provides the justification for Ricardian Equivalence. I also exhibit why this equation does non agree if term premia are non-zero. The nautical chart inwards a higher house gives an instance that shows the fault inwards its prediction close the Net Present Value of hereafter primary surpluses tin instruct arbitrarily large. This has obvious implications for models that contain this constraint, equally good equally the usage of the concept inwards the analysis of financial sustainability.

An Incomplete Version Of The Inter-Temporal Budget Constraint

I volition start alongside an incomplete version of the inter-temporal budget constraint. The ground I start alongside this version is that this is how I accept seen the equation stated inwards many places on the internet. (In fact, it took me awhile to break the equation stated correctly.)

The incomplete version of the equation is:

(1)   Amount of authorities debt outstanding = Net nowadays value of all hereafter primary surpluses.

Note: The primary surplus is the financial residual excluding involvement payments (see this post for to a greater extent than details).

As an instance of a usage of this incomplete version of the equation, it was used inwards the Wikipedia entry for “Fiscal Sustainability” (at the fourth dimension of writing). To live on fair, the equation is noted inwards passing, without details on embedded assumptions.

An Incorrect Interpretation

Equation (1) is frequently loosely interpreted equally important that the stock of debt outstanding must live on “paid off” past times hereafter primary surpluses. This interpretation together with hence leads to a mutual unloosen Definition of Ricardian Equivalence – if you lot increment the amount of debt, hereafter taxes volition arise to pay dorsum that debt.

This wrong interpretation would appear to live on refuted past times the fact that governments whorl debt, together with hence “the debt is never paid back”. However, the equation does non imply that authorities debt must live on reduced to zero; it is equivalent to assuming that the Net Present Value (NPV) of the debt goes to zippo equally fourth dimension goes to infinity. In other words, the stock of debt tin grow exponentially over time, yet the growth charge per unit of measurement is less than the discount rate.

Seigneurage – The Missing Term

The missing term inwards equation (1) is the outcome of seigneurage; which is typically interpreted equally the turn a profit the authorities earns from creating (“printing”) non-interest bearing coin or reserves.

The adjusted version of the equation is:

(2) Amount Of Government Debt Outstanding = NPV(future primary surpluses + seigneurage “revenue”).

The add-on of seigneurage is manifestly necessary. Debt tin live on cancelled alongside “printed money” without the ask for a primary surplus. However, fifty-fifty if the increment inwards the amount of coin is non permanent, the equation needs to live on modified.

As an example, assume a rather pocket-size authorities has $100 inwards debt outstanding, together with the 1-year involvement charge per unit of measurement is 5%. Let us together with hence assume the authorities buys dorsum the debt alongside $100 inwards the cast of money. After ane year, it runs a primary surplus of $100, which together with hence cancels out the increment inwards the monetary base. (Since the debt was bought back, the primary surplus equals the overall financial surplus.)  The NPV of the sequence of primary surpluses was $100/(1.05) = $95.24. This is less than the initial stock of debt ($100).


Money printing is associated alongside inflation, equally a resultant of the quantity theory of money. That is beyond the reach of this article. However, the fundamental indicate to note: seignorage has to live on accounted for equally it creates a liability alongside an involvement charge per unit of measurement less than is assumed inwards the discount bend used to derive the governmental inter-temporal budget constraint.

Why The Equation Does Not Hold In The Real World

Equation (2) volition non agree inwards the existent world. The ground why is hinted inwards the previous section: involvement costs for the government should live on expected to be below the path of forrad rates generated past times the authorities bend used to discount the NPV of surpluses.

Take equally an instance a authorities alongside $100 debt outstanding inwards the cast of a 1-year debt issue; it pays annually alongside a charge per unit of measurement of 5%. The next fix of operations are expected to occur:

1. At yr 1, the debt matures together with the novel outstanding is $105. This debt is rolled into a novel 1-year debt issue, together with the expected charge per unit of measurement is also 5%.
2. At yr 2, the minute debt number matures, together with the outstanding is instantly $110.25. Influenza A virus subtype H5N1 primary surplus of $110.25 is used to repay the debt completely.

The NPV of the serial of primary surpluses volition equal $100 (the initial amount of debt) if together with only if the 2-year annual involvement charge per unit of measurement used to discount the surplus inwards yr two is equal to 5%. This implies that the 2-year term premium has to live on equal to zero. (See this article for a Definition of the term premium.)

