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A ‘rational’ explanation for ‘irrational’ forecasts of inflation
Journal of Monetary Economics 13 (1984) 387-392. North-Holland
A *RATIONAL’ EXPLANATIOW FOR ‘IRRATIONAL’ FORECASTS OF IMXATION James VANDE Rutgers Umoersi@-Nm~ar&, Newark. NJ 07102. LS.4
This paper analyzes professionals’ forecasts of nominal income and the inflation rate. The analysis indicates that both monetary and fiscal policy data was used efficiently to forecast income. but the monetary policy data was not used efficiently to forecast the inflation rate. Further analvsi~ suggests that the apparent inefficient use of the monetary data r;;~uits from the non- ,tatione money-inflation relatiomhip predicted by rational expectations models. These models then provide an explanation for the inconsistent coaclusions regarding the income forecasts and the inflation rate forecasts.
1. Introduction
Several studies of inflation forecasts derived from survey data indicatethat the forecasts do not incorporate available information efficiently and are biased downard.’ Researchers suggest that this ‘irrationality’ is characteristic of survey-based forecasts but not of the forecasts that govern market transactions. Their rationtie is the survey respondents, unlike market participar.ts. lack the incentives required to make forecasts that are unbiased and information efficient. This paper tests an alternative explanation: the forecasters used all available information efficiently, but this information did not include the fact that the impact of money growth on the inflation rate was increased during the 1970’9. As a result, their estimates of the effects of money growth were too low and the infiation rate was underpredicted. This type of parameter non-stationarity is consistent with rational expectations models. Therefore. these models provide a ‘rational’ explanation for the ‘irrational’ forecas:s of inflation. This paper is o anized as follows: Section 2 analyzes nominal income and inflation rate forecasts derived from surveys of professional forecasters. Section 3 proposes and tests the explanation ;‘or the results presented in the prttvk~s section. Section 4 concludes the paper. estions. conclude that the kingston fore I Brown and Maital (1981) and Pearce (1 consistent with the Rational Expectations hypothesis. Mullineau?i 1981)) rear hes conclusion. *I wish to thank Mary Golden for useful
03W-3923/X4,‘53.(x)C lQK4, Elsevrer Scrence Publishers B.V. (North-H~Gnd)
J. VunderHo$.
388
A ‘rationul’
ecplurtution for ‘irrutiorrul’~(~recwstinK
2. The foreccasts Sirm 1968, the American Statistical Association and the National Bureau of Economic Research (ASA-NBER) have surveyed about fifty professiclnal
forecasters each quarter. The participants are provided with the most recent data on several variables, including the previous quarter’s National Income accounts data. The respondents then report the levels af the variables expected at the end of rhe current quarter and the three subsequent quarters. This paper analyzes two- and four-quarter forecasts derived from the median predicted levels of Norninal GNP and the GNP Implicit Price Deflator.’ Part A of table 1 reports summary statistics pertaining to the forecast errors for the period 1968:4 to 1977:4. The income forecasts are more accurate and Iess biased than the inflation forecasts. For the income forecasts, the ratio of the average: error to the average change is 0.06 and the portion of the MSE attributed IO bias is less than 0.13. In contrast, the average error is about 0.2 of the average value and the portion of the error attributable to bias is about 0.40 :.vith the inflation forecasts. The positive average error indicates a tendency to underpredict the actual value. Paft B of table 1 reports the efficient-use-of-information test results. The test involves regressing the forecast errors on the information sei., represented by X,, yt -
Y:e= SX,+
e,.
