Economies. By. Michele Fratianni and Mustapha Nabll ...... 326-334. MaeCallum, Bennett T., "Rational Expectations and the Estimation of Econometric Models:.
Inflation and Output with Rational Expectations in Open Economies By
Michele Fratianni and Mustapha Nabll
Contents: I. Introduction. - II. The Theoretical Framework. - III. Description of the Data. - IV. Estimation Procedure and Findings. - V. Conclusions. - Appendices.
I. Introduction
T
he objective of this paper is to develop a theoretical framework of the real sector of a small open economy which will then be tested using yearly data from five EEC member countries.
The model we intend to develop must include several crucial aspects of open industrial economies. First, the economies export on the whole manufactured goods while importing both manufactured goods and raw materials which are used as intermediate goods in the production process (the oil-producing United Kingdom and the natural-gas producing Netherlands are two exceptions.). To the extent that domestically and foreign produced goods are imperfect substitutes, there will be changes in the terms of trade which will in turn affect the domestic real sector. Second, it is possible in an open economy, apart from misperceptions of the current price level, to generate an aggregate supply curve which is positively sloped with respect to domestic prices. This result derives from the behavioral postulate that, while the demand for labor responds to the domestic price level, the supply of labor responds to the overall expected price level. Third, several industrial economies have institutionalized to different degrees wage indexation schemes which insulate labor from the effects of forecast errors in the overall price level [cf. e.g. Romanis Braun, 1976]. The intuitive implication is that wage indexation tends to reduce changes in output attributable to misperceptions of the current overall price level. Finally, economic agents behave rationally in the Muth [1961] sense, that means they form expectations consistent with the underlying model.
Remark: Wegratefullyacknowledgefinancialsupportfrom"GeconcerteerdeOnderzoeksacties" (GOA80/85-1), which madethis researchpossible.Thisstudyis part of a largereconometricproject, the LouvainEuropean Project, which is currently under way at the Catholic Universityof Louvain. We benefitedfrom commentsby P. de Grauwe and competentresearch assistance by J. Mont. Weltwirtschaftliches Archiv Bd. CXXI.
3
34
Michele F r a t i a n n i and M u s t a p h a Nabli
The above considerations suggest that the Lucas [1973] aggregate supply function, which has been widely used in recent years, is too restrictive for open economies and thus requires appropriate modificationsk This will be done in Section II of the paper which develops the theory and its testable implications. Section III discusses the selection of the data, countries and sample period as well as the stylized facts of the crucial variables under investigation. Section IV deals with the estimation strategy and presents the results based on annual data. Summary and conclusions will be drawn in Section V.
II. The Theoretical Framework 1. T h e A g g r e g a t e S u p p l y F u n c t i o n We begin our theoretical discussion with the supply side of the model which stresses, among other things, the role of intermediate goods 2. The representative firm in our open economy produces a final goods Y under the following production function Y=AN alH ~
al+a2 0 a 2 = a 2 / ( 1 - a 1 - 0t2) > 0
1 Argy [1978] in his comment to the papers by Fratianni [1978], Four,arts [1978], and Korteweg ~1978], who adopt the standard Lucas-supply function, argues the same point. 2 On this point we have been particularly influenced by the papers of Bruno and Sachs [1979], Leiderman [1982] and Darby [1982].