More generally, equation (2) volition only agree if the term premium is exactly equal to zippo for all maturities. However, at that spot is a really large academic literature - affine term construction models – which is predicated just on the fact that term premia are non-zero. In fact, the profitability of borrowing curt together with lending long (which exploits the term premium), is an empirical regularity that has been known close for centuries. (From the indicate of persuasion of a bond investor, rolling bonds is expected to generate higher returns than rolling T-Bills over long fourth dimension horizons.) Meanwhile, governments typically accept a large amount of short-dated newspaper that is repeatedly rolled over. This creates a really large amount of debt that volition live on rolled at rates below the forwards implied past times the discount curve.

The errors introduced past times ignoring the term premium are non trivial. Since the growth rates of nominal gross domestic product tin live on close the discount rate, the specification fault inwards the equation tin instruct arbitrarily large. (Making the  supposition that debt/GDP ratios rest inwards a constant range. This supposition is a stock-flow norm, together with it appears to live on a required supposition for capitalist economies.)

Take equally a elementary example:

1. The province has $100 inwards 1-year debt (annual pay) outstanding. The involvement charge per unit of measurement on 1-year debt is 5%, together with volition ever live on rolled at 5%.
2. Nominal gross domestic product growth is 6%. Influenza A virus subtype H5N1 primary deficit is run each year, inwards guild to proceed the debt/GDP ratio constant.
3. After yr 2, the discount charge per unit of measurement is some value greater than 6%. (Note that the spread of the discount charge per unit of measurement over the expected charge per unit of measurement of 5% is the term premium.)

How the cash flows work:

1. In yr 1, the authorities has to pay $5 inwards interest, taking the debt outstanding to $105. However, the debt outstanding has to ascent to $106 hence that the debt outstanding grows at the same measuring equally nominal gross domestic product (6%). Therefore, a $1 primary deficit is run.
2. In yr 2, the authorities has $5.30 inwards involvement expenses (5% of $106). However, it needs to increment its debt past times $6.36 (6% growth rate), hence that the primary deficit has to live on $1.06.
3. It tin live on easily verified that the primary deficit volition grow at 6% per yr thereafter. 

The budget constraint equation (2) insists that the NPV of the primary surpluses for all hereafter fourth dimension would live on $100. Instead, increasingly large deficits are run each year. The nautical chart at the kickoff of the ship service shows the magnitude of the fault inwards the “equation”, equally a business office of the discount rate.

One could debate that I am "cheating" past times using a discount charge per unit of measurement that is non determined past times actual traded instruments (the only bond outstanding has a 1-year maturity). This tin live on addressed past times either:

1. assume a swap bend exists, allowing us to impute the discount rates for times beyond the 1-year point; or
2. assume some epsilon-small amount of debt is outstanding at each maturity beyond the 1-year  point. This creates the discount bend needed. In this case, the forecast errors of the NPV volition live on slightly smaller than is shown inwards the chart. Since the fault is unbounded equally the discount charge per unit of measurement tends to 6%, this is non-material. 

In whatsoever event, some like extrapolation would accept to live on done inwards the existent world, equally most governments accept maximum bond maturities some 30-50 years.

Finally, ane could debate that the errors are really unknown, since nosotros cannot break the term premium or long-term growth rates. This may live on true, but that simply implies that the errors inwards the inter-temporal authorities budget constraint are unknown but tin live on arbitrarily large. This makes it only useless equally an analytical tool.

 

Conclusion

The touchstone “inter-temporal governmental budget constraint” does non agree nether the existent basis status of the term premium beingness strictly positive, together with tin generate arbitrarily large errors. However, ane could examine to relieve the concept by:

1. making the manifestly wrong supposition that the term premium is identically equal to zero; or
2. redefining how to calculate the “net nowadays value”.

Even so, the constraint volition soundless neglect equally the resultant of weaknesses inwards the assumptions regarding the deportment at infinity. Moreover, fifty-fifty if all of these non really sensible assumptions are imposed on the model inwards guild for the constraint to hold, a welfare province volition bear inwards the contrary fashion than is usually supposed past times the usual interpretation of Ricardian Equivalence (hint).  I volition verbalize over these points inwards ane or to a greater extent than follow-up posts.

(c) Brian Romanchuk 2013