The determinants of inflation volatility: a panel data analysis for US-product categories

ABSTRACT

Some macroeconomic dimensions like the economic business cycle, the exchange rate movements when the degree of country openness is significant, or the level of inflation are often considered to explain measured-inflation dynamics. However, inflation volatility may also be affected by statistical agencies methodological changes. This paper explores both potential explanations in a panel data for 100 United States CPI-U subcategories. Using both unconditional and conditional variances, we find that crucial changes in how agencies consider quality adjustment in products, together with the macroeconomic variables help to understand CPI volatility over time, both in the short-run and in the long-run.

KEYWORDS:

• CPI inflation volatility
• volatility persistence
• quality adjustment
• panel data
• GARCH
• EWMA

JEL CLASSIFICATION:

• E31
• E58

Acknowledgements

The authors are thankful to Pinar Deniz, Thanasis Stengos and Thomas A. Doan for the helpful comments and discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 See Figure 1 for the evolution of aggregate inflation and its trend and Figure 2 to notice the differences in the magnitude of the volatility for several CPI-U subcategories.

2 For the first decades in our timeseries, CPI-U series were only available in their not-seasonally-adjusted version. Nevertheless, being worried about seasonality, we introduced monthly dummy variables to clean our results from its effects. All these dummies turned out to be not significant, even at the 10% confidence level. Remember that the dependent variables and the main independent variable are constructed over 36-months of data in an overlapping rolling window. This makes stationarity effects vanish.

3 Calling volatility to the standard deviation of the cyclical component of a time series is somewhat misleading. We followed many authors in the use of this measure to explore the volatility of the deviations of a macroeconomic time series from its long-term path (see, for instance, Afonso and Furceri 2010; Chauvet and Guillaumont 2009; Hnatkovska and Loayza 2005). Rizvi et al. (2014) explains this measure is suitable to extract inflation volatility for countries where inflation series is suspected to be non-stationary.

4 The exchange rates react to asymmetric movements between internal and foreign monetary policies. Indeed, evidence indicates they react quickly, and they do it even more in periods in which interest rates are in the zero lower bound (See Rosa 2011and Holtemöller, Kriwoluzky, and Kwak 2020). Therefore, the use of EER instead of the import price indexes helps to capture the differential between foreign (imported) and national inflation; and the transmission of the asynchronized business-cycles among countries that trade (See MacDonald & Swagel, 2000).

5 The use of robust errors to correct for our problems of heteroskedasticity and serial correlation is not always the optimal solution. We follow King and Roberts (2015) and run our regressions both with normal standard errors and with robust errors. Then, we observe whether they differ substantially. For all our regressions, errors vary only slightly, and coefficient significances do not change. The only exception is found in the standard errors for the coefficient of π, which turns to be only significant at the 10% level with robust standard errors. Therefore, we conclude that the use of robust errors does not hide, in our case, a problem of misspecification.

6 The level of unemployment and its monthly growth turned to be not significant, and its inclusion or exclusion caused no changes in the rest of coefficients.

7 See BIS manual for details on the construction of EER indices; We use Stata to test for unknown structural breaks in the logs of total exports and total imports for US and the logs of exports and imports over GDP. The tests report 1973, 1988 and 2008 as breaks.

8 Andolfatto (1997) shows how unemployment rate increases sharply during recessions, while during expansions, it declines only gradually.

9 In the regressions with inflation, EER and unemployment variations computed as year-over-year change, our main conclusions are still valid. However, the coefficients for EER and its volatility are highly significant and positive, except for the combination of inflation in levels as the main regressor and its volatility as dependent variable. Moreover, for the latter combination, the coefficient of inflation in levels turns significant and, this is true regardless of the use of robust or normal residuals. Finally, when variables are computed for year-over-year changes, the coefficient for crisis changes sign (becoming now positive) and it is significant at 1%.

10 These models are not included in Tables 1 to 3 for space reasons. The introduction of the monetary aggregates in the regression, together with EER or the volatility of EER makes the former or the latter become no-significant, and the coefficient of EER variables vary considerably. This is not surprising, since EER is an exchange rate measure, which is crucially affected by monetary policy. The models with both blocks of variables are not displayed to save space.

11 The correlation between the changes in the monetary base and in M3 index is 0.34 when one considers the entire period. However, it reduces to 0.05 and becomes not significantly different from 0 for the period before 2007m12. For 2016–2020, the correlation increases to 0.79.

12 The coefficient for the first lag of the dependent variable is below one, which guarantees its dynamic stability. Moreover, when we introduce a second lag, its coefficient is negative and the sum of both coefficients is below unity.

13 We use RATS software for panel GARCH estimations. We initially tried with all 58 panels and went on reducing the number of panels until the software was able to handle it. The rest of outputs (estimations and tests) are obtained with Stata.

14 We use the variable in differences to ensure its stationarity in every panel.

15 See Deniz et al (2021) for the first paper that includes independent variables in the conditional equations.

16 However, unlike in GARCH, EWMA volatility does not have a mean reverse parameter, i.e. it does not return to a long-run volatility.

17 ${\lambda }_{\hspace{0.17em}}^{EWMA}=.97$ for all volatility variables are fully robust to those in Tables 8–9 too.

18 The use of the first lag of the monetary growth brings the same conclusions the variable at time t do.

Additional information

Funding

The work was supported by the Ministerio de Ciencia, Innovación y Universidades [PGC2018-094364-B-100,RTI2018-093543-B-I00, MCIU/AEI/ FEDER, UE] 1. Spanish Ministry of Science, Innovation and Universities through grant RTI2018-097434-B-I00 2. Junta de Andalucía through grant B-SEJ-544-UGR20 from the Programa Operativo FEDER de Andalucía 2014-2020