Price stability is the key goal of almost every central bank in the world. But does that mean stable price levels or inflation rates? The main difference between inflation targeting and price-level targeting is the consequence of missing the target.

- Unanticipated shocks to inflation lead to corrective action when the price is the target.
- Under inflation targeting, past mistakes and shocks are treated as ‘bygones’.

If, for example, inflation is unexpectedly high today, this would be followed in the future by below average inflation under a price-level targeting regime. By contrast, inflation targeting aims for average (i.e. on-target) inflation in future years regardless of the level of current inflation (see Figure 1).

**Figure 1** Inflation and price-level targeting compared

Figure 1 makes clear that expectations depend crucially on the regime in place. For example, suppose the central bank announces an inflation target of 2%. When inflation unexpectedly rises to 3% in period 3, rational households and firms will anticipate future inflation of 2% in periods 4 and 5. By contrast, expected inflation in period 5 would be only 1% with a price-level target, because price targeting calls for below-average inflation in this period. Because the central bank is obliged to offset past inflationary shocks in this way, targeting prices is ‘history dependent’ (Woodford 2003). This mechanism is important for understanding why price-level targeting gives different outcomes to inflation targeting in New Keynesian models.

# A survey of new evidence and thinking

This question of targets – inflation or the aggregate price level – has excited economists for decades. Knut Wicksell first presented the view that Swedish monetary policy should stabilise the price level in 1898. A little over three decades later, Sweden experimented with price-level targeting for the first time (see Berg and Jonung 1999). But price-level targeting did not take-off; it has not been adopted by a major central bank since.

In recent years, however, economists have re-assessed the merits of price-level targeting in the light of new research and better models.^{1} We recently wrote a survey of this new research (Hatcher and Minford 2014), designed to bring an earlier survey by Ambler (2009) up to date. A key new development is the potential role of price-level targeting in helping monetary policy deal with the ‘zero bound’ on nominal interest rates.

# Inflation targeting and the zero bound on interest rates

Consider, for instance, a situation where the economy has been hit by a large negative shock to aggregate demand, and nominal interest rates have been cut to zero in an attempt to stimulate the economy back to full capacity. Because inflation expectations remain anchored at 2% under inflation targeting, the only route by which monetary policy could stimulate the economy is further cuts in nominal interest rates – an option which has been exhausted at this point.

If households and firms understand the impotence of monetary policy in this situation, they might even expect lower future inflation. This would raise real interest rates, thus pushing down demand even further. With real interest rates either constant or rising, a lengthy recession is likely to ensue.

Targeting the price level leads to a different dynamic for inflation expectations. After the demand shock has hit and inflation falls below 2%, a credible price-level target would create the expectation of future inflation of more than 2%. In turn, this expectation will lower real interest rates today and provide necessary stimulus to aggregate demand and upward pressure on prices. This expectations mechanism has additional bite in New Keynesian models because an increase in expected inflation raises current inflation, and higher output expectations raise aggregate demand.

Both Eggertsson and Woodford (2003) and Nakov (2008) confirm this intuition. Welfare losses conditional on reaching the lower bound are much larger under inflation targeting than price targeting in New Keynesian models. More recently, Coibion et al. (2012) consider an extended model with the feature that the optimal rate of inflation can be computed. Because targeting the price level reduces the frequency and severity of zero bound episodes through its effect on expectations, the optimal inflation rate is somewhat lower than under inflation targeting. Since there are additional welfare gains associated with a lower trend rate of inflation, the potential welfare gains from price-level targeting are much larger and amount to 0.4% of GDP per year.^{2}

Covas and Zhang (2010) and Bailliu et al. (2012) show that including in the New Keynesian model some basic financial frictions underlined by the recent financial crisis does not overturn the beneficial effects of price targeting – essentially because the main mechanism via expectations remains powerful in these models. It is important to note, however, that this mechanism rests crucially on the assumption that the price-level target is credible. Also, we cannot yet say much about the relative merits of price-level targeting in models with more sophisticated financial frictions, though we expect to see additional research soon.

