*Guest Blog – The Integral Reviews: Paper 2 – Ball (1999)*

*By “Integral”*

**Reviewed:** Laurence Ball (1999), *“Efficient Rules for Monetary Policy.”* International Finance 2(1): pp. 63–83

also featuring

Henrik Jensen (2002), *“Targeting Nominal Income Growth or Inflation?”* The American Economic Review 92(4): pp. 928–956.

Glenn Rudebusch (2002), *“Assessing nominal income rules for monetary policy with model and data uncertainty.”* The Economic Journal 112(479): pp. 402–432.

*Introduction*

Larry Ball’s 1999 paper makes two claims that are relevant for Market Monetarists. One is uninteresting, the second is interesting.

1. NGDP targeting is actively destabilizing

2. NGDP targeting is inferior to inflation targeting in a wide range of contexts.

The monetary economics blogosphere has analyzed the first claim to exhaustion. For a review see Adam P’s first post on the paper, replies by Scott Sumner and Bill Woolsey, Adam’s rejoinders (1,2), Adam again, and a contribution from Nick Rowe.

The result of that exchange was identical to the result of the academic response to Ball’s paper: the first claim is generally false and holds only under restrictive assumptions, but the second result is more robust and is typically left unaddressed during responses. For detailed responses to the stability claim see McCallum (1997) and Dennis (2001).

I’m going to take a stab at the second claim. Let’s start with Ball’s model.

*Model*

Ball sets up a simple two-equation model, though containing the essential features of the larger-scale models usually employed for policy analysis. The first equation is an IS curve that relates output to its own lag and the lagged interest rate. The second is a Phillips curve that relates inflation to its own lag and lagged output. Mathematically we have:

p(t) = p(t-1) + a*y(t-1) + n(t)

y(t) = c*y(t-1) – b*r(t-1) + e(t)

where p is inflation, y (log) output, and r the interest rate, all measured relative to their steady-state values.

The model contains two important features: a unit root in inflation and a lag structure in which the central bank can affect output one year out but inflation only two years out. This model is trivially simple: there is no explicit accounting for private-sector expectations and there is only a single transmission mechanism of monetary policy, from the interest rate to output to inflation. The model is closed with an interest-rate rule chosen by the central bank to hit some objective.

The unit root is key for Ball’s first claim; the lag structure is key for his second claim. In a model where the interest rate affects output and inflation with a lag in the Phillips Curve, targeting nominal GDP causes the economy to cycle, hitting the NGDP target every period but doing so by causing undesirable oscillations in output and inflation. However, if one changes the Phillips curve to eliminate the lag in ouptut, nominal GDP targeting becomes an extremely attractive alternative to inflation targeting. It is difficult to prove this in closed-form so I will appeal to two recent simulation-based papers.

*Assessment*

Rudebusch (2002) tests the efficacy of two distinct NGDP targeting rules against a Taylor Rule. All three policy rules are evaluated relative to a social loss function which weighs the variance of output, inflation, and the nominal interest rate. Rudebusch’s model is identical to Ball’s except for adding a role for private-sector expectations. His simulation results mirror Ball’s theoretical result: for reasonable weighs on the forward-looking and backward-looking elements of the Phillips Curve, NGDP targeting severely underperforms relative to the Taylor Rule.

A second simulation is provided by Jensen (2002), whose model is identical to Rudebusch’s save for the lag structure: in Jensen’s model output, inflation and the interest rate are co-determined simultaneously. He tests five different central bank rules, each calibrated to be optimal within their own class: the fully optimal pre-commitment rule, a policy of pure discretion, inflation targeting, nominal income targeting, and a “combination” regime of targeting a weighted average of NGDP and inflation. He finds that NGDP targeting oupterforms inflation targeting in nine parameter specifications covering many economically “interesting” cases. In the simulation where supply shocks dominate, a case of much concern to Market Monetarists, NGDP targeting strongly outperforms inflation targeting and indeed comes close to mimicking the results of the fully-optimal rule.

So what is left of Ball’s claim? Rudebusch shows that NGDP targeting provides subpar performance in a model with lags in the Phillips curve. However it is equally true that NGDP targeting outperforms inflation targeting in a model without lags in the Phillips curve. The exercise provides two main results. First, the desirability of NGDP targeting is sensitive to the lag structure of a model, and of course the relevance of the lag structure remains an empirical question. This undermines NGDP targeting’s appeal as a rule which is robust to model structure. Second, the desirability of NGDP targeting is robust within the class of IS-PC models that employ a properly microfounded Phillips curve

*References*

Ball, Laurence. 1999. “Efficient Rules for Monetary Policy.” International Finance 2(1): pp. 63–83

Dennis, Richard. 2001. “Inflation expectations and the stability properties of nominal GDP targeting.” The Economic Journal 111(468):103–113.

Jensen, Henrik. 2002. “Targeting Nominal Income Growth or Inflation?” The American Economic Review 92(4):928–956.

McCallum, Bennett T. 1997. “The Alleged Instability of Nominal Income Targeting.” NBER Working Paper No. 6291.

Rudebusch, Glenn D. 2002. “Assessing nominal income rules for monetary policy with model and data uncertainty.” The Economic Journal 112(479): 402–432.

Two technical notes

1. Ball and Rudebusch measure society’s loss via the weighted sum of the variances of output, inflation, and the interest rate. Jensen by contrast uses a societal loss function that depends on the sum of weighted squared deviations of output and inflation from their steady-state values. Cursory inspection of Jensen’s tables shows that if one reformulates his societal loss in terms of variances, IT and NGDPT deliver outcomes which are nearly equivalent. However even if one uses variances NGDPT still weakly outperforms IT in most specifications.

2. The NGDPT and IT regimes in Jensen are themselves “mixed” regimes which put some weight on the output gap. Given that all inflation targeting in practice gives some weight to the output gap, the inclusion of such a term in both rules is innocuous.

——

See Integral’s earlier guest post: *“The Integral Reviews: Paper 1 – Koenig (2011)”*

## David Eagle

/ January 16, 2012I wish to address the issue Integral primary addresses which is whether Nominal GDP (NGDP) targeting is inferior or superior to inflation targeting. Ball’s analysis was based on assuming an ad hoc social loss function “which weighs the variance of output, inflation, and the nominal interest rate.” Other than including the nominal interest rate, this ad hoc loss function is similar to the macroeconomic profession’s standard ad hoc loss function which weighs the variance of inflation and output gap or inflation. However, that macroeconomic standard ad hoc loss function and the one used by Ball conflicts with Pareto efficiency. It treats inflation as bad regardless whether that inflation was caused by aggregate-demand shocks or aggregate-supply shocks. As Koenig (2011) points out and as Dale Domian and I (2005) point out, aggregate-supply-caused inflation or deflation is useful to help achieve the Pareto-efficient sharing of Real GDP risk. When we follow Pareto efficiency rather than making an ad hoc assumption of a social loss function, then NGDP targeting Pareto dominates inflation targeting except in the unlikely extreme that lenders have very high relative risk aversion compared to the rest of the economy and borrowers have low relative risk aversion compared to the rest of the economy.

## Integral

/ January 16, 2012Prof. Eagle,

Thank you for the comment.

I know you have done some work in the area of NGDPT vs IT optimality so I was hoping to see you here. Your claim that NGDP targeting Pareto dominates inflation targeting is quite strong, and if true, exceedingly useful. I didn’t want to go that far in my own post but look forward to reading your work on the issue.