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Empirical Economics

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24.11.2018

The Neo-Fisherian hypothesis: empirical implications and evidence?

verfasst von: William J. Crowder

Erschienen in: Empirical Economics | Ausgabe 6/2020

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Abstract

The Neo-Fisher hypothesis is the idea, first suggested by Jim Bullard (FRB St. Louis Rev 92(5):339–352, 2010) and then thrown into the public debate by John Cochrane on his blog (http://johnhcochrane.blogspot.com/), that trend inflation can be increased by increasing the nominal policy rate. The reasoning is that the Fisher relation must hold in the long run, so given a constant steady-state real rate of interest, raising the nominal interest rate will eventually lead to a higher inflation rate. Cochrane (Do Higher Interest Rates Raise or Lower Inflation? Hoover Institution, 2016) demonstrates that this Neo-Fisher result is consistent with virtually all dynamic general equilibrium macroeconomic models, like the new Keynesian and DGSE models employed by policymakers. The implication of the hypothesis is that an increase in expected (trend) inflation can be caused by an increase in nominal interest rates. An empirical analysis using US data reveals that, contrary to the Neo-Fisherian hypothesis, trend inflation causes nominal interest rates.

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Source: http://www.federalreserve.gov/monetarypolicy/bst_recenttrends.htm.

While it is still the case that official FOMC policy is an inflation target of 2%, it is clear from the meeting minutes that members of the committee have been and continue to be concerned about the potential for a significant and potentially damaging deflation.

The genesis of the idea seems to be Bullard (2010).

Note that in such equilibrium it will also be the case that expected inflation will equal the trend inflation rate. This may be the target rate of inflation chosen in a central banker’s policy rule, or it may simply be the long-run trend growth rate of inflation as determined under a monetary aggregate target, exchange rate target, etc.

Such changes in the nominal rate must, of course, be sustained over a long period so as to be considered permanent.

It is important to note that the policy action described in the text is not equivalent to raising the central bank’s target inflation rate \( \pi^{*} \) in (3). The dynamic adjustment in the NK model may be significantly different, especially under the Taylor principle.

Andolfatto and Williamson (2015) build a DGSE model with a very interesting mechanism where firms use short-term government (risk-free) debt as a transactions technology. When the central bank hoards the risk-free debt through its open market operations, transaction costs rise in the economy, resulting in lower output and inflation.

This is a feature of virtually all long-run equilibria in dynamic macro-models.

Besides making inference asymptotically standard in the VECM-MLE, several studies, e.g., Gonzalo(1994) and Haug (1996), using Monte Carlo analysis reveal the procedure to perform well under most data-generating processes.

An appendix provides a complete discussion of the relevant issues and testing procedures. Using the LR tests described in the appendix, I am able to conclude that model specification \( H_{0}^{*} (q) \) is most consistent with the data.

The mnemonics for these series are FEDFUNDS, TB3MS, GS1 and GS5.

This is the Fed’s preferred inflation measure. The data were retrieved from the FRED database at the St. Louis Federal Reserve Bank. The series mnemonics are PCEPILFE. I also repeated the analysis (results not reported) using the PCEPI and CPI inflation measures with no qualitative difference in results.

Tests for cointegration in the four-variable VECM that includes the nominal interest rates are consistent with three cointegrating relationships, implying the four nominal rates all share a common stochastic trend.

The VECM included an unrestricted constant and six lags of the endogenous variables to eliminate significant serial correlation in the residuals as revealed through an LM test for fourth-order autocorrelation with a test statistic of 3.34 distributed as a \( \chi^{2} (4) \) with a p value of 50%.

Results derived from performing the same analysis with each of the other inflation measures yield qualitatively identical results.

I performed a battery of unit root tests on the data, and the results are consistent with both nominal interest rates and inflation evolving as I(1) processes. Furthermore, the residuals from the VECM have significant conditional heteroscedasticity (ARCH) effects. As a consequence, all VECM parameters are reported with heteroscedasticity-robust standard errors.

The appendix discusses the restrictions and inference on the deterministic components imposed in the empirical analysis. For example, in the fed funds model the LR test of \( H_{1}^{*} (1) \), the specification, used in the analysis, that restricts the constant to lie in the cointegration space, versus \( H_{1}^{{}} (1) \), the more general model that allows for linear trends in the data, yields a value of 0.05 which is distributed \( \chi^{2} (1) \).

The 5% critical value of this test statistic from MacKinnon et al. (1999) is 20.26.

The hypothesis being tested is equivalent to the null that the non-excluded variable is stationary alone.

The conditions for dynamic stability in the bivariate VECM, \( \alpha_{i} - \alpha_{\pi } < 0 \) and \( \alpha_{i} - \alpha_{\pi } > - 2 \), are met for all four Fisher systems.

The calculated trace statistics of the null hypothesis that \( q = 0 \) for TB3, GS1 and GS5 Fisher systems are 16.33, 16.89 and 16.18, respectively. The 5% critical value is 15.49. This point is worth emphasizing. Had I used the more general VECM specification, Case 3 in the appendix, I would have rejected no cointegration at the 5% level or higher for all three longer-maturity systems. Given the trade-off between the power of the cointegration test or model specification accuracy, the latter prevails in the present analysis.

See Laubach and Williams (2003) and Kiley (2015).

The unit Fisher effect restriction is imposed throughout the remainder of the analysis.

Hansen and Johansen (1999) show that the asymptotic distribution of the fluctuation test is a poor approximation in finite samples and suggest using a bootstrap procedure to simulate finite sample critical values. The 5% critical values shown in Fig. 7 are calculated using a block bootstrap of length 12 which draws bootstrapped residuals from the original estimated residuals without replacement such that each observation block has an equal probability of being drawn. Bootstrap results were not sensitive to the block size.

Given the conditional heteroscedasticity in each system, the error variance is allowed to also be regime dependent. The estimates can then be distinguished by estimated volatility as measured by the conditional variance in each regime.

Andolfatto D, Williamson S (2015) Scarcity of safe assets, inflation, and the policy trap. In: Working Paper 2015-002A. Federal Reserve Bank of St. Louis

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Titel: The Neo-Fisherian hypothesis: empirical implications and evidence?
verfasst von: William J. Crowder
Publikationsdatum: 24.11.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 6/2020
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-018-1591-8

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