Inflation a n d O u t p u t
35
bl -- (1 - al)/(1 - al - a2) > 0 b2 = (1 - a2)/(1 - al - a2) > 0 ai = In (ai)
Factor demands depend positively on the fixed input and the two relative prices. The intermediate good is supplied at the foreign currency price p~' which is given for the small open economy. The domestic price of h is simply (p~ + e) where e is the log of the exchange rate expressed as the domestic price of one unit of foreign currency. Labor supplies services according to the following wage-setting function w t = E (Pt In-l) + b [Pt - E (ptln-0] t-1
(5)
t-1
Labor contracts are negotiated at the end of period t-1 at which time workers make their best forecast concerning the overall price level for period t. The forecasts are conditional on the information set ~')-1 which includes the history of all variables up to t-1. Nominal wages respond fully to changes in the overall expected price level. In addition, workers may bargain for indexation clauses which will insulate them from the effects of forecast errors in the general price level. The degree of protection is reflected in the value of 0 < b < 1; when b = 1 wages adjust completely to changes in the current, but unknown, price level. The price level is defined as a weighted average of the domestically and foreign produced final goods prices P = }'Pd + (1 - h) pf
(6)
where pf = p?+ e. The domestic economy is a price taker in the foreign produced goods market. Eqs. (1), (3), (4), (5) and (6) yield Yt = ao + a, (1 - b) - a2 (Ph, t -
Pf,t)
(Pt -
Ep,) + [a 1 (1 - )0 + a21 (P,,,t - Pf, t)
"[- Vs, t
(7)
where a0 = a + a~n0 + a2h0, vs, t is a white-noise error term and t-1 of the expectations variables has been dropped to simplify notation. This is a Lucas-type aggregate supply function extended to our open economy. The first term on the right hand side of (7) gives the "normal" level of output; the second term is the Lucas price-level misperception effect; the last two terms capture the impact of the final goods terms of trade and the intermediate goods terms of trade on domestic output supplied. An increase in domestic goods prices relative to foreign goods prices raises y supplied; an increase in the intermediate goods prices relative to foreign final goods prices lowers it. Indexation lowers the effect of the surprise variable on output 3*
36
Michele Fratianni
and M u s t a p h a
Nabli
supplied, disappearing altogether when b = 1. Note that the closed-economy Lucas supply curve is obtained from (7) by setting b < 1, ~, = 1 and ignoring intermediate goods. 2. A g g r e g a t e
Demand
We postulate that aggregate d e m a n d depends positively on real cash balances, m t - Pt, and other real impulses, I t - Pl, and negatively on the final goods terms of trade. This formulation, which is fairly standard, allows a variety of outcomes and in particular it is neutral with respect to the issue of whether monetary or fiscal impulses dominate1: Yt = [31 (mr - Pt) - [32 (Pd, t -- Pf, t) + [~3 (It - Pt) +
Vd, t
(8)
with VO,t being a white-noise error term. Although (8) is simply stated here it could be derived from a standard Keynesian aggregate demand function. 3. S o l u t i o n
Equations
Eqs. (1), (3), (4), (5), (6) and (8) form a system which solves for the six endogenous variables y, h, n, w, p and Pd for given values of p~', p~', m, I and e. The exchange rate e is parametrically given in this real sector model. Since our primary interest in this paper is the behavior of prices and output, we will use (7) and (8) to obtain first, using the terminology of Wallis [1980], the "nonobservable" reduced form equation for Pd 1 Pd, t = ~ { - a0 + [31mr + [al (1 - A) b + (A - 1) ([31 + 63) + [32] Pt, t + a2ph, t + al (1 - b)Ept + [33I~+ v t } where
(9)
D = al (1 - bA) + a2 + [32 + A ([31 + [33) > 0 Vt =
Vdt --
Vst
which is homogeneous of degree one with respect to mt, Pft, Pht, E p t and I t. All these variables exert a positive impact on Pd except for pf which has an ambiguous sign. Complete indexation removes the effect of the expected price level on Pd. The overall expected price level can be decomposed in a domestic AEpd, t, and foreign component, (1 - ~ ) E p f , t. The domestic c o m p o n e n t is internally generated by the model; that is, take the conditional expectation of both sides of (9) and solve for Epd, t:
1 See for example the studies cited in the footnote 1, p. 34. Argy and Spitiiller [1980] derive estimate such an equation, see their Eq. (10).
