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An overview of the empirical evidence on the relationships between inflation, inflation uncertainty, and output. The author discusses the theoretical foundations for these relationships and reviews the empirical literature on inflation and relative price variability, inflation and inflation uncertainty, and the costs of inflation. The document also includes appendices with empirical evidence on the relationship between inflation and relative price variability, inflation and inflation uncertainty, and the costs of inflation as summarized in various studies.
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The views expressed in this report are solely those of the author. No responsibility for them should be attributed to the Bank of Canada.
April 1998
Brian O’Reilly
Printed in Canada on recycled paper
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Empirical evidence on the costs of inflation as summarized in Black, Coletti, and Monnier (1998) ..................................................
APPENDIX 3: Empirical evidence on the costs of inflation as summarized in Haslag (1997)................................................................................
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Thanks to Don Coletti for discussions on the empirical results of selected
papers and to Irene Ip, David Longworth, and Tiff Macklem for their feedback on
an earlier version of this paper. The Bank’s reference librarians, Marilyn Hawley,
Romie Kelland, and Lisette Lacroix, were particularly helpful in finding, and
obtaining, various relevant articles and books while Patricia Buchanan did an excel-
lent job on the final editing.
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This paper surveys the empirical literature on the benefits of low inflation, emphasizing contributions since 1990. It follows the framework of a section in the Bank’s 1990 Annual Report , “The benefits of price stability.” This framework looks at the costs of inflation, or the benefits of price stability, in the context of four themes: inflation creates uncertainty about the future; there are costs of having to cope with inflation; inflation affects equity and fairness; and ‘living with inflation’ is no answer.
In this survey, the section on each theme begins with a brief summary of the points raised in the article in the 1990 Annual Report. The empirical literature, including surveys, is then reviewed extensively enough to establish a context. This is followed by a discussion of those benefits of low inflation that have been well quantified in the relevant literature and those that have not; how the literature on this issue has advanced since 1990; and what areas might benefit most from more research in the future.
Overall, the empirical evidence on the nature of the relationship among inflation, inflation uncertainty, relative price variability, and output has made substantial progress since 1990. Although a consensus view cannot be said to exist on the basis of this survey, there are indications (especially in the work that allows for the interaction of inflation, money balances, and the tax system) that the gross benefits of low inflation are larger than thought at the beginning of the 1990s.
The papers surveyed here imply that the choice of an optimal inflation rate for monetary policy depends on (i) how well papers showing sizeable benefits stand up in future research; and (ii) the results of ongoing research on the magnitude and persistence of various costs.
L’auteur examine les recherches empiriques consacrées aux avantages d’un bas niveau d’inflation, en particulier les études menées depuis 1990, en faisant appel à la grille d’analyse retenue dans la section qui traitait de ces avantages dans le Rapport annuel du gouverneur de la Banque du Canada pour l’année 1990. Dans ce document, les coûts de l’inflation, partant, les avantages de la stabilité des prix, étaient regroupés sous quatre thèmes : l’inflation crée de l’incertitude au sujet de l’avenir; se protéger contre elle comporte des coûts; elle est source d’iniquité; composer avec elle ne règle rien.
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Les parties du rapport technique consacrées à chacun de ces thèmes s’ouvrent sur une brève synthèse des points soulevés dans le Rapport annuel pour
Dans l’ensemble, l’étude empirique de la nature des relations entre l’inflation, l’incertitude entourant celle-ci, la variabilité des prix relatifs et la production a beaucoup progressé depuis 1990. Bien qu’on ne puisse pas parler de consensus sur la foi des résultats obtenus jusqu’à maintenant, il existe des indications, surtout dans les travaux qui tiennent compte de l’interaction entre l’inflation, les encaisses monétaires et le régime fiscal, que les avantages bruts d’une faible inflation sont plus importants que ce que l’on croyait au début des années 90.
Avant de pouvoir tirer une conclusion concernant le choix du taux d’inflation optimal, il faudra attendre de voir si les études qui prêtent des avantages considérables à la stabilité des prix seront corroborées par les recherches ultérieures; les résultats des travaux en cours sur la taille et la persistance des coûts de l’inflation seront également déterminants.
