JOHN MCDONALD Flinders University of South Australia An Econometric Test of Inflation Neutrality Using Observable Variables Only* A modification to Startz (1981) test of some basic assertions of the resurgent neo- classical school of macroeconomics is undertaken. The assertions suggest the neu- trality of the real economy with respect to anticipated inflation and the advantage of the new test is that it can be implemented using observable variables only. Re- sults similar to Startz’s were obtained when the test was rerun. 1. Introduction In an interesting paper, (l%l), Startz undertakes an ingenious test of some basic assertions of the resurgent neoclassical school of macroeconomics, namely that, the expected real interest rate is in- dependent of the expected inflation rate, deviations of the unem- ployment rate from the natural rate of unemployment are associated only with unanticipated inflation, and expectations are rational so that the anticipated inflation rate is uncorrelated with the unanti- cipated rate. Taken together the three hypotheses suggest the neu- trality of the real economy with respect to anticipated inflation. Startz’s regression test suffers from the difficulty that it involves the unobservable explanatory variable “the deviation of the unemploy- ment rate from the natural unemployment rate.” In this paper I develop a procedure that allows the test to be implemented using observable variables only. The test involves applying the instru- mental variables method allowing for autocorrelated disturbances. Results similar to Startz’s were obtained when the test was rerun. 2. Stat-h’s Test The Fisher equation states that the nominal interest rate, R, is equal to the sum of the expected real interest rate, r, and the anticipated inflation rate, W. *I would like to thank the Australian Research Grants Commission for sup- Porting this project financially, Richard Startz for sending me his data, and Adrian Pagan for allowing me to use his AUTREGALS program. ]ournal of Macroeconomics, Spring 1986, Vol. 8, No. 2, pp. 193-199 193 Copyright 0 1986 by Wayne State University Press.
Transcript
JOHN MCDONALD Flinders University
of South Australia
An Econometric Test of Inflation Neutrality Using Observable Variables Only*
A modification to Startz (1981) test of some basic assertions of the resurgent neo- classical school of macroeconomics is undertaken. The assertions suggest the neu- trality of the real economy with respect to anticipated inflation and the advantage of the new test is that it can be implemented using observable variables only. Re- sults similar to Startz’s were obtained when the test was rerun.
1. Introduction In an interesting paper, (l%l), Startz undertakes an ingenious
test of some basic assertions of the resurgent neoclassical school of macroeconomics, namely that, the expected real interest rate is in- dependent of the expected inflation rate, deviations of the unem- ployment rate from the natural rate of unemployment are associated only with unanticipated inflation, and expectations are rational so that the anticipated inflation rate is uncorrelated with the unanti- cipated rate. Taken together the three hypotheses suggest the neu- trality of the real economy with respect to anticipated inflation. Startz’s regression test suffers from the difficulty that it involves the unobservable explanatory variable “the deviation of the unemploy- ment rate from the natural unemployment rate.” In this paper I develop a procedure that allows the test to be implemented using observable variables only. The test involves applying the instru- mental variables method allowing for autocorrelated disturbances. Results similar to Startz’s were obtained when the test was rerun.
2. Stat-h’s Test The Fisher equation states that the nominal interest rate, R,
is equal to the sum of the expected real interest rate, r, and the anticipated inflation rate, W.
*I would like to thank the Australian Research Grants Commission for sup- Porting this project financially, Richard Startz for sending me his data, and Adrian Pagan for allowing me to use his AUTREGALS program.
]ournal of Macroeconomics, Spring 1986, Vol. 8, No. 2, pp. 193-199 193 Copyright 0 1986 by Wayne State University Press.
]ohn McDonald
R=r+rP. 0)
The neutrality hypothesis as it relates to financial markets is that r and lY are uncorrelated.
The neutrality hypothesis appears in real markets as the ex- pectations augmented Phillips curve,
rl=iY+@i, (2)
where ll is the actual inflation rate and ii = u* - u is the difference between the natural and actual unemployment rate (u* and u, re- spectively). ti is associated only with unanticipated events, so since the expected inflation rate and expected real rate of interest are known to agents when contracts are drawn up, the following pairs of variables are uncorrelated: ii and lY, Q and r, hence from Equa- tion (2) ll and r and from Equation (l), R and ti.
Substituting Equation (2) into Equation (l), we obtain
R=r-flii+iI. (3)
If A is regressed on ii and ll, the error term in the regression is r which is uncorrelated with the explanatory variables ii and ll. Providing r is suitably modelled, it follows that consistent estimates of p and the coefficient on ll will be obtained. If the neutrality hypothesis is true, then the estimate of l3 is the estimate of the slope of the Phillips’ curve and the estimated coefficient on ll should be insignificant from unity.