(1)
The rejection of the hypothesis B = 0 indicates these data contribute to the forecast error, hence were not used effciently. For the income forecasts tests, the: information set is assumed to consist of the current and lagged values of monetary and fiscal policy data. For the inflation rate forecasts, the information ses also includes a measure of potential output growth and the lagged inflation rak3 The test results indicate the income forecasts incorporate data efficiently, but the inflaition rate forecasts do not.. The regression F statistic, Fr, is not significa!mtlydifferent from zero in either income regression. However, both the regression F statistic and the monetary policy data test statistic, Fw,, tire significant in both inflation rate regressions. Also, the monetary coeficients are all positive. These results indicate the forecasters underestimated the impact of money sn the inflation rate. Notia that potential output, the la rate, and &e kcal policy data are estimated to be independent of the forecast *For a r’ulldescriptiofi of this data, see Zarnowitz (1979) and the refercnccs he cites. Also, the analysis OFthe one- and thrmquarter fovtxasts yield results similar to those presented below. ‘These specifications of the forecasting equations arc:similar to the reduced form equations that st modeled recent U.S. dab. See KanderHofT(1983). Also, all regressors are growth rates over uarter spans t9 akw long lags and to economizn on the number of parameters.
Tabfc 1
Analysis of forecasts: 196X:4-1977:4* (A) Sumnam~
vtcmrms
Norlund
_--.-_----_-------___-.
IllLx9IllC
_ f? _- _^_. ___~.~ _~.__~~~~ ~_~~ 0.06
f MSE due to bi __.__ -- . .. .
0.07
--._
_
._
I”4 0.06
0 13 _
(8) E$&3em v test repwsrorr rtwh (Y&7-
Y?‘)
- 0.43 ( .- 0.13) o.ou (0.34) -0.19 ( 0.80) 0.2x (1.17) 0.05 (0.21) __.. 0 09 (- 1.3’i 0.07 (0 nx,
0.17 c 0.86 0.49 1.64
(Y4
Y4e)
-0SS
(-0.24) - 0.14 ( 0.90) 0.14 (0.84) 0.11 (0.691 - 0.07 ( - 0.411
(P,T- P?-)
_-. _._. .- .-_ _ - K.23 ( -2 1)
(i.17 (1.&j O.f? (1.1) 0.21 (1.58) 0.W
(2.27) __ 0.16 ( 1.30) -”0.03 0.02 ( - d.76) (0.33) - 0.03 0.08 (0.72) (1.54) _-. 1.20 (1 1-U 0.09 (0 57) 0.19 0.46 e 1.51 2.61’ 1.Ol 2.49” 0.56 0.42 1.21 _._“_“” D_” . .. _ ;l. “-C-r.i_“_,.__I_~li?
(P4
tw;
390
J. VanderWo$. A ‘rational’ expbnatim for ‘irrational’~orecusting
errors. To summarize, the income forecasts incorporate information efficiently and are unbiased but the inflation rate forecasts do not incorporate monetary policy data efficiently and are biased towards underprediction04 3. The explanation The Rational Expectations Models developed by Robert Lucas (1973) md others predict that the impact of money on nominal income is stable, but the impact of money on the inflation rate is not stable. Lucas shows that suppliers’ output decisions based on rationally formed expectations of relative prices cause an increase in the ‘Phillips Curve’ slope during periods of volatile aggregate demand; that is, money induced changes in income result in higher inflation rates. Two recent studies find evidence of parameter non-stationarity. My previous paper (1983) shows that money supply and government expenditure growth rates had a stable impacl on nominal income, but not on the inflation rate. Furthermore, money affected the inflation rate more quickly during periods of tnore volatile aggregate demand changes. Also, Keith Carlsor, (1980) concludes that nominal income reduced form parameters are stationv, but that the inflation equation parameters are not stationary. Also. he finds thai money growth rate s affected inflation rates faster and to a greater extent in the 1970’s relative to the 1955:1--1969:4 period. The non-stationary impact of the money supply indicates that an alternative efficiency test must be applied to the inflation forecasts. The previous test may falsely reject efficient itlformation use because unbiased estimates of the money supply parameters cannot be obtained for several periods after the changes in their values.5 The strategy adopted here is to compare the inflation forecasts with benchmark forecasts that incorporate available information efficiently, assuming the inflation equation parameters were stable. Although evidence now exists that this assumption is invalid, the forecasters most likely adopted this assumption. The benchmark forecast is derived from the Least Squares estimates of the inflation rate reduced form equation; the estimates are based only on data available at the time the forecast was made. The forecasts at time t for the rate of inflation ending at time t + i are Pi, =,brXt,
(2)
i = 2,4,,
where ,b, are the Least Squares estimates at time
t.