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Overall, the empirical evidence on the relationships among inflation, inflation uncertainty, relative price variability, and output has made substantial progress since 1990. While a consensus does not yet exist, there are indications that the gross benefits of low inflation could be greater than was thought at the beginning of the 1990s. This is especially evident in the work that allows for the interaction of inflation and the tax system. The evidence, even if viewed with some skepticism, would suggest that focussing monetary policy on a higher inflation rate would be counterproductive, now that the cost of achieving inflation in the 2 per cent range has been paid. The only reason to change this conclusion would be if the weight of the evidence suggested there were net benefits to operating the economy at a higher rate of inflation.
As for the evidence on what net benefits would suggest about the optimal inflation rate, Akerlof, Dickens, and Perry (1996) and Fortin (1996) express the view that inflation should be higher than its current level because of the existence of nominal rigidities. However, they have not proven their case. When combined with historical estimates of the costs of disinflation, the evidence from recent partial-equilibrium and general-equilibrium work (which incorporates the interaction of inflation with the tax system) suggests that inflation should be lower than its current level in steady state. However, it cannot be considered to be unequivocal proof.^2 It is uncertain what further work will provide clear enough results so that there is agreement on the optimal rate of inflation on the basis of its net benefits. At some point, the balance of the evidence may have to be looked at in a manner similar to that used by Black, Coletti, and Monnier (1998). This paper essentially weighs the evidence in the framework of a model of the Canadian economy. It shows the net benefits of low inflation in Canada to be positive when account is taken of the interaction of inflation, money balances, and the tax system—under various assumptions about the sources and magnitudes of the costs of disinflation and using various estimates of the benefits from the literature.
There has been more progress on the relationships between inflation and relative price variability or between inflation and inflation uncertainty than on establishing the link between these “noise” variables and output. For the first relationship, the menu-cost model appears to be empirically robust in the United States and Canada. This implies that this relationship is bidirectional and that, in a world of zero inflation, the distribution of price changes should become more
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symmetric. For the second relationship (between inflation and inflation uncertainty), the empirical evidence suggests that it is positive, although some work finds inflation uncertainty increases mainly when inflation regimes change. In contrast, the empirical evidence is neither extensive nor strong on the relationship between either relative price variability or inflation uncertainty and output growth. A better understanding of the interrelationships among inflation, inflation variability, inflation uncertainty, and growth may help both in interpreting the existing empirical results and in designing experiments to measure the strengths of the various links.
As for the cost of coping with inflation, the benefit arising from the reduced need for individuals to replenish cash balances as frequently at low rates of inflation (lower shoe-leather costs of inflation) is estimated in the literature to be quite small, no matter what technique is used. However, as Howitt (1997) points out, this benefit of low inflation could still be economically significant if allowance is made for the public-good aspect of holding money (Laidler 1977) and for the spillover effect of inflation on all liquid assets, not just those in M1 (Fried and Howitt 1983). Further research should focus on how best to conceptualize these aspects for analysis in a more complete framework, perhaps within the context of a general-equilibrium model.
Another result of economic agents trying to protect themselves against inflation is the use of a greater number of productive resources in the financial sector than would be required with low or no inflation and given the fundamentals of the economy. The limited work on this question suggests that inflation increases the size of the financial sector in high-inflation countries but is equivocal for low- or even moderate-inflation countries. Further research here might involve first studying how the size of the financial sector is related to fundamental factors and then examining whether the actual size is what might be expected.
As for the effect of inflation on the physical costs of changing prices (the menu costs of inflation), direct estimates for some industry sectors suggest that the costs can be economically significant. From a broader perspective, though, the direct saving from menu costs is not considered as important as that achieved through improving the overall efficiency of the price system—when prices more clearly reflect the underlying demand and supply conditions. How exactly to capture this effect empirically needs more thought.