and
37
Inflation and Output
1 EPd, t = ~7 { - ao + 131Emt
+ [a, (l-A) + (A-l) (131+ 133)+ 132]EPf,t + a2Eph, t + [33EIt }
(10)
where D ' = a 1 (I-A) + a2 + 132+ A (131+ 13~) which again is homogeneous of degree one in nominal variables Emt, Epf, t, EPh. t and E It. Note that the sign of Epf, t remains potentially ambiguous and that Epd ' t is independent of the indexation parameter b. To obtain the "observable" reduced form for Pd, where only exogenous and expectations of exogenous variables appear on the right hand side, we replace (10) in (9) to obtain: Pd, t
=
--
ao 13t 131 Em t ~D - + -D-- (mt - Emt) + --WD
133 133 a2 + D - (It - EIt) + D---- EIt+ - ~ -
a2 (Ph,t - Eph,t) + ~ - Eph,t
+ 6 [a, (l-A) b + 132+ (A-I) (13, + 13~)] (Pf,t - Epf, t) + al (l-A) + 132+D,(A-1) (131+ 133) Epf. t "b bl
(Vs, t _ V d ' t )
(11)
Finally, substituting (9) and (10) in (1) we derive the "observable" reducedform equation for output: ao13" a'132 [a2 + a, (1 - A)] 131 D' + ~ D - - ( m r - Emt) + D' Emt
Yt -
+
a'133 - D - - (It
-
EIt)
+
[a2 + al (l-A)] 133 EIt D,
a213" a213" D (Ph,t - Eph, t) - ~ Z Eph, t 3* -
a*
D - [a~ (l-A) b - ~ - (132+ (A-l) ([3~ + 133))] (Pf, t - Epf, t) 1
+ D7 [a213" - (a 2 + a~ (1-~)) (13~+ 13~)] Epf, t + b1 (13. vd, t - 13" vs, t)
(12)
38
Michele
Fratianni
and Mustapha
Nabli
where a* = a~ (l-b) ~,+ a~ (1-~) + a2 and [3* = [32+ ~ ([3~+ 63) are the slopes of the supply and demand curves for output with respect to Po. It may surprise that money has non-neutral effects: indeed both the unexpected and the expected component of m appear on the right hand side of (12). This non-neutrality, however, stems from the fact that the real sector takes the exchange rate as parametrically given. In a fuller model the exchange rate adjusts to changes in m and the impact of Em on Pd is compensated by the impact of Em on e. It remains, however, the possibility that these two effects may not be quantitatively the same; which, in turn, implies changes in real exchange rates and hence a non-zero impact on y. Needless to say, exchange rate arrangements such as EMS facilitate the emergence of non-neutralities. 4. S h o r t a n d L o n g - R u n E f f e c t s It is instructive at this point to trace in more detail the short and long-run impacts on Pd and y of a few shocks. We begin with a devaluation in the exchange market, which occurs after a long period of fLxed rates and, therefore, is unexpected. Figure I will aid the discussion. The ss and dd curves are respectively the supply and demand schedules (see (7) and (8)). Their slopes are unambiguously positive and negative. The vertical line is the "normal" output condition which depends on a0 and the intermediate goods terms of trade Ph - Pf = PC - P?" An unexpected devaluation (i) lowers the terms of trade Pd - Pf, (ii) raises the unexpected foreign goods prices in domestic currency pf - Epf and (iii) lowers real cash balances and the real value of other impulses. Shock (i) causes the supply curve to shift to the left; shock (ii) to the right; combined they exert a depressive impact on output supplied, this impact is stronger the higher the degree of indexation 1. Shock (i) causes the demand curve to move to the right; shock (iii) to the left; combined they exert an ambiguous impact on output demand. Only if the substitution effect prevails over the real cash balance and other real impulses effects will the demand schedule shift to the right 2. To make a devaluation work the shift in demand not only has to be positive, but larger in absolute value than the shift in the supply schedule. This is the situation we have assumed in Figure 1 with the short-run equilibrium point 2. The likelihood that point 2 may be realized, as opposed to a short-run equilibrium point to the left of the normal output line, depends among other things on the degree of indexation.
' T h e shift of t h e ss c u r v e m e a s u r e d a l o n g the y axis is e q u a l to - b a 1 (1-~,) - a 2, 2 This is so if [~2 + (1 - 1) ([31 + [3s) > 0, t h e shift m e a s u r e d a l o n g t h e y axis.
39
Inflation and Output
Figure 1 - Effects of a Devaluation 1 initial position
2 short- run impact /S2s 1 3 long-run impact
=1 d 2
,,//s
\..-., \ ".,"4
,','7
",2: ./,,2
d s((
- - d
In the long run, devaluation has neutral effects provided m and I rise proportionately to the rise in e. Our model does not formally spell out the long-run conditions; for that one has to link m and I to the current account of the balance of payments, a task which is beyond the scope of this paper. Our discussion will proceed as if such a link had been made. The devaluation will produce a current account surplus, Marshall-Lerner conditions obliging, which will raise m and I and hence shift the demand curve outward. Also expectations will incorporate the higher value of e, m and I. Both Epd and Epf rise shifting the supply curve further to the left. The process comes to an end when Pt = Ept and the real cash balance and other real impulse effects have vanished. This is the situation depicted by point 3 in Figure 1. There the final goods terms of trade have returned to the initial level 1. The adjustment process from point 1 to point 2 implies a real depreciation of the domestic currency; from point 2 to point 3 a real appreciation. At point 3 the real exchange rate has returned to its initial value. Consider now the case of an unexpected increase in the price of intermediate products relative to manufactured goods, i.e. a rise in p~'- p~', with a maintained exchange rate. The supply curve shift, measured along the y axis, is proportional to -a2 (cf. point 2 in Figure 2); as the increase in p~' becomes incorporated into a permanent component the supply will further shift to the left (point 3). At this point the total impact on output is -a213"/[al (1-~,) + 15" § a2] where 15" is the slope of the demand curve measured from the horizontal axis. All along we have kept the demand curve unchanged by assuming that the outflow of money prompted by a current account deficit is sterilized and that p~' is unaffected by p~'. Since substitutability among goods rises over time, Pd approaches pf in the long run.