A major problem is that fi is unobservable. Startz proceeds by making the alternative assumptions (i) that the natural rate of un- employment is constant, (ii) that the natural rate of unemployment is the systematic part of the actual unemployment time series and ti is the white noise component, and (iii) accepting Perloff and Wachter’s estimates of the natural rate of unemployment. None of these approaches is satisfactory. With respect to (i), few theorists would agree that the natural rate of unemployment is constant over time [see, for example, Parkin (1974, p. 40) and Santomero and Seater (1978, p. 515)]. With respect to assumption (ii), although theory suggests that ti should be a white noise series, as Startz indicates in footnote 8, there is no reason why it should be the white noise series that is extracted by applying the filter rule. Per- loff and Wachter’s natural unemployment rate estimates are also based on strong assumptions.
194
Test of inflation Neutrality Using Observable Variables
3. The Relationship between the Observed and Natural Rate of Unemployment
The idea that the observed unemployment rate, u, is the sum of two uncorrelated components u *, the natural or equilibrium rate, and -ii, unemployment resulting from the economy being in dis- equilibrium due to inflationary expectations not being fulfilled, is implicit in much of the analysis conducted by the resurgent neo- classical school. For example, the filter rule for extracting -ii used by Startz requires that ux and -ii are uncorrelated. Thus Startz decomposes u, into p. + P~u,-~ + P~u,-~ + p3ut+ = uf and the white noise innovations, -ii,. If -I& is correlated with U* then when ut is regressed on a constant, ut-r, utm2 and ut+, inconsistent estimates of po, pr, p2 and p3 would be obtained and the method would fail. Sargent [(1973, pp. 450-51) and (1976, pp. 214-17)], Barro (1977, 1978), and many others also regard u* and -ii as uncorrelated com- ponents of u.
The rationale behind the idea is as follows. Given the neo- classical model and rational expectations, u* and -ZC are unaffected by systematic monetary policy. u* is the equilibrium rate of un- employment which depends only on equilibrium real forces. -ii is affected by unanticipated monetary policy. -fi is also affected by other unanticipated events that affect the real economy, but at the macro level, these are regarded as unimportant compared with the influence of unanticipated monetary policy and are ignored. Con- sequently, -6 and u* are regarded as uncorrelated components of the observed unemployment rate.
An important implication of this is that the actual rate of in- flation (as well as the anticipated rate) is uncorrelated with the nat- ural rate of unemployment. This result follows directly from Equa- tion (2). The actual inflation rate is the sum of two uncorrelated components, the anticipated rate and the unanticipated rate. By the neutrality hypothesis, the anticipated rate of inflation is uncorre- lated with u*, but the unanticipated inflation rate depends only on li. Since 6 is uncorrelated with u*, fI must be uncorrelated with u*.
Also note that over a monthly time period equilibrium real forces are unlikely to vary much, so movements in the natural rate of unemployment relative to unemployment changes due to unan- ticipated inflation are likely to be small. Consequently, we may pre- sume that most of the variation in the observed unemployment rate is due to variation in -ii.
These considerations allow us to mount a test of the neutrality hypothesis using only observable variables.
195
John McDonald
4. Modification of Stark’s Test Equation (3) can be written
R=pu+rl+E, (4)
where the error term E = -Bu* + r- . In Section 3, I have argued that ll is uncorrelated with u*.
By the neutrality hypothesis II and r are uncorrelated, so II is un- correlated with E.
u is correlated with u* and hence E. Since one of the explan- atory variables in Equation (4) is correlated with the error term, it follows that a direct least squares procedure will give inconsistent estimates of the coeffkients in Equation (4). Nevertheless, if we can find a variable correlated with IA but not with E, the instrumental variables method can be applied to obtain consistent estimates of the coefficients in Equation (4).
The unanticipated inflation rate, II - IY = Bii, is highly cor- related with ii and if, as seems plausible, monthly variations in u are due mainly to variations in ii (rather than u*), it will be highly correlated with u. The unanticipated inflation rate is uncorrelated with u* and r and hence E. Consequently, the unanticipated infla- tion rate is a valid instrumental variable for u in Equation (4).
Although the anticipated inflation rate, Ile, is not observable, we can estimate it as the predicted value from an autoregressive moving average (ARMA) model fitted to the time series of actual inflation rates [e.g., McDonald (1977)]. This estimate of IP depends only on past actual inflation rates which are uncorrelated with U* and r and hence E, and the resulting estimate of the unanticipated inflation rate will be highly correlated with the actual unanticipated inflation rate and hence highly correlated with U, but not correlated with u* or r and hence E*. The estimated unanticipated inflation rate is therefore also a valid instrument.
Since E, = -Bu*, + r, may be autocorrelated over time, the in- strumental variables estimation procedure must allow for autocor- related residuals. We must also allow for et having a non-zero mean by introducing a constant term into the regression.
5. The Estimation Procedure and Results If we assume that the stochastic processes {UT} and {rt} can be
represented as autoregressive moving average (ARMA) processes, then the results of Granger and Morris (1976) and Ansley et. al.