For the forecasts Pi,
+ ,,
the
*The results obtained by Brown and Maital (1981) with the Livingston data are similar with respect to the policy variables. Both monetary and fiscal policy data arc used efficiently in the income forecasts, but only the fiscal policy data is used efficiently in the inflation forecasts. Efficiency is rejected in alillforecasts due to the effects of endogenous variablbleson the forecast errors. %hiller (1978) and Taylor (1975) discuss this point.
data base is updated to estimate ,!J,+,. The modified efficiency test requires the estimation of the folEowingequation: (hi,-Pi))=(,b,-,c,)X,+u,,
(3)
where ,c, are the parameters of the forecasters’ predicting equation. Evidence that the regression parameters are zero suggests alt available information was used efficiently to forecast the inflation rate. Note, however, the modified procedure tests the joint hypotheses that the data X, identifies the information set and that Xf is used in the same efficient manner as the Least Squares forecasts. That is, efficient information use may be falsely rejected in the modified efficiency test if the forecasters used data other than that contained in .Y‘. The modified efficiency tests suggest that the professionals’ forecast and the Least Squares forecasts incorporate the monetary policy data in the same manner. As reported in the last two columns of part B in table 1, the hypothesis that the monetary policy coefficients are zero cannot be rejected at the 5% significance level. However. the hypothesis that the regression coefficients are zero is rejected as a result of the effects of the non-monetary data. The results that the inflation forecasts incorporate the non-monetac data efficiently and that this data is used differently than the Least Squares forecasts probably occurs because the modified efficiency test investments joint hvpotheses and the fiscal policy data and potential output data have been revised extensively since the time the forecasts were made. 4. Conclusion This paper provides support for a ‘rational’ explanation for ‘irrational’ forecasts in inflation. The analysis indicates that professional fcJreCaSt&X’s incorporated data on monetary and fiscal policy effkiently to produce reiatively accurate and unbiased forecasts of nominal income. But this same group underpredicts the inflation rate due to underestimates of the impact of rnow~ on inflation. Additional tests indicate that ,thc:impact of the money supply tJn these inflaGon forecasts does not din’er from the impact of this dntia on enerated from estimates of an inflation rate reduced form equa;ion. These results suggest that forecasters ’ ‘inefficient’ use of the monetary cfata results from th: non-stational!: money supply parameters m the intlati~~nr;lte equation. Rational Expectations Models predict a stationary money--income relationship and a non-stationary money-inflation relationship. These models then provide an explanation for the results that the forecasters muds ‘rtition~l‘ forecasts of nominal income, but made ‘irrational‘ forecasts i)f the intkkn rate.
392
J. Vanderlbf,
A ‘rational’ explanation for ‘irrational’forecusting
References Brown, B.W. and S. Maital, 1981, What do economists know? An empirical study of experts’ expectations, Econometrica 49. March, 491-504. Carlson, KC.. 19S0, Money, inflation and economic growth: Some updated reduced form results and their implications, St. Louis Federal Reserve Bank Review 62, April, 13-19. Granger. C.W.J. and P. Newbold, 1977, Forecasting economic time series (New York). Lucas, R-E.. 1973, Some international evidence on outpu;-inflation tradeoff’s,American Economic Review 63, June, 326-334. Mullineaux. D.J., 1980, Inflationary expectations and monetary growth in the United States, American Economic Review 70, March, 149-161. Pearce. D.K.. 1979, Comparing survey and rational measures of expected inflation, Journal of Money, Credit and Banking 11, Nov., 447-456. Shiller, P., 1978, Rational expectations and the dynamic structure of macroeconomic models, Journal of Monetary Economics 4, Jan., l-44. Taylor, J.. 1975. Monetary policy during transition to rational expectations, Journal of Political Economy 83. Oct.. 1009-1021. VanderHoff. J.. 1983, Support for rational expectations models with U.S. data, Journal of Monetary Economics 12, Aug., 297-308. Zamowitz, V.. 1979. An Analysis of annual and multiperiod :!!:dterly forecas:s of aggregate income, output, and the price level, Journal of Business X3 Jhn., l-33.