40
M i c h e l e F r a t i a n n i and M u s t a p h a Nabli
Figure 2 - Effects of a Rise in the Intermediate Goods Terms of Trade s2 / / s1
[ I
d
1 initial position 2 short- run impact 3 long-run impact
//
s1// s-
I
The normal output line will move to the left in response to the rise in the intermediate goods terms of trade p~ - p~' which is an external shock comparable to a tax levied by a foreign government. A further shift of the vertical line is to be expected when the capital stock adjusts to the new values of p~- p~ 1. In summary, the increase in p~' produces the familiar phenomenon of stagflation. Finally, assume a rise in the foreign goods price in foreign currency. In the model this translates into a simultaneous fall of both the final goods and intermediate goods terms of trade. Hence the comparative statics of an increase in pff is a combination of the effects graphed in Figure 1 and the converse of the effects graphed in Figure 2. 5. N o n - T r a d e d S e c t o r Even in economies as open as the ones we are considering the weight of Pd and pf in the overall price level is less than fifty percent. Food and services, our measure of non-traded goods, is too big a sector to be ignored without serious consequences in the empirical work. Denoting with P0 the log of the non-traded goods price level we redefine the overall price level as: P = ~lPd + ~2Pf + ~,3P0
(6')
Keeping Po exogenous, the supply of output now responds to a new relative price, the internal terms of trade, P0 - Pd: Yt = a0 + al ( l - b ) - a2 (P*-
(Pt -
P~') -
Ept) + (a1~'2 + a2) (Pd - Pf)
a1~,3 (Po -
Pal) + Vs
(7')
Darby [1981] discusses the implications of an oil price increase on output after the stock of capital has fully adjusted.
41
Inflation and Output
Eq. (7') replaces (7). The reduced-form for Pd with (6') becomes 1 Pd, t ----~ { - a 0 + [31mt q- [a1~2 b - ~2 ([31 + [33) + [52] Pf, t -b a 2 Ph, t + a I (l-b) EPt + 133It + ~3 [alb - ([51 + B~)] Po, t + vt }
(9')
which replaces (9). The unit homogeneity properties of Pd with respect to all nominal magnitudes are maintained. An increase in the price of non-traded goods relative to traded goods lowers manufacturing output which is our proxy of the rate of traded goods production. A rise in Po has an ambiguous effect on Pd under an indexation regime, whereas it is negative when b = 0. lII. Description of the Data The theory of Section II explains domestically produced output, domestic prices and the overall price level in terms of foreign prices, money, the exchange rate, and other impulses. To test the main implications of this theory we employ annual data for the period 1957-1980 from five European countries: Belgium (B), France (F), Germany (G), Italy (I) and the Netherlands (N). Appendix 1 provides a list of data, sources and sample period. Not knowing the outcome of our findings, we employed three different definitions of outpuP. After preliminary tests we gave preference to an index of manufacturing production. The growth rate of this series, which is very variable, displays a downward trend for the 1970s and a sharp drop in 1975. These features are common to the five countries, although to different degrees. Similarly, prices of domestic final goods were approximated by three different series (see again Appendix 1). In the end, due to data limitations we concentrated on the wholesale price index for France, Italy, the Netherlands and on domestic goods prices published by the United Nations for Belgium and Germany. However, we carried out some tests using Germany for which the three indexes are available, and found little sensitivity of the results to the type of index chosen. Apd has a distinctive upward trend in the 1970s and peaks in 1974 and again in 19802. The rate of change in the overall price level, the consumer price index, also peaks in 1974 and 1980 and displays the same trend of APd, although its variance is substantially smaller. The general impression one gets from a "visual" study of Ay, Apd and Ap is that the five countries under consideration have shared a similar cycle, an observation which is consistent with a common shock affecting these economies in roughly the same manner.