Significant progress has been made in one area in capturing some of the interactions of inflation with elements of the economic system. This is the area of
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measures or consumption-poverty measures, as opposed to income-poverty measures, were suggested as possible alternatives to use in time-series–type analysis. Survey results for Brazil, Germany, and the United States indicated that the general public sees inflation as leading to unfair situations that result in a lower standard of living. One avenue for future research into this question is to calibrate a heterogeneous-agent general-equilibrium model to some of the distributional as well as macroeconomic characteristics of the Canadian economy. Experiments could then be undertaken to better understand how inflation might affect the welfare of various groups.
The debate on whether indexation or price stability is the best way to address the inflation–tax-system interaction requires a clearer understanding of why full indexation was not introduced in the past in most industrial countries. From a conceptual viewpoint, indexation lowers the marginal cost of inflation. Hence, its adoption could undermine the credibility of the government’s commitment to a low-inflation regime. Since governments in many industrial countries fought inflation conspicuously with variants of income policies, concern for their reputations may have been one of the reasons that indexation was not introduced. Technical and administrative costs of introducing such a major change to the tax system may have been another. Certainly at points in the post-WWII period, various bodies in the economy spent many resources to look at adjusting for the effects of inflation. However, market activities and their associated records continue to be mainly in nominal terms. This obviously implies that the costs of undertaking an initiative to adjust for inflation more than outweigh any perceived benefit. Another implication is that the best way to address this cost is to have as low an inflation rate as is consistent with the structure of the economy. Further research on this question might want to list, in as detailed a manner as possible, what might be the explicit and implicit costs of attaining full indexation.
The part of the article in the 1990 Annual Report dealing with inflation creating uncertainty noted that decisions to buy or sell and to borrow or invest are based on both current and future prices, and inflation creates confusion about the information that these prices convey. As a result, there can be overinvestment in some products relative to the underlying demand for them and underinvestment in others with the resultant need for adjustment.
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This section of the paper surveys the empirical evidence of a link between inflation and relative price variability, and between inflation and inflation uncertainty. It ends by addressing the evidence of a link between either relative price variability or inflation uncertainty and real output growth. Golob (1993) describes reasonably well the views on these various relationships up to the early 1990s. This survey is therefore drawn upon to summarize the status of the empirical work on each of these issues until then. The need, as noted in Golob’s survey, to distinguish between relative price variability and inflation uncertainty remains, since an association between inflation and relative price variability does not necessarily imply a link with greater inflation uncertainty.
Relative price variability (or price dispersion) has to do with prices of goods and services changing relative to one another without there needing to be any change in the aggregate price level. This is generally measured as the dispersion of individual inflation rates with respect to aggregate inflation. A recurring theme in models that consider price dispersion is that it leads to the misallocation of economic resources (Friedman 1977). Inflation uncertainty describes the extent to which future inflation is unknown. Since uncertainty cannot be measured directly, the definition of inflation uncertainty can vary widely. Two broad approaches are (1) to base the definition on the dispersion of survey forecasts (surveys of forecasters, businesses, or consumers); and (2) to calculate uncertainty from an economic or statistical model.
With respect to the theoretical foundations of the relationship between inflation and relative price variability, Golob’s taxonomy of three classes of models is as good as any other for identifying the main strands. The class of limited- information models implies that lower inflation would reduce relative price variability and improve economic efficiency (the “equilibrium misperceptions model” of Lucas (1973); the “sticky prices” contract model of Taylor (1981); or some fixed “menu cost” of price adjustments as in Sheshinski and Weiss (1977) or in Ball and Mankiw (1994a; 1994b; 1995)). The second class, models that are agnostic about the level of aggregate inflation, attributes the movement in inflation and relative price variability to a common shock (Fischer 1981). Finally, there are sticky-price models that imply economic efficiency may be reduced if aggregate inflation is too low (the “asymmetric price response” model of Marquez and Vining (1984) or the “nominal wage rigidity” model of Akerlof, Dickens, and Perry (1996)).
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research and for a low-inflation target. Finally, the evidence on the link of either relative price variability or inflation uncertainty with real activity is reviewed briefly.
