Assessing sticky price models using the Burns and Mitchell approach

Abstract

This article evaluates sticky-price models using the methods proposed by Burns and Mitchell, focusing on the monetary aspects of the business cycle. Recent research has emphasized the responses of models to shocks at the expense of its systematic component. Whereas sticky-price models have been successful at replicating impulse response functions from vector autoregressions, this article highlights that they are unable to mimic the data for nominal variables. Moreover, the results are robust to the specification of the Phillips curve, including its backward-looking variant, calibrated values and the inclusion of fiscal policy shocks. Since being able to mimic the data is the lowest hurdle a Model must pass, these results pose a challenge for sticky price models.

Acknowledgements

I am grateful to an anonymous referee, Max Gillman, Patrick Minford, Laurence Copeland and seminar participants at Cardiff Business School, the Bank of England and the Money, Macro and Finance Conference for many helpful comments. All errors are my own.

Notes

¹ These are defined as models embodying nominal rigidities (see Goodfriend and King, (1997)), of which New Keynesian models are one variant, which assumes Calvo pricing with the resulting New Keynesian Phillips curve (Equation 5 below).

² See among others, van Els (1995), Fiorito and Kollintzas (1994) and Millard et al . (1997).

³ As in Judd and Rudebusch (1998) and Clarida et al . (2000), there are reasons to believe that the Fed's reaction function was stable during the Volcker–Greenspan chairmanship of the Fed.

⁴ With a value of λ = 1600.

⁵ See McCandless and Weber (1995) or Hoel (1954). The standard deviation of the correlation coefficient can be computed as: (n − 3)^−1/2, where n is the sample size.

⁶ Representative among these are Walsh (2003, Ch. 5), Galí (2003) and McCallum and Nelson (1999a).

⁷ Both the cost-push and monetary policy shocks are assumed to be i.i.d. disturbance with constant variance, whereas the technology shock is assumed to follow an AR(1) process.

⁸ A lucid discussion on the importance of intertemporal substitution of labour supply in business cycle analysis is provided by Blanchard and Fischer (1989, p. 338).

⁹ Assuming that money enters the utility function in separable form has the consequence that the quantity of money can be ignored in the present Model.

¹⁰ In principle the NK Phillips curve would relate inflation to real marginal costs, but in the absence of endogenous state variables, as in the present Model, there is a one-to-one correspondence between the output gap and real marginal costs, so one can use the former directly.

¹¹ See for example, Clarida et al . (2000).

¹² For example, the Bank of England's target is in symmetrical with a target of 2% for the inflation rate.

¹³ Cobham et al . (2004) calculate this menu for a variety of developed economies.

¹⁴ For a discussion on this issue from a central bank perspective see ECB (2000).

¹⁵ As a result, all the models can be solved as functions of the four shocks and the lagged interest rate only, as there are no endogenous state variables present. Given that the shocks are all stationary, stability of the equilibrium requires focus on the behaviour of interest rates.

¹⁶ Using the alternative value of 11 (implying a markup of 1.1) does not affect the main results in this article.

¹⁷ Values of φ₁ = [0.05, 0.1], often used in the literature were considered, but these do not alter the main conclusions of the article. These results are available from the author on request.

¹⁸ See McCallum (2001a) for a lucid discussion of some of the issues.

¹⁹ In this article the term NNS will be used to define all models embodying nominal rigidities, not just the NK Phillips curve.

²⁰ All the Model variants are described in Appendix A.

²¹ According to Mankiw (2001), this formulation is superior to its forward-looking variant as it better represents the economy's response to monetary shocks.

²² Results for all the other models considered in this article are available from the author upon request.

²³ Also, they treat de-trended output as the output gap, whereas in this article that variable would be cyclical output and the gap would be the difference between this variable and its flexible price counterpart.

²⁴ It is worth pointing out that these results are robust to changes in parameter values, as often used in the literature.

²⁵ It is important to note that this refers to cyclical output and not the output gap, which is a different concept in the present Model.

²⁶ The coefficient relating the flexible price level of output to the technology shock is generally close to one for standard calibrated values.

²⁷ This follows Canzoneri et al . (2004), except that, as with output, government purchases are detrended using the Hodrick–Prescott filter. The resulting AR(1) coefficient and SD of the shocks are ρ _g = 0.97 and σ _g = 0.007, respectively.

²⁸ Including investment as in Canzoneri et al . (2004) does not change this result.

²⁹ As is well known, the inclusion of these shocks is often essential for NNS models if these are to argue that there is a trade-off between output and inflation stabilization.

³⁰ Issues of uncertainty about the output gap is ignored in this article.

³¹ See, for example, the arguments put forward by McCallum (1997).