The Taylor Condition for U.S Time Series Data

The econometric techniques used to evaluate model-simulated data are now applied to a post-war sample of U.S. data. The data are obtained from the Federal Reserve Bank of St. Louis Economic Data (FRED) directory and have been seasonally adjusted at source where applicable. The full sample comprises of 205 quarterly observations between 1960q1 and 2011q1. Quarterly data is used both in order to comply with empirical studies in the Taylor rule tradition and in order to provide a reasonably large sample of data for the estimation techniques to exploit. Inflation is calculated from the GDP deflator [FRED series code: GDPDEF], consumption growth is calculated from the Personal Consumption Expenditure [PCE] index, non-leisure hours are represented by the civilian employment-to- population ratio [EMRATIO] and the consumption velocity of money is constructed by taking the ratio of nominal consumption expenditures [PCE] to the M1 money supply [M1SL]. Growth rates are calculated as year-over-year percentage changes in the level of the relevant series. We follow the interest rate rule literature and use the effective federal funds rate [FEDFUNDS] as the dependent variable. The intuition behind this choice is clear in an interest rate rule setting where policymakers are deemed to implement their policy decisions by ‘selecting’ an appropriate level for a short-term nominal interest rate.

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Empirical studies in the interest rate rule tradition typically treat the data as stationary without undertaking a rigorous analysis to formally verify this approach. Clarida et al. (2000, p.154), for example, cite the low power of conventional unit root tests as justification for this assumption.22 _{Accordingly, the}

data are initially analysed using conventional econometric methods which require stationary series. Also in keeping with the empirical literature, actual data is analysed in unfiltered form, unlike the model-simulated data studied previously. Following Clarida et al. (2000), the data is split into pre-Volcker (1960q1-1979q2) and Volcker-Greenspan (1979q3-onwards) subsamples, where Paul Volcker’s appointment as Chairman of the Federal Reserve is used as an arbitrary break- point.23 _{Three endpoints are considered for the post-Volcker subsample: the first}

is consistent with Clarida et al.’s (2000) Volcker-Greenspan subsample which ends in 1996q4 (denoted “CGG post-Volcker”), the second ends in 2000q3 in order to incorporate Taylor’s (2009a) claim that monetary policy veered “off track” during the early 2000s (“Taylor post-Volcker”) and the third utilises the remainder of the sample (“extended post-Volcker”, 1979q3-2011q1).24 _Coefficient

estimates are also obtained for the ‘full sample’ period of 1960q1-2011q1, although Clarida et al. (2000) do not consider an estimation period of comparable length.

The forward-looking interest rate rule proposed by Clarida et al. (2000) is first estimated as a preliminary check on the econometric procedure employed. The GMM technique described above is used to evaluate an empirical specification in which the nominal interest rate is regressed on a constant, expected future inflation, the expected output gap and up to two lags of the nominal interest

22 _{Siklos and Wohar (2005) and Österholm (2005) are critical of the empirical literature for not}

adequately addressing the time series properties of the data. We consider this issue in greater detail in Section 4.5 when assessing the Fisher relation; in that literature it is common to establish formally whether the data is stationary or not as a preliminary step.

23 _{It would, of course, be more rigorous to use a formal econometric procedure (e.g. Bai and}

Perron, 1998) to identify the appropriate break-point in the data. However, the purpose of the current exercise is to evaluate the Taylor Condition within Clarida et al.’s (2000) econometric framework given that it has been frequently applied in the empirical literature. Furthermore, Gavin and Kydland (1999) identify 1979q3 as an important break-point in U.S. data for nominal variables, noting that the Federal Reserve announced a major change in operating procedures in favour of control of the money supply at the end of this quarter.

24 _{The ‘Taylor post-Volcker’ subsample coincides with Jondeau et al.’s (2004) ‘Volcker-Greenspan’}

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rate.25 _{These lagged dependent variable terms are often interpreted to capture}