A *RATIONAL’ EXPLANATIOW FOR ‘IRRATIONAL’ FORECASTS OF IMXATION James VANDE Rutgers Umoersi@-Nm~ar&, Newark. NJ 07102. LS.4
This paper analyzes professionals’ forecasts of nominal income and the inflation rate. The analysis indicates that both monetary and fiscal policy data was used efficiently to forecast income. but the monetary policy data was not used efficiently to forecast the inflation rate. Further analvsi~ suggests that the apparent inefficient use of the monetary data r;;~uits from the non- ,tatione money-inflation relatiomhip predicted by rational expectations models. These models then provide an explanation for the inconsistent coaclusions regarding the income forecasts and the inflation rate forecasts.
1. Introduction
Several studies of inflation forecasts derived from survey data indicatethat the forecasts do not incorporate available information efficiently and are biased downard.’ Researchers suggest that this ‘irrationality’ is characteristic of survey-based forecasts but not of the forecasts that govern market transactions. Their rationtie is the survey respondents, unlike market participar.ts. lack the incentives required to make forecasts that are unbiased and information efficient. This paper tests an alternative explanation: the forecasters used all available information efficiently, but this information did not include the fact that the impact of money growth on the inflation rate was increased during the 1970’9. As a result, their estimates of the effects of money growth were too low and the infiation rate was underpredicted. This type of parameter non-stationarity is consistent with rational expectations models. Therefore. these models provide a ‘rational’ explanation for the ‘irrational’ forecas:s of inflation. This paper is o anized as follows: Section 2 analyzes nominal income and inflation rate forecasts derived from surveys of professional forecasters. Section 3 proposes and tests the explanation ;‘or the results presented in the prttvk~s section. Section 4 concludes the paper. estions. conclude that the kingston fore I Brown and Maital (1981) and Pearce (1 consistent with the Rational Expectations hypothesis. Mullineau?i 1981)) rear hes conclusion. *I wish to thank Mary Golden for useful
03W-3923/X4,‘53.(x)C lQK4, Elsevrer Scrence Publishers B.V. (North-H~Gnd)
J. VunderHo$.
388
A ‘rationul’
ecplurtution for ‘irrutiorrul’~(~recwstinK
2. The foreccasts Sirm 1968, the American Statistical Association and the National Bureau of Economic Research (ASA-NBER) have surveyed about fifty professiclnal
forecasters each quarter. The participants are provided with the most recent data on several variables, including the previous quarter’s National Income accounts data. The respondents then report the levels af the variables expected at the end of rhe current quarter and the three subsequent quarters. This paper analyzes two- and four-quarter forecasts derived from the median predicted levels of Norninal GNP and the GNP Implicit Price Deflator.’ Part A of table 1 reports summary statistics pertaining to the forecast errors for the period 1968:4 to 1977:4. The income forecasts are more accurate and Iess biased than the inflation forecasts. For the income forecasts, the ratio of the average: error to the average change is 0.06 and the portion of the MSE attributed IO bias is less than 0.13. In contrast, the average error is about 0.2 of the average value and the portion of the error attributable to bias is about 0.40 :.vith the inflation forecasts. The positive average error indicates a tendency to underpredict the actual value. Paft B of table 1 reports the efficient-use-of-information test results. The test involves regressing the forecast errors on the information sei., represented by X,, yt -
Y:e= SX,+
e,.
(1)
The rejection of the hypothesis B = 0 indicates these data contribute to the forecast error, hence were not used effciently. For the income forecasts tests, the: information set is assumed to consist of the current and lagged values of monetary and fiscal policy data. For the inflation rate forecasts, the information ses also includes a measure of potential output growth and the lagged inflation rak3 The test results indicate the income forecasts incorporate data efficiently, but the inflaition rate forecasts do not.. The regression F statistic, Fr, is not significa!mtlydifferent from zero in either income regression. However, both the regression F statistic and the monetary policy data test statistic, Fw,, tire significant in both inflation rate regressions. Also, the monetary coeficients are all positive. These results indicate the forecasters underestimated the impact of money sn the inflation rate. Notia that potential output, the la rate, and &e kcal policy data are estimated to be independent of the forecast *For a r’ulldescriptiofi of this data, see Zarnowitz (1979) and the refercnccs he cites. Also, the analysis OFthe one- and thrmquarter fovtxasts yield results similar to those presented below. ‘These specifications of the forecasting equations arc:similar to the reduced form equations that st modeled recent U.S. dab. See KanderHofT(1983). Also, all regressors are growth rates over uarter spans t9 akw long lags and to economizn on the number of parameters.