These are as indicated in Appendix 1: index of industrial production, index of manufacturing production, value added in manufacturing. 2 The 1974 values are 34.2 percent (I), 25.5 (F), 13.5 (B), 13.2 (G), and 9.1 (N); the 1980 values are 18.3 percent (1), 8.4 (F), 6.07 (B), 7.7 (G) and 7.8 (N).
42
Michele F r a t i a n n i and M u s t a p h a Nabli
Moving from endogenous to exogenous variables, we note that the price of foreign goods measured in dollars (p~) displays a movement which resembles Apd with peaks occurring in 1974 and in 1980: Ap~'has pronounced autoregressive characteristics. Petroleum prices in dollars (p~ decline from 1957 to 1970, then rise dramatically in 1974, and less so, in 1980. The intermediate goods terms of trade, p~' - p~, are dominated by the behavior of p*. The exchange rate, the domestic price of the dollar, has the distinctive features of a random walk: the past history of Ae seems to yield no information concerning its future course. The final goods terms of trade, Pd - Pf, appear volatile. Germany, Belgium and the Netherlands exhibit very similar variations in their terms of trade: strong peaks in 1964, 1974 and 1977-1978, and sharp drops in 1961, 1968, 1975 and 1980. France and Italy, show on the other hand a different pattern: peaks in 1964 and 1974, and troughs in 1968/69, 1975/76 and 1980. The five countries share a sharp drop in their terms of trade in 1980, although we detect no strong trend. The money stock is defined exclusive of time deposits and is measured as yearly averages; its growth rate is highly volatile. Our variable I, impulses other than money, consists of the fiscal impulse, AF, and the growth rate of exports at current prices. The fiscal impulse was calculated so as to eliminate the induced part due to changes in income, i.e. AF
= { A G - [AT - (T/GDP)_, A G D P ]
}/GDP_ 1
GDP G T
= gross domestic product at current prices = nominal government expenditures = nominal tax revenues
IV. Estimation Procedure and Findings Our estimation procedure is to generate at first the expected value of Pd and p from the underlying variables of the model. This process permits us to transform the unobserved endogenous ~Pd and ~ in "observable" variables Epd , Ep. The rational expectations estimates Epd and Ep and the unexpected underlying exogenous variables will be employed to generate Pd and ~, i.e. the estimates of Pd and p. Finally, using Epd, Ep, Pd and ~ we estimate the output equation (7') which will yield classical two-stage estimates of the parameters. Thus, estimation of the supply of output equation is based on limited information methods for structural equations estimation. Only in the estimation of the price equations do we use the overall structure of the model and the rational expectations hypothesis. Since we do not impose all resulting constraints in the actual estimation we test rational expectations in the weak sense: the estimates of the coefficients are consistent with rational expecta-
Inflation and Output
43
tions but we do not provide positive evidence for their existence. On this point see Wallis [1980, pp. 66-69] and Wickens [1982, p. 59] 1. 1. R a t i o n a l E x p e c t a t i o n s a n d t h e I n f l a t i o n R a t e Eq. (10) provides the basis for estimating the expected domestic price level. In first differences it can be rewritten as: EApd = f (EAZ)
(10')
where EAZ is a vector consisting of EAm, EApf, EAph, EAP0 and EAI. EAZ is quantified by the systematic component of univariate time series ARIMA models. The non-white noise part of the models yields an estimate of E-'~Z. The expected rate of domestic price inflation is obtained from the regression: APd = A0 + "~1 E - ~ + error
(13)
where EApd = Apd - error A similar procedure holds for EAp. Recalling that: EAp = hI EApa + ~2 EApf + ~3 EAp0
(14)
and using Off) we derive: EAp = ~zf (EAZ) + h2EApf + h3EApo Since EApf and EAp0 are included in the vector EAZ, we obtain EAp = g (EAZ)
(15)
where g depends on f, hi, ~,2 and ~,~. Using the ARIMA models for Z we can transform the non-observable form (15) into a testable equation of the type (13): Ap = Bo + I31 EA"-Z+ error
(16)
We refer the reader to Appendix 2 for the estimates of EAZ. Here a few general comments suffice. EArn is best measured by an AR (1) process for three countries; the hypothesis of Am being white noise for Germany and the Netherlands could not be reiected. For the other countries there is a slight first-order autoregrressive component. Ae, Ap~ and AX are also white noise 2. Ap~follows an AR (3) and Ap0 an AR (1) scheme. Finally, no systematic component could be detected in the fiscal impulse a. These findings restrict the Note that the errors-in-variables method proposed by MacCallum [1976] cannot be applied in our case because we have Pt on both sides of the equation. 2 Korteweg [1979] finds that the volume of world imports (X/P)* follows a MA(2) model. a This evidence contrasts with the findings of Fratianni [1979] and Korteweg [1979] who define the fiscal impulse in a more detailed manner (i.e. they purge the series of other induced components). Fratianni obtains that AF is a MA(1) process with a coefficient of .8 and Korteweg obtains that A(6F) is a MA(1) scheme with a coefficient of .75.
