Inflation and the Formation of Expectations: Some Empirical Results

Leventakis, John A. Article Inflation and the Formation of Expectations: Some Empirical Results Kredit und Kapital Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Leventakis, John A. (1985) : Inflation and the Formation of Expectations: Some Empirical Results, Kredit und Kapital, ISSN 0023-4591, Duncker & Humblot, Berlin, Vol. 18, Iss. 4, pp. 515-526, https://doi.org/10.3790/ccm.18.4.515 This Version is available at: https://hdl.handle.net/10419/293037 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Introduction The role of expectations and their treatment is perhaps the most important issue concerning the process of inflation. Since inflationary expectations are not an observable variable, in estimating the effects of price expectations on actual inflation various proxies have generally been used for the unobservable expected rate of inflation (see e.g., Turnovsky and Wachter, 1972; Lahiri, 1976; Mullineaux, 1980). One procedure for modelling price expectations is the rational expectations approach, in which the expression for the expected rate of inflation is derived from the general rational expectations solution of the structural model for the process generating inflation. An alternative procedure is to use independent measures of inflationary expectations which are employed for estimating price equations. In this paper we follow the second approach. In particular, we develop and estimate a model of price determination using alternative expectations hypotheses, all taking into account the role of money growth in the formation of inflationary expectations. The model is estimated with quarterly data from the small open economy of Greece over the period 1975.1 - 1983.IV. The plan of the paper is as follows: section II sets up the model of price formation. In section III we discuss various hypotheses on the formation of expectations. Empirical results are presented in section IV and concluding remarks are given in section V. II. The Model The model presented in this section is a variant of a general model developed by Tobin (1972) and is representative of much of the recent empir- * The author is grateful to S. N. Brissimis and A. S. Courakis for their helpful comments. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 516 John A. Leventakis ical work on price and wage behaviour (see Eckstein and Girola, 1978; Spitaller, 1978). The model contains five equations - an identity for the general price level, a price adjustment equation, a wage adjustment equation, an equation relating the unemployment rate to the output gap, and an equation for price expectations with alternative hypotheses as to how inflationary expectations are formed. The overall rate of inflation is expressed as a weighted average of the rate of change of the price level of domestically produced goods and the rate of change of price of imported goods (1) Apt = ¡iAph t + (1 - ^)Ap? where p is the log of the general price level, ph is the log of price of domestically produced goods, pm is the log of the domestic price of imported goods, [i and (1 - (i) are the weights of domestically produced and imported goods respectively and A is the first difference operator; AX is rate of change on an annual basis. The prices of domestic goods are assumed to respond to both domestic and foreign factors (2) Aph t = a0 + ax Awt + a2 Aqt + a3 Aph t + a4 (y - y)t alf a3, a4 > 0; a2 < 0 where w is the log of the money wage rate, q is the log of productivity (output per man-hour), y is the log of real output and y is the log of normal production capacity proxied by the trend level of actual output. The first term in eq. (2) gives the influence of the rate of change of wage rate on inflation, while the second term represents that of the rate of change of productivity. The third term captures the influence of foreign inflation (in domestic currency) on domestic inflation. The fourth term represents the extent to which prices adjust to a gap between actual and the normal level of output. When actual output is above its capacity level, inflationary pressure is present in the goods market. The wage equation is the well known expectations augmented Phillips hypothesis where the rate of change of money wages is positively related to the expected rate of inflation and to the rate of change of productivity, and negatively related to the unemployment rate. (3) Awt = b0 + b xAp\ + b2Aqt + bzUt bu b2 > 0: b3 < 0 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 Inflation and the Formation of Expectations 517 where pet is the log of the expected price level in period t and U is the unemployment rate. The expected rate of inflation enters equation (3) to allow wage earners to protect their purchasing power against inflation. Assuming Okun's law (1962), in which the output gap is related to the unemployment rate, we have (4) Ut = y0 47l (y-y)t Yo > 0; Yi < 0 where the constant term, y0> represents some frictional unemployment which it is assumed that does not respond systematically to the variations in the demand pressure in the market for goods. The above formulation involves the restrictive assumption that all changes in the output gap necessarily cause changes in unemployment rate in the opposite direction. Combining equations (1) - (4), we obtain (5) Apt = c0 + cx Apmt + c2 (y-y)t + c3Aqt + c4z\pf Ci, C2, c4 >0; c3 ^ 0. The sign of the coefficient c3 can be either positive or negative depending on the relative magnitudes of the coefficients a2 and b2 = b2av The expected value of a2 is between minus one and zero while that of b2 lies between zero and one. Thus, two opposing forces are present in the effect of the rate of change of productivity on the rate of inflation. III. Alternative Hypotheses for the Formation of Inflationary Expectations To complete the model we need to specify how expectations are formed. Since the primary purpose of the study is to test alternative hypotheses of inflationary expectations which take account of the role of monetary changes in the formation of expectations, the selected hypotheses include monetary changes as one variable affecting inflationary expectations. One hypothesis that omits monetary changes has been considered but only as a basis of comparison for the set of hypotheses containing monetary changes. Thus, in estimating the price equation (5) the following hypotheses for the expectational variable are considered: (i) The first hypothesis we consider is the standard adaptive expectations learning model (see Cagan, 1956; Frenkel, 1975) OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 518 John A. Leventakis (6) A p\ - A pU = \(A pt.x - A pUi) where X is the error adjustment coefficient. Recursive substitution of the expected rate of inflation in the above equation allows us to express the expected rate of inflation as the weighted sum of past (actual) inflation rates (V A Pi= SoiPt-i-l i = 0 where at = A.