‘interest rate smoothing’ behaviour on the part of policymakers (e.g. Clarida et al., 2000, p.152) but from an econometric perspective they simply serve to relieve the estimated residuals of serial correlation.26 _{The Q-statistic and the statistical}

significance of the coefficients on the lagged dependent variable terms are used to judge the appropriate lag length and the most parsimonious specification is always preferred.27 _{As with the simulated data above, the instrument set}

comprises of lagged variables, but unlike Clarida et al. (2000) it does not include variables which do not otherwise feature in the estimating equation. Coefficient estimates obtained for Clarida et al.’s (2000) interest rate rule using our dataset – results not reported in full – show that the ‘pre-Volcker’ subsample is characterised by an interest rate rule with an inflation coefficient of 0.80 (compared to CGG's estimate of 0.83), an output gap coefficient of 0.39 (CGG: 0.27) and a sum of lagged dependent variable coefficients of 0.75 (CGG: 0.68). The ‘CGG post-Volcker’ subsample yields an estimated inflation coefficient of 2.17 (CGG: 2.15), an output gap coefficient of 0.94 (CGG: 0.93) and an estimated coefficient of 0.78 on the lagged dependent variable (CGG: 0.79).28 _{Overall, the}

econometric procedure replicates Clarida et al.’s point estimates rather well, despite the slight difference in the instrument set used.

The same econometric techniques are now applied to the ‘correctly specified’ Taylor Condition for U.S. time series data. The results are presented in Table 4.5. Specification tests suggest that one lagged dependent variable term is required for the ‘pre-Volcker’ period but that lagged terms are not required for the post- Volcker subsamples, or for the full sample period.29 _{Table 4.5 reports a point}

estimate of 1.170 for the inflation coefficient during the ‘pre-Volcker’ period and a

25 _{The output gap is calculated using the CBO’s estimate of potential output [GDPPOT].}

26 _{The interest rate smoothing interpretation of such lagged dependent variable terms is not}

universally accepted (e.g. Rudebusch, 2002).

27 _{The Q-statistic is now used because the Durbin-Watson statistic is not appropriate for testing for}

autocorrelated residuals if the estimating equation contains lagged dependent variable terms.

28 _{Only one lagged dependent variable was found to be necessary to relieve the estimated}

residuals of serial correlation for the ‘CGG post-Volcker’ subsample as opposed to Clarida et al.’s (2000) specification which includes two lags.

29 _{The pre-Volcker specification with no lagged dependent variable terms produces a D-W statistic}

of 1.580 (critical values 1.482-1.769) and a Q-statistic P-value of 0.068. The estimated coefficient on inflation is not statistically significant for this specification.

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point estimate of 1.973 for the ‘CGG post-Volcker’ subsample. Extending the post- Volcker subsample to 2000q3 yields an estimated inflation coefficient of 1.955 and further extending this subsample to 2011q1 yields an inflation coefficient of 1.747. It is apparent that the statistical significance of the coefficients on consumption growth, productive time growth and velocity growth diminish for the ‘extended post-Volcker’ subsample, whereas all variables are found to be statistically significant to at least the 5% level for the two post-Volcker subsamples which stop short of the point at which the Federal Reserve allegedly departed from a stabilising interest rate rule (Taylor, 2009a). Nevertheless, the point estimate for the inflation coefficient remains above unity and is statistically significant to at least the 5% level for all subsamples. In short, the ‘Taylor principle’ is satisfied. Over the full sample period the point estimate for the inflation coefficient is estimated to be 0.919. However, the P-value for the Q- statistic is 0.010, so we reject the null hypothesis of no serial correlation in the estimated residual series at the 5% level of significance; the D-W statistic concurs given that it falls below its critical range.30 _{Although serial correlation in the error}

term does not bias the reported estimates, it can lead to an understatement of the standard errors and thus provide unwarranted confidence about the precision with which the coefficients are estimated. We address this problem by using alternative econometric techniques to analyse the full sample period at a later stage.

Concerns about serial correlation do not apply to the subsamples, however. The result that the inflation coefficient exceeds one for the pre-Volcker subsample differs from Clarida et al.’s (2000) well-known and oft-replicated result that monetary policy progressed from violating the Taylor principle during the pre- Volcker era to adhering to it for the post-Volcker period. Moreover, for the pre- Volcker subsample the coefficients on velocity growth and the forward interest rate – terms which do not feature in conventional interest rate rules – are found to be statistically significant at the 1% level, thus pointing to the potential importance of these terms to the unconventional result in terms of the inflation

30 _{Adding lagged dependent variables to the full sample specification does not ameliorate this}

serial correlation: Pr(Q) falls to 0.001 with one lag and 0.000 with two lags (results not reported in full).

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coefficient. The forward interest rate term in particular is found to be statistically significant at the 1% level across all estimation periods. This latter finding motivates one of the specification restrictions considered in Section 4.5.

[Table 4.5 here]