# The importance of rational expectations

Because the expectations mechanism under targeting the price is central to its performance, the crucial issue for policymakers is whether expectations are rational and the economy New Keynesian. One way to get at whether expectations are rational is surveys and experiments. Like many economists, however, we remain sceptical about the usefulness of these approaches and think applied macro evidence is preferable when it can be established on strong statistical grounds.^{3}

We, therefore, turn to this literature. Early attempts to test rational expectations in macro models were made by Fair (1993) and several others. When we look at modern New Keynesian models with rational expectations imposed, we find a steady improvement over time in their empirical performance. For instance, Christiano et al. (2005) and Smets and Wouters (2007) show that New Keynesian models can match key dynamic features of US data and perform impressively in out-of-sample forecast tests. Nowadays, most major central banks consider New Keynesian models useful tools for policy analysis.^{4}

*The next logical step* is to test these models directly against the data using statistical tests that accept or reject the basic model and variants of it. This challenge has been taken on by a recent strand of applied macro literature that exploits vector autoregressions (VARs) as a description of macro data. A statistical testing procedure can be built on this, known as indirect inference (see Smith 1993). The basic idea is to simulate the models to create a large number of counter-factual histories, and the VAR relationships implied by them, and then to ask whether the actual history and the VAR estimated on this actual data could be rejected as coming from this distribution at some level of statistical confidence. It turns out that this test has substantial power against mis-specified models (Le et al. 2012), quite a lot more so than tests based on likelihood which can struggle to distinguish between alternative models (see Canova and Sala 2009). Bayesian ranking is based on likelihood and can also suffer from lack of power. Though this could, in theory, be remedied by the use of strong priors, in practical terms it is difficult to come up with a set of at once uncontroversial and strong priors.

The indirect inference test can be applied to any model and its proposed parameters. Furthermore, the possibility that the original set of parameters could simply be wrongly calibrated can be explored by searching over the full range of parameter values permitted by theory.^{5} In recent years, a number of studies have carried out this test on New Keynesian models with rational expectations, largely on US data. For example, Le et al. (2011) reworked the Smets and Wouters (2007) model by adding a competitive sector to both the labour and the product markets and re-estimating it as above. They found that for the post-1984 Great Moderation period, the model passed the indirect inference test comfortably (p-value = 0.16), and that the ‘best’ model over this period was strongly New Keynesian.

Liu and Minford (2012) considered, again on US data, a smaller New Keynesian model. Usefully for our focus here, they tested the model under both rational expectations and behavioural expectations as in De Grauwe (2010). The behavioural expectations are the weighted average of a ‘fundamentalist’ forecasting rule, in which the output gap or inflation are forecasts at their steady state values, and a rule extrapolating the most recent value. Many policymakers have considered such behavioural rules to be probable and have had doubts about the ‘strong’ rational expectations assumption. So, the comparison is pertinent for them. Perhaps surprisingly, the rational expectations model does far better than the behavioural version. Indeed, the latter is strongly rejected even after full re-estimation, whereas the rational expectations version passes after re-estimation by a fair margin (p-value = 0.20).

# Conclusion

Price-level targeting is found in modern macro models to be a good mechanism for helping the economy to recover from deflationary shocks driving monetary policy to the zero bound. It does this because when such shocks occur price-level targeting implies that future inflation will be boosted and so real interest rates are lowered. Moreover, this mechanism would make it feasible for trend inflation to be lowered, which would bring additional benefits. These beneficial effects hang importantly on the structure of New Keynesian models and rational expectations. The empirical literature we have surveyed does not reject these assumptions and favours rational expectations over behavioural ones. We, therefore, conclude that policymakers should continue to pay attention to price-level targeting in the future.

# References

Ambler, S. (2009), “Price-level targeting and stabilisation policy: a survey”, *Journal of Economic Surveys* 23(5), 974–997.

Ambler, S. (2007), “The costs of inflation in New Keynesian models”, *Bank of Canada Review* (Winter), 5–14.

Andolfatto, D., Hendry, S., Moran, K. (2008), “Are inflation expectations rational?”, *Journal of Monetary Economics* 55(2), 406–422.

Bailey, M.J. (1956), “The welfare cost of inflationary finance”, *Journal of Political Economy* 64(2), 93–110.

Bailliu, J., Meh, C. and Zhang, Y. (2012), “Macroprudential rules and monetary policy when financial frictions matter”, Bank of Canada Working Paper 2012-6.

Bank of Canada (2011), Renewal of the inflation-control target.