Tabfc 1
Analysis of forecasts: 196X:4-1977:4* (A) Sumnam~
vtcmrms
Norlund
_--.-_----_-------___-.
IllLx9IllC
_ f? _- _^_. ___~.~ _~.__~~~~ ~_~~ 0.06
f MSE due to bi __.__ -- . .. .
0.07
--._
_
._
I”4 0.06
0 13 _
(8) E$&3em v test repwsrorr rtwh (Y&7-
Y?‘)
- 0.43 ( .- 0.13) o.ou (0.34) -0.19 ( 0.80) 0.2x (1.17) 0.05 (0.21) __.. 0 09 (- 1.3’i 0.07 (0 nx,
0.17 c 0.86 0.49 1.64
(Y4
Y4e)
-0SS
(-0.24) - 0.14 ( 0.90) 0.14 (0.84) 0.11 (0.691 - 0.07 ( - 0.411
(P,T- P?-)
_-. _._. .- .-_ _ - K.23 ( -2 1)
(i.17 (1.&j O.f? (1.1) 0.21 (1.58) 0.W
(2.27) __ 0.16 ( 1.30) -”0.03 0.02 ( - d.76) (0.33) - 0.03 0.08 (0.72) (1.54) _-. 1.20 (1 1-U 0.09 (0 57) 0.19 0.46 e 1.51 2.61’ 1.Ol 2.49” 0.56 0.42 1.21 _._“_“” D_” . .. _ ;l. “-C-r.i_“_,.__I_~li?
(P4
tw;
390
J. VanderWo$. A ‘rational’ expbnatim for ‘irrational’~orecusting
errors. To summarize, the income forecasts incorporate information efficiently and are unbiased but the inflation rate forecasts do not incorporate monetary policy data efficiently and are biased towards underprediction04 3. The explanation The Rational Expectations Models developed by Robert Lucas (1973) md others predict that the impact of money on nominal income is stable, but the impact of money on the inflation rate is not stable. Lucas shows that suppliers’ output decisions based on rationally formed expectations of relative prices cause an increase in the ‘Phillips Curve’ slope during periods of volatile aggregate demand; that is, money induced changes in income result in higher inflation rates. Two recent studies find evidence of parameter non-stationarity. My previous paper (1983) shows that money supply and government expenditure growth rates had a stable impacl on nominal income, but not on the inflation rate. Furthermore, money affected the inflation rate more quickly during periods of tnore volatile aggregate demand changes. Also, Keith Carlsor, (1980) concludes that nominal income reduced form parameters are stationv, but that the inflation equation parameters are not stationary. Also. he finds thai money growth rate s affected inflation rates faster and to a greater extent in the 1970’s relative to the 1955:1--1969:4 period. The non-stationary impact of the money supply indicates that an alternative efficiency test must be applied to the inflation forecasts. The previous test may falsely reject efficient itlformation use because unbiased estimates of the money supply parameters cannot be obtained for several periods after the changes in their values.5 The strategy adopted here is to compare the inflation forecasts with benchmark forecasts that incorporate available information efficiently, assuming the inflation equation parameters were stable. Although evidence now exists that this assumption is invalid, the forecasters most likely adopted this assumption. The benchmark forecast is derived from the Least Squares estimates of the inflation rate reduced form equation; the estimates are based only on data available at the time the forecast was made. The forecasts at time t for the rate of inflation ending at time t + i are Pi, =,brXt,
(2)
i = 2,4,,
where ,b, are the Least Squares estimates at time
t.