Interest in the relationship between inflation and relative price variability increased with high inflation in the 1970s, but it waned somewhat with low inflation in the 1990s. This subsection first presents Golob’s (1993) conclusions on the relationship between inflation and relative price variability and then goes on to discuss the major empirical development in this area in the 1990s, the evidence on the menu-cost model.
Golob (1993) reports that different measures of relative price dispersion were used in the studies he surveyed. However, both weighted and unweighted variances of inflation in the components of the relevant-price measure, relative to aggregate inflation in it, were common. With respect to data, either consumer or producer prices were used at levels of aggregation that varied from one study to the next. The empirical work ranged from graphical or tabular analysis through formal tests of statistical significance, as opposed to structural models, so that no conclusive distinction could be made among various theories. As for results, Golob indicated the studies were not unanimous but his view was that there was substantial empirical evidence of a positive relationship between inflation and the variability of relative prices. The top part of Table 1 in Appendix 1, excerpted from Golob’s paper, presents his evidence on the relationship between inflation and relative price variability.
As for evidence on the menu-cost model, Ball and Mankiw (1995) find strong support in U.S. data for the proposition that inflation is positively related to the skewness of the distribution of relative price changes. This is true both for simple correlations between inflation and skewness that control for the inertia in inflation, and in the context of estimated Phillips curves. Moreover, Ball and Mankiw find that, when they add their measure of skewness to an otherwise conventional Phillips curve that includes the relative prices of oil and food, the coefficients on these relative prices are close to zero and statistically insignificant. The coefficient on the skewness variable continues to be positive and statistically significant. In addition, they also find some evidence in their Phillips curves of an independent effect of the variance of relative prices on inflation. These empirical results are based on annual data, inflation is defined in terms of the producer price
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index, and the distribution of relative price changes is computed for each year based on four-digit producer price index components.
Using Canadian data, Amano and Macklem (1997) find considerable empirical support for the predictions of Ball and Mankiw’s (1994b; 1995) menu- cost model of price adjustment. In particular, Amano and Macklem find that the asymmetry in the distribution of disaggregated relative producer-price changes has considerable explanatory power for inflation. This exists both in the context of partial correlations and in price Phillips curves that control for other important influences on inflation. This is true whether they measure inflation using the GDP deflator, the CPI, or the CPI excluding food and energy. It is true for different measures of the degree of economic slack, and it holds when key relative prices are included separately in the Phillips curve. Indeed, by the standards of the Phillips curve literature, the importance of the asymmetry in the distribution of relative price shocks is one of the most robust features of aggregate price adjustment in Canada. This appears to reflect the fact that the skewness of this distribution contributes importantly to explaining inflation dynamics, particularly in key periods when inflation has changed rapidly.
In addition, Amano and Macklem’s Phillips curve evidence suggests that the variance of the distribution of relative price changes also affects inflation. Since there is trend inflation in much of the sample, this finding is consistent with the prediction of menu-cost models that the variance of cost shocks will affect inflation in the presence of trend inflation. This Phillips curve evidence, together with the results from Granger-causality tests, suggests the presence of bidirectional causality between inflation and relative price variability.
Analysis of inflation uncertainty requires a model or strategy for estimating inflationary expectations. Early papers used the variability of inflation (usually the standard deviation over some time interval) as a proxy for uncertainty. This was inadequate as an uncertainty measure, and more sophisticated techniques developed that involved the use of either surveys or more formal statistical/economic models. The latter approach can take the form of forecasting models (in which the variance of the prediction errors is the measure of inflation uncertainty) or conditional heteroskedastic models (in which the conditional heteroskedasticity becomes the estimate of uncertainty). For some indication of the approaches used in the literature
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relationship between inflation and uncertainty. Holland (1995) investigates, using Granger causality, whether an increase in inflation precedes an increase in inflation uncertainty. He concludes that it does for the postwar United States and, hence, that higher inflation uncertainty can be considered part of the welfare costs of inflation.
