DSGE macro models criticism, a round up. Part 5, the intertemporal government budget constraint

Guest post by Brian Romanchuk (see also his blog Bond Economics)

Earlier posts in this series, which consists of concise posts looking at DSGE models using the lens of statistical concepts, were about money, market fundamentalism, unemployment and capital.

Problems With Fiscal Policy In DSGE Models

Dynamic Stochastic General Equilibrium (DSGE) models suffer from a great many defects, but the specification of fiscal policy in standard models stands out. Given the ongoing wave of publications of these models, it is hard to generalise about them. My statements here are based on how fiscal policy is represented within the models presented in the Chapter 12 of the text Advanced Macroeconomics by Paul Romer (fourth edition). The models in Romer are fairly indicative of much of the literature, but my criticisms here will not apply to all of them.

Behavioural Assumptions

One of the key results used within DSGE models is that the timing of taxes has no effect on household behaviour.  This assumption is known as “Ricardian Equivalence”. There is an academic literature which questions this behavioural assumption. Although this is an interesting debate, my view is that the specification of fiscal policy within DSGE is internally inconsistent, and so the quality of the behavioural assumptions around Ricardian Equivalence appears to be a secondary issue.

Poor Specification Of Fiscal Policy

The standard specification of fiscal policy (if it is present at all) is as a series of exogenous primary fiscal balances. (The primary fiscal balance is defined by: (fiscal balance) = (primary balance) + (interest expense).) By stripping out interest payments, it appears that fiscal policy is completely decoupled from interest rate policy.

This makes little sense, for three reasons. Firstly, taxes are paid on interest receipts from government, and so changes in the interest bill will affect the primary balance, even if we hold all else equal. Secondly, unless we assume that interest income has no effect on household spending, interest costs have a multiplier effect which will affect non-interest spending, such as unemployment insurance. Finally, it makes no sense to make primary balances entirely exogenous to the state of the economy (although it should be noted that some DSGE models relax that assumption).

The Accounting Identity

Within a mathematical system, constraints determine the possible solutions to the system. Within DSGE models, there are two types of constraints: firstly, an accounting identity, and secondly, a constraint that allegedly sets the limits on the feasible set of future primary surpluses. The second constraint is the subject of the article, but some DSGE treatments will lump these two types of constraints together.

The accounting identity used within DSGE models is obviously correct. (Although it is sometimes expressed as an expectation, which is rather bizarre, as the probabilistic framing implies that there is some probability that the accounting identity will be violated.)

The accounting identity is abused sometimes in non-mathematical discussions of fiscal policy, as it is restated as:

Government spending = (Increase in debt) + (Increase in money) + (Taxes).

This is converted to the verbal formulation that “Government spending is financed either by debt, money-printing, or taxes.” This then leads to discussion how the different modes of finance have different effects. Such discussions are not supported by the theory, and are just another example of how verbal discussions of accounting constraints break down (the S=I identity is the classic example of how projecting beliefs onto accounting identities leads to confusion).

The Infinite Horizon Constraint

If we assume that there are no money holdings, the infinite horizon constraint is:

Present Value of Government Debt = Expected Discounted Value of Projected Primary Surpluses.

This condition is equivalent to stating that the present value of the stock of government debt will go to zero as time goes to infinity. If we add in money holdings, one needs to add corrective terms for the effect of money growth (although this is often ignored).

The problem with this constraint is that it is either trivial or wrong.

• If the rate of interest rate on debt is higher than the growth rate of the economy, all the constraint says that the debt-to-GDP ratio will not allowed to become arbitrarily large. Primary surpluses are needed to act as a brake on debt growth. However, having the debt-to-GDP ratio becoming arbitrarily large is an outcome that would never happen within a sensible model framework. This has been analysed in the Stock-Flow Consistent modelling literature; Marc Lavoie’s tekst Post-Keynesian Economics: New Foundations gives an overview of this in Section 5.6.3. Therefore, this is not really a “constraint”.
• If the rate of interest is less than the growth rate of the economy, the constraint implies that the debt-to-GDP ratio will tend to 0 as time goes to infinity. Since government debt is needed for liquidity management within the financial system, such an outcome seems implausible.

It should be noted that not all models impose this constraint; for example, overlapping generations models with infinite generations do not. See [Fullwiler 2006] for a longer discussion.

Moreover, it is unclear why the constraint is supposed to hold.

The justification is based on a “no-Ponzi” microeconomic logic: households will lend to other entities, but they will not finance a “Ponzi scheme”.  For example, in Romer (page 589):

And if there are a finite number of agents [households], at least one agent must be holding a strictly positive fraction of this debt. This means that the limit of the present value of the agent’s wealth is strictly positive; that is, the present value of the agent’s spending is strictly less than the present value of his or her after-tax income.

However, this appears to be a fallacy of composition. Since the household sector can juggle between money and debt holdings, and the price of debt varies based on a varying interest rate, it is difficult to describe the full solution. In order to simplify matters, we can consolidate government liabilities into a single variable L(t), which is equal to money holdings at time t plus the present value of government debt at time t.  Although an individual household can reduce its financial assets by buying goods, this implies that its counterparty will increase its financial assets accordingly. There is nothing that the household sector can do at time t to affect the level of L(t).

We can then apply the governmental accounting identity to realise that L(t+1) is greater than or equal to L(t) plus the primary deficit. (It is equal if the interest rate is zero, and greater if interest expense is greater than zero. I assume that interest rates are greater than or equal to zero.) There is nothing that the household sector can do about this, since the fiscal balance is assumed to be exogenous to the state of the economy (or nearly so) in the specification of fiscal policy within the DSGE model.

Since the government can set an arbitrary lower bound to the amount of debt outstanding within a DSGE model on any finite horizon, it contradicts the assumption that the present value must tend to zero on an infinite horizon. This contradicts the infinite horizon budget constraint.