Berg, C., Jonung, L. (1999), “Pioneering price-level targeting: the Swedish experience 1931-1937”,* Journal of Monetary Economics* 43(3), 525–551.

Canova, F., Sala, L. (2009), “Back to square one: Identiﬁcation issues in DSGE models”, *Journal of Monetary Economics* 56, 431–449.

Christiano, L.J., Eichenbaum, M.S., Evans, C.L. (2005), “Nominal rigidities and the dynamic effects of a shock to monetary policy”, *Journal of Political Economy* 113(1), 1–45.

Coibion, O., Gorodnichenko, Y., Wieland, J. (2012), “The optimal inflation rate in New Keynesian models: should central banks raise their inflation targets in light of the zero lower bound?”, *Review of Economic Studies* 79, 1371–1406.

Covas, F. and Zhang, Y. (2010), “Price-level versus inflation targeting with financial market imperfections”, Canadian Journal of Economics 43(4), 1302–1332.

De Grauwe, P. (2010), “Top-down versus bottom-up macroeconomics”, *CESifo Economic Studies* 56(4), 465–497.

Eggertsson, G.B. and Woodford, M. (2003), “The zero bound on interest rates and optimal monetary policy”, *Brookings Papers on Economic Activity* 1:2003, 139–211.

Fair, R.C. (1993), “Testing the rational expectations hypothesis in macroeconometric models”, *Oxford Economic Papers* 45(2), 169–190.

Hatcher, M., Minford, P. (2014), “Stabilization policy, rational expectations and price-level versus inflation targeting: a survey”, CEPR Discussion Paper No. 9820.

Le, V.P.M., Meenagh, D., Minford, P. and Wickens, M.R. (2011), “How much nominal rigidity is there in the US economy? Testing a New Keynesian DSGE model using indirect inference”, *Journal of Economic Dynamics and Control* 35(12), 2078–2104.

Le, V.P.M., Meenagh, D., Minford, P., and Wickens, M. (2012), “Testing DSGE models by Indirect inference and other methods: some Monte Carlo experiments”, Cardiff University Economics working paper E2012_15.

Liu, C., Minford, P. (2012), “Comparing behavioural and rational expectations for the US post-war economy”, CEPR Discussion Paper 9132.

Nakov, A. (2008), “Optimal and simple monetary policy rules with zero floor on the nominal interest rate”, *International Journal of Central Banking* 4(2), 73–127.

Smets, F. and Wouters, R. (2007), “Shocks and frictions in US business cycles: a Bayesian DSGE approach”, *American Economic Review* 97(3), 586–606.

Smith, A.A. Jr. (1993), “Estimating nonlinear time-series models using simulated vector autoregressions”, *Journal of Applied Econometrics* 8, 63–84.

Woodford, M. (2003),* Interest and prices: Foundations of a theory of monetary policy,* NJ: Princeton University Press.

1 This re-assessment has not been confined to academia: the Bank of Canada recently investigated in detail whether it should switch to a price-level targeting mandate (Bank of Canada 2011).

2 Positive trend inflation has three distinct costs in New Keynesian models (see Ambler 2007). The traditional welfare cost due to inflation acting as a tax on money holdings (see Bailey 1956) is not one of them. It is therefore conceivable that the welfare gains attainable from lowering trend inflation under price-level targeting could be larger than estimated by Coibion et al. (2012). The figure of 0.4% of GDP was arrived at by multiplying the gain of 0.5% of aggregate consumption reported in Coibion et al. by the model ratio of consumption to GDP of 0.8.

3 We provide a brief discussion of the pros and cons of survey and experimental evidence in Hatcher and Minford (2014). One important caveat highlighted by recent research is that statistical results in which survey inflation expectations differ persistently from actual inflation cannot be construed as conclusive evidence against rational expectations because this behaviour could be the result of occasional changes in monetary policy regime combined with a period of (rational) learning by the private sector (see Andolfatto et al. 2008).

4 In practice, most central banks rely on a variety of models, some of which are heavily reliant on economic theory and others which are closer to econometric models.

5 In effect this search amounts to re-estimation via indirect inference (which is asymptotically equivalent to full-information maximum likelihood but in small samples finds the model that gets closest to passing the test).

The weights on each type of forecasting rule vary over time according to the relative past success of each rule.