(l - X)1 (ii) The second model of expectations formation considered is called monetary model, which refers to the hypothesis that price expectations are formed as a weighted average of current and past rates of growth of the money supply (8) Apet= ^biAmt-t i = 0 where m is the log of the money supply. This type of hypothesis was suggested by Flemming (1976, p. 58) who writes that "on this basis a monetarist is required to assume that other people's price expectations are based on recent changes in the money supply"1. (iii) The third model of expectations formation is the model that combines both adaptive and monetary hypotheses (9) Apet = 1 + i=0 i=0 The basic idea underlying the above hypothesis, which has been formulated by Rutledge (1974), is that inflation expectations are formed on the basis not only of past values of the variable itself, but also of the information contained in the history of the rate of growth of the money supply2. Substituting equations (7), (8) and (9) into (5) we obtain the alternative price equations: (10) Apt = c0 + cxAp? + c2{y - y)t + czAqt + ^MPt-z-i i = 0 1 McGuire (1976) and Holden and Peel (1977), among others, provide support for this hypothesis by explaining the expected rate of inflation in terms of monetary changes. 2 Recent support for this hypothesis is provided by Mullineaux (1980) who shows that inflation forecasts are systematically influenced by past inflation rates and past rates of money growth. OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 Inflation and the Formation of Expectations 519 (11) Apt = c0 + ClApT + c2(y - y)t + c3Aqt + ^M^-* i = 0 Apt = c0 + CiAp? + c2(y-y)t + c3Aqt + 2M Pt-i- -1 i = 0 (12) + 2 M mt - i i = 0 which are all in terms of observable variables and can be directly estimated. As is immediately obvious, equations (10) to (12) are a set of nested models. Equation (12) comprises the complete set of explanatory variables contained in the other models. Proceeding in terms of the conceptual framework expounded by Courakis3, we can examine the validity of alternative hypotheses regarding the formation of price expectations. In particular, comparison of (12) with (10) can throw light on the validity of the monetary expectations hypothesis. The null hypothesis that Z = 0 can be tested by using an F-Test on the nested models. If the hypothesis is rejected, it can be argued that monetary changes acting as a proxy for inflationary expectations affect actual inflation. On the other hand, comparison of (12) with (11) enables us to examine the validity of the adaptive expectations hypothesis. It will be noticed that the above relationships do not commit us to any particular lag configuration. On the other hand, the general tendency has been to proceed in terms of specific lagged structures. Typical of the latter type of study are relationships that employ Almon lags. In what follows the results derived from relationships constrained to conform to Almon structures are presented while subsequently the pertinence of such constraints is examined. The results of estimation are presented in Table 1. All coefficients have the correct signs and, with the exception of the intercept, are significant at the 5 percent level. The estimates indicate that expectations play an important role in the determination of actual inflation. In equation (10') the expected rate of inflation is represented by a distributed lag in past rates of inflation. It is interesting to notice that the sum of the coefficients on lagged inflation is significantly less than unity (0.153), implying that the long-run Phillips curve is not vertical. Moreover, lagged values of the rate of inflation, except the first lag, are insignificant, a finding indicating that in forming their expectations people attach great significance to the most recent history of the IV. Empirical Results 3 See for example Courakis (1978, 1981). OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 520 John A. Leventakis w co £ Q .2 £ e #o V» co tt H a S HM toi) C H « o £ «4H O -Û g o O < Oh < Cr I Sï> I a tí £ O ' O o tí u tí <D CÜ CVr! 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V d w o ^ o S I g nhO S OS . s a « o S 5 J; « OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 Inflation and the Formation of Expectations 521 variable itself. The significant effects of the other variables deserve special mention. The magnitude of the foreign inflation on domestic inflation is smaller than that one might expect in the small open economy of Greece, which imports more than one-fifth of its final goods. Excess demand, as measured by deviations of actual output from its normal capacity level4 (of the previous period), appears to have a rather weak effect, while the influence of the rate of change of productivity is strong and negative. Equation (11') incorporates the hypothesis that price expectations are proxied by changes in money supply. It appears that only the third lag of money growth is significant. The sum of the coefficients of current and lagged values of money growth is considerably less than unity (0.112), a finding indicating the weak influence of money growth on actual inflation. Thus there is little evidence of systematic changes in prices in response to changes in money supply. As to the effects of the other variables, it can be seen that on the whole there are no substantial differences between the estimates of eq. (11') and those of eq. (10'). Equation (12') embodies the hypothesis that past rates of inflation as well as current and past values of money growth act as a proxy for inflationary expectations. Inspection of Table 1 reveals that inflation is explained a little better by this model than by the other two models. The F-tests indicate, however, that money growth does not contribute to the explanation of actual inflation, given the effect of past inflation. The hypothesis that money growth coefficients all equal zero cannot be rejected (see Table 2 for the Fstatistics). In addition, the evidence does not enable us to reject the hypothesis that all the past inflation coefficients equal zero. The results therefore do not yield conclusive evidence as regards the selection of the appropriate expectational variable. Table 2: A Comparison of Alternative Hypotheses: General Form (12) Compared Critical equations Hypothesis F-statistic F (0.05) (12) -(10) Ißi = 0 1.15 2.92 (12) -(11) Zai = 0 1.63 2.92 (12a)-(10a) 2ßi = 0 0.71 2.92 (12a)-(11a) lai = 0 0.92 2.92 Note: The letter a denotes a variant including the unit labour cost variable. 4 Capacity output is measured by its trend value, which is given by Y = 4.911 + 0.009t R2 = 0.753 DW = 0.436. 34 Kredit und Kapital 4/1985 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/ccm.18.4.515 | Generated on 2023-01-16 12:52:06 John A. 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