Abstract
US inflation and output developments since the 1970s are considered using the P-star model and the VAR-based Diebold–Yilmaz spillover index approach. Shocks to monetary variables explain a substantial share of US GDP deflator inflation shocks over time, particularly in the late 1980s and early 1990s but also in recent years, a time when quantitative easing was employed by the Federal Reserve. Monetary factors, and not oil shocks, underlie price developments in the 1970s and early 1980s. Monetary shocks’ influence on oil prices has become noticeably stronger over the past ten years or so, supporting the greater attention being paid of late to the impact of the monetary environment on commodity markets. Shocks to the velocity-of-money variable affect output developments, with the exception of the 1970s and early 1980s when inflation shocks and, to a lesser extent, oil inflation shocks dominate the cross-variance share of output gap shocks. After the Volcker disinflation, the influence of both inflation and oil price shocks on the output gap wane and those of velocity gap shocks increase.
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Notes
The relevance of monetary conditions to commodity price changes was highlighted in the financial press during the mid-2000s; see, for example, Clover and Fifield (2004) and Fifield (2004). Academic contributions that have considered the influence of monetary conditions on commodity markets include Frankel (2008) and Browne and Cronin (2010).
Humphrey (1989) identifies precursors to the P-star approach in the early economics literature, stretching as far back as David Hume.
Note that the two gap variables are mostly usually stated as and in regression specifications with the estimated sign on both expected to have a positive value in explaining inflation, or changes in it.
Variants of the P-star model have been presented over the years. For example, Gerlach and Svensson (2003) put forward a real money gap, i.e. the gap between the current real money stock and the long-run equilibrium money stock, alongside the output gap in a model of inflation, and find it to have significant predictive power for inflation in the euro area. Trecroci and Vega (2002) present a model of inflation where both a money gap and an output gap are explanatory variables.
Carlson et al. also use M2M as a third money aggregate in their study. It is not available over a sufficiently long period (data are available from 1967 to 2013 only) for the rolling-window estimations used here.
This atheoretical approach to estimating an equilibrium value from a series is often applied to real output data, with the difference between the two series providing measures of the output gap.
The GDP implicit deflator, velocity and real GDP series are all seasonally adjusted, while those of potential real GDP and oil prices are not.
The 22.9% value is arrived at by dividing the sum of the “directional from others” entries for each of the four variables (located above it in that column and totalling 91.4%) by four (the number of variables in the VAR).
In the appendix, robustness tests of the impact on the TSI values of different choices of lag length, forecast horizon, window size, form of shocks, and number of variables used are considered.
They point out that only two of the five major oil price shocks between 1970 and the time of their study were followed by significant changes in GDPD inflation rates.
When M2 is the money stock used, the velocity gap accounts for an average 21% of the inflation decomposition over all the windows, compared to 17% for the output gap. When MZM is used, the velocity gap has a 21% average share, while that of the output gap is 14%.
The definition and refinement of the broad money stock has been an important feature of studies relating the real money to economic activity since, at least, Goldfeld (1976). The particular money stock affecting the results at different junctures here is then unsurprising.
The effects of quantitative easing on asset prices more generally are considered in Cronin (2014).
The remaining two panels of Fig. 4 (vii) and (viii) show the impact of GDPD inflation rate shocks to oil price inflation. It is generally low but does pick up in the windows ending in the 1990s and has a share of the forecast error variance decomposition of over 20% for most of the second half of that decade, before falling off thereafter.
For example, the price of West Texas Crude tripled between 1998Q4 and 2000Q3. It fell sharply from a value of $133 per barrel in 2008Q2 to €41 per barrel two quarters later. The lesser impact of oil market developments on the output gap in recent decades, however, should not be unexpected given its diminished role in economic activity compared to, say, the 1970s.
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Acknowledgements
The author would like to thank Frank Browne, Kevin Dowd and an anonymous referee for their comments. The views expressed in this article, nevertheless, are those of the author and do not necessarily reflect those of the Central Bank of Ireland or the European System of Central Banks.
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Appendix: Robustness tests
Appendix: Robustness tests
Tests of the sensitivity of the TSI to the choices required in estimating the VAR model are reported in Figs. 6, 7, 8, 9 and 10. In each figure, the solid line represents that found in the same column of Fig. 2, where (a) the VAR lag length is 4, (b) the forecast horizon is 10 quarters, (c) the estimation window is 60 quarters, (d) the forecast error variance decomposition is of the orthogonalised form, and (e) there are four variables. In turn, each of these five settings is changed in turn in Figs. 6, 7, 8, 9 and 10 while holding the other four unchanged.
Total spillover index (%)—different lag lengths. i M2 velocity as money variable. ii MZM velocity as money variable
Total spillover index (%)—different forecast horizons. i M2 velocity as money variable. ii MZM velocity as money variable
Total spillover index (%)—different window sizes. i M2 velocity as money variable. ii MZM velocity as money variable
Total spillover index (%)—orthogonalised versus generalised decomposition. i M2 velocity as money variable. ii MZM velocity as money variable
Total spillover index (%)—four variable versus five variable. i M2 velocity as money variable. ii MZM velocity as money variable
The lag length of the VAR was allowed vary from 4 lags, to 3, 5 and 6 lags. The minimum and maximum TSI value at each window from the four lag options, 3–6, is then plotted in Fig. 6. The TSI moves in a similar pattern for all three lines in that chart, albeit with some variation in values. Figure 7 reports minimum and maximum values where the forecast horizon varies between 8 quarters ahead and 12 quarters ahead. The TSI values are in a narrow range. This is reassuring as it indicates variance shares being broadly unchanging at longer forecast horizons.
In Fig. 8, the rolling windows are 40 quarters, 60 quarters and 80 quarters in size. One feature of the 40-quarter rolling-window TSI series is that there are many windows where no TSI is generated. That arises when there is a lack of convergence in decomposition shares as the forecast horizon lengthens. This supports the selection of the longer, 60-quarter window (where only 1 or 3 windows out of the estimated 164 windows do not provide decompositions) over the shorter window. The differences in TSI values between the 60-quarter windows and the 80-quarter windows are relatively small. An advantage of using 60 quarters over 80 quarters for the window size is that with the latter the first TSI value is not provided until a sample period ending in 1980Q3, thus excluding the 1970s. Figure 9 shows that the TSI is not particularly sensitive to the choice of orthogonalised or generalised decompositions. Finally, in Fig. 10, a comparison is made with a five-variable system where the additional variable is a measure of the openness of the US economy. It is the quarterly change in a ratio, that of the sum of US exports and imports divided by US GDP (shown in panel (viii) of Fig. 1). The addition of this variable does not have any noticeable effect on the pattern of the TSI over time.
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Cronin, D. US inflation and output since the 1970s: a P-star approach. Empir Econ 54, 567–591 (2018). https://doi.org/10.1007/s00181-017-1229-2
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DOI: https://doi.org/10.1007/s00181-017-1229-2