For the forecasts Pi,
+ ,,
the
*The results obtained by Brown and Maital (1981) with the Livingston data are similar with respect to the policy variables. Both monetary and fiscal policy data arc used efficiently in the income forecasts, but only the fiscal policy data is used efficiently in the inflation forecasts. Efficiency is rejected in alillforecasts due to the effects of endogenous variablbleson the forecast errors. %hiller (1978) and Taylor (1975) discuss this point.
data base is updated to estimate ,!J,+,. The modified efficiency test requires the estimation of the folEowingequation: (hi,-Pi))=(,b,-,c,)X,+u,,
(3)
where ,c, are the parameters of the forecasters’ predicting equation. Evidence that the regression parameters are zero suggests alt available information was used efficiently to forecast the inflation rate. Note, however, the modified procedure tests the joint hypotheses that the data X, identifies the information set and that Xf is used in the same efficient manner as the Least Squares forecasts. That is, efficient information use may be falsely rejected in the modified efficiency test if the forecasters used data other than that contained in .Y‘. The modified efficiency tests suggest that the professionals’ forecast and the Least Squares forecasts incorporate the monetary policy data in the same manner. As reported in the last two columns of part B in table 1, the hypothesis that the monetary policy coefficients are zero cannot be rejected at the 5% significance level. However. the hypothesis that the regression coefficients are zero is rejected as a result of the effects of the non-monetary data. The results that the inflation forecasts incorporate the non-monetac data efficiently and that this data is used differently than the Least Squares forecasts probably occurs because the modified efficiency test investments joint hvpotheses and the fiscal policy data and potential output data have been revised extensively since the time the forecasts were made. 4. Conclusion This paper provides support for a ‘rational’ explanation for ‘irrational’ forecasts in inflation. The analysis indicates that professional fcJreCaSt&X’s incorporated data on monetary and fiscal policy effkiently to produce reiatively accurate and unbiased forecasts of nominal income. But this same group underpredicts the inflation rate due to underestimates of the impact of rnow~ on inflation. Additional tests indicate that ,thc:impact of the money supply tJn these inflaGon forecasts does not din’er from the impact of this dntia on enerated from estimates of an inflation rate reduced form equa;ion. These results suggest that forecasters ’ ‘inefficient’ use of the monetary cfata results from th: non-stational!: money supply parameters m the intlati~~nr;lte equation. Rational Expectations Models predict a stationary money--income relationship and a non-stationary money-inflation relationship. These models then provide an explanation for the results that the forecasters muds ‘rtition~l‘ forecasts of nominal income, but made ‘irrational‘ forecasts i)f the intkkn rate.
392
J. Vanderlbf,
A ‘rational’ explanation for ‘irrational’forecusting
References Brown, B.W. and S. Maital, 1981, What do economists know? An empirical study of experts’ expectations, Econometrica 49. March, 491-504. Carlson, KC.. 19S0, Money, inflation and economic growth: Some updated reduced form results and their implications, St. Louis Federal Reserve Bank Review 62, April, 13-19. Granger. C.W.J. and P. Newbold, 1977, Forecasting economic time series (New York). Lucas, R-E.. 1973, Some international evidence on outpu;-inflation tradeoff’s,American Economic Review 63, June, 326-334. Mullineaux. D.J., 1980, Inflationary expectations and monetary growth in the United States, American Economic Review 70, March, 149-161. Pearce. D.K.. 1979, Comparing survey and rational measures of expected inflation, Journal of Money, Credit and Banking 11, Nov., 447-456. Shiller, P., 1978, Rational expectations and the dynamic structure of macroeconomic models, Journal of Monetary Economics 4, Jan., l-44. Taylor, J.. 1975. Monetary policy during transition to rational expectations, Journal of Political Economy 83. Oct.. 1009-1021. VanderHoff. J.. 1983, Support for rational expectations models with U.S. data, Journal of Monetary Economics 12, Aug., 297-308. Zamowitz, V.. 1979. An Analysis of annual and multiperiod :!!:dterly forecas:s of aggregate income, output, and the price level, Journal of Business X3 Jhn., l-33.