Batchelor and Dua (1996) compare a direct, ex ante measure of inflation uncertainty in the United States with a number of proxies used in empirical studies (forecasted standard deviations from ARIMA, ARCH, and structural models of inflation). The direct measure is the root mean-square subjective variance of the probability distributions for future inflation, constructed by respondents to the ASA-NBER surveys of U.S. economic forecasters. Batchelor and Dua find that the proxies are not significantly correlated with the direct measure or with one another and do not give the same results in regressions with the typical set of independent variables (past and expected inflation, past forecast errors, and a lagged dependent term). Batchelor and Dua conclude that use of such proxies leads to incorrect inferences about the correlation between inflation and inflation uncertainty and between inflation uncertainty and the real interest rate. As caveats, they mention measurement error and the possibility that their measure may be drawn from a group that is not representative of the relevant population.
With respect to countries other than the United States, Joyce (1995) estimates U.K. quarterly inflation uncertainty over 1950–94, conditional on a univariate specification of mean inflation using a variety of ARCH-related volatility models. Results reject the symmetry restriction imposed in standard ARCH and GARCH models, suggesting that inflation uncertainty is much more sensitive to “bad news.” Preferred estimates of the conditional variance of inflation are found to be positively associated with the level of inflation. Sauer and Bohara (1995) find, for the 1966–90 sample period, that uncertainty about (steady-state) inflation is lower, less variable, and less persistent in Germany. German inflation uncertainty declines along with actual inflation whereas (long-term) U.S. uncertainty remains at high levels.
Ricketts and Rose (1995) apply Markov switching models to CPI inflation in the G-7 countries. They find that there is systematic evidence of a relationship between higher levels of inflation and higher volatility of inflation. Ricketts (1995) indicates that the Markov switching model provides for two types of uncertainty: (1) given the regime, uncertainty about the shocks to inflation within one of the states; and (2) the possibility of uncertainty about the state. With respect to the latter, Ricketts’ work with the Canadian CPI shows two periods of extended uncertainty about the state: in the late 1960s when inflation began an upward trend,
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and at the end of the 1980s. Ricketts (1996) makes similar points but suggests that it is difficult to say much about uncertainty at the end of the 1980s and in the early 1990s, given the introduction of the GST.
Crawford and Kasumovich (1996) report on tests of the hypothesis that inflation uncertainty increases at higher levels of inflation. The tests applied generalized autoregressive conditional heteroskedasticity (GARCH) techniques to two models of the inflation process in Canada: a simple autoregressive model and a reduced-form Phillips curve model. Crawford and Kasumovich find the link between inflation and its uncertainty to be somewhat model dependent with a significant positive relationship between inflation and inflation uncertainty in the autoregressive case but not in the reduced-form model. They suggest that the true relationship may lie somewhere between the two sets of results, given the extreme assumptions in each case. By excluding all explanatory variables other than past inflation, the simple autoregressive approach ignores some information that agents would have used to forecast inflation. Hence, this approach will tend to overstate the actual uncertainty faced by agents. Conversely, the reduced-form model may understate the uncertainty that existed, since the model implicitly assumes that agents had more information on the structure of the economy than was actually available at each point in time.
Hess and Morris (1996) discuss the costs of inflation uncertainty, real- growth variability, and relative price volatility and examine their empirical relationship with inflation. Hess and Morris conclude that inflation uncertainty, real-growth variability, and relative price volatility all tend to rise as long-run inflation rises from low to moderate levels. They believe that their results suggest that there are long-run benefits to keeping inflation from rising from even low levels.
Caporale and McKiernan (1997) apply a GARCH model to post-WWII monthly inflation data for the United States. They find a significant positive relationship between the level of inflation and its conditional variance (uncertainty). They claim that their results are robust to an alternative (ARMA) model of inflation and do not depend on the high-inflation 1970s.
Howitt (1997), looking at a number of indicators for Canada, notes that the level and volatility of the inflation rate have come down since 1990, making the process of taking decisions less uncertain over a longer horizon. As evidence, he cites the fall in the level and dispersion of inflation expectations, and in nominal interest rates; the lengthening of the average term of household mortgages; less