196
Test of Inflation Neutrality Using Observable Variables
(lQ77) indicate that (et} can be represented as an ARMA process. It follows that if
0, = e, - a , (5)
(03 can be represented as a zero mean, ARMA process, with white noise process (WNP) {a,}, say. Equation (4) can then be estimated in the form
R, = a + f3u, + ZXI, + q. (6)
General methods for estimating this kind of nonlinear model by in- strumental variables and developing testing procedures are de- scribed by Gallant (1977) and Gallant and Jorgenson (1979). Sargan (1959) deals with the case when u, is a pure autoregressive process. It is not essential that the WNP {a,} is a normal stochastic process but its characteristics must be such that a normal central limit theo- rem operates. For the method to give consistent estimates, the in- strumental variables must be uncorrelated with a,. The estimations were carried out on Pagan’s AUTREGALS computer program using Startz’s monthly data. (The time period is 1953(l) to 1971(7)). The intercept dummy, current and lagged inflation and current and lagged estimated unanticipated inflation rates were used as instrumental variables.’ The estimated anticipated inflation rate was obtained by fitting an ARMA model to the observed inflation time series and calculating the predicted values from this model. The estimated model was
where L is the lag operator, estimated standard errors are given in brackets and c’e is the WNP estimated standard error. This model is very similar to that obtained by Nelson and Schwert (1977, p. 481) with similar data. The unanticipated inflation rate was esti- mated as the actual rate of inflation less the predicted rate.
‘The nonlinear instrumental variables method used, unlike Fair’s (1970) method, does not require that R,-, and IL-, are in the instrumental variable list. If, however, R,-, and u,-, are added to the instrumental variable list, very similar results are obtained.
The estimate of the autocorrelation function of the a, residuals sug- gested that {a3 is a WNP and, consequently, that ot approximately follows a random walk and E, = u, + (Y a random walk with drift. [The autocorrelation coefficient estimates made allowance both for simultaneity and lagged dependent variables; see Godfrey (1976) and Pagan (1981)]. The estimate of J3 has the “correct” sign but is not quite significantly different from zero at the five per cent sign& cance level. The estimate of 6 also has the “correct” sign, but is very close to zero and over 100 standard errors away from unity. The results are similar to equation (8a’), Table 1A of Startz and clearly do not support the neutrality hypothesis. They cast consid- erable doubt on the validity of the simple representation of the neo- classical school of macroeconomic thought as interpreted by Startz.
Receiued: June 1985 Final uerston: September 1985
References Ansley, C.F., Spively, W.A., and W. J. Wroblesbi. “On the Struc-
ture of Moving Average Processes,” Journal of Econometrics, 6 (July 1977): 12134.
Barro, R. J. “Unanticipated Money Growth and Unemployment in the United States.” American Economic Review 67 (March 1977): lOl- 15.
-. “Unanticipated Money, Output, and the Price Level in the United States.” Journal of Political Economy 86 (August 1978): 549-80.
Fair, R.C. “The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Corre- lated Errors.” Econometrica 38 (May 1970): 507-16.
198
Test of Inflation Neutrality Using Observable Variables
Gallant, A.R. “Three-Stage Least Squares Estimation for a System of Simultaneous, Nonlinear, Implicit Equations.” Journal of Econometrics, 5 (January 1977): 71-88.
and D.W. Jorgenson. “Statistical Inference for a System of Simultaneous, Non-Linear, Implicit Equations in the Context of Instrumental Variable Estimation.” Journal of Econometrics, 11 (October 1979): 275-302.
Godfrey, L. “Testing for Serial Correlation in Dynamic Simulta- neous Equation Models. ” Econometrica, 44 (Sept. 1976): 1077- 84.
Granger, C.W.J. and M.J. Morris. “Time-series Modelling and Interpretation.” Journal of the Royal Statistical Society, Series A. 139 (1976): 246-57.
McDonald, J. “The Relationship Between Wage Inflation and Ex- cess Demand-New Estimates Using Optimal Extrapolative Wage Expectations.” Economic Record, 53 (December 1977): 490-507.
Nelson, C.R. and G.W. Schwert. “Short-Term Interest Rates as Predictors of Inflation: On Testing a Hypothesis that the Real Rate of Interest is Constant.” American Economic Review 67 (June 1977): 478-86.
Pagan, A. “AUTREGALS Computer Program Write-Up.” (mimeo) Australian National University, 1981.
Parkin, M. “United Kindom Inflation: The Policy Alternatives.” Na- tional Westminster Bank Quarterly Review, (May 1974): 33-47.
Sargan, J. D. “The Estimation of Relationships with Autocorrelated Residuals by the Use of Instrumental Variables.” Journal of the Royal Statistical Society, Series B. 21 (1959): 91-105.
Sargent, T.J. “Rational Expectations, The Real Rate of Interest and the Natural Rate of Unemployment.” Brookings Papers 2 (1973): 429-73.
-. “A Classical Macroeconometric Model for the United States.” Journal of Political Economy. 84 (April 1976): 207-37.
Santomero, A.M. and J. J. Seater. “The Inflation-Unemployment Trade-Off: A Critique of the Literature.” Journal of Economic Literature 16 (June 1978): 499-544.
Startz, R. “Unemployment and Real Interest Rates: Econometric Testing of Inflation Neutrality.” American Economic Review 71 (December 1981):