44
M i c h e l e F r a t i a n n i and M u s t a p h a Nabli
vector EA'Z to EA-"m,EA~'p~and EAP0. The estimates of (13) and (16) are reported in Table 1. The results show that the expected part of the inflation rate is relatively small and money seldom turns out to be significant 1. On the whole, estimates for EAp are better than for EApd, where "better" is judged on standard statistical criteria. This is mainly due to Ap0 which is a component of Ap. A favorable outcome is that homogeneity conditions are satisfied in many instances. The estimates for EApd and EAp of Table 1 are employed to explain the current rate of inflation. The procedure followed is that implied by (11): we Table 1 - Rational Expectations Equations for Expected Inflation Rates
1959-1980 De-
Coun- pendent try Variable
C
EAm
EAp~'
EAP0
~2
SE
p
DW
0.269 (1.80) 0.226 (2.59)
-0.073 (0.24) -0.582 (3.31)
0.28
0.028
0.033 ] 1.55
0.71
0.016
0.046 I 1.54
0.353 (1.18) 0.364 (3.93)
0.756 (0.61) 1.025 (2.66)
-I t.004
0.064
0.052 12.43
0.61
0.020
0.064 [2.00
0.124 (1.03) 0.073 (0.74)
0.954 (2.65) 0.894 (3.02)
0.41
0.023
0.035 ] 1.81
0.47
0.019
0.051 12.20
0.467 (1.21) 0.170 (1.16)
0.855 (2.19) 0.892 (6.00)
0.47
0.064
0.075 12.33
0.83
0.024
0.077 12.05
0.236 (1.36)
1.245 (1.41)
0.23
0.034
0.0251 1.62
0.123 (2.06)
0.728 I (2.39)
0.53
0.011
0.03511.57
I
I
I
I I
I I
I I
Note: All variables are in natural logarithms. - Numbers in parentheses under each coefficient are Student t-values. - Statistical indicators are: ~2: adjusted coefficient of determination; SE: standard error of equation; p: mean value of dependent variable; - DW: DurbinWatson statistic. - Country symbols are B = Belgium, F = France, N = Netherlands, I = Italy, G = Germany.
For Germany and the Netherlands Earn entered as AR(1) with virtually no explanatory power. Moreover, some experiments show that using M2 improves the forecast of money and expected prices, but does not improve the explanation of unexpected inflation and output supply functions.
Inflation and Output
45
regress APd - EA"~d and fip - ~ p on the unexpected value of the model's determinants, i.e. AZ - EAZ. The estimates of these regressions are presented in Table 2. All unanticipated variables, except for money, affect the unanticipatTable 2 - Unexpected Inflation Rates Equations 1959-1980 Coun- Dependent try Variable
C
{Am-EArn Ap~'+Ae -EAp~' AP~176
AX
~2
SE
DW
!
hpd-~Pd
-0.002 (0.29) 0.008 (2.18)
0.09,~ (0.90) 0.095 (1.92)
0.330 (3.63) 0.199 (4.51)
0.691 (3.52) 0.637 (6.70)
0.088 0.69{0.01~ 1,11 (1.53) -0.035 0.78[0.007 1.37 (1.28)
APd-EAPd -0.061 (3.16) •p -E--'~p - 0.005 (0.73)
0.25G ( 1.21) - 0.002 (0.03)
0.364 (2.44) 0.103 (1.87)
0.144 (0.49) 0.360 (3.31)
0.452 0.64{0.03~ 1.44 (3.75) 0.043 0.49[0.01Z 1.77 (0.97)
~,pd-E--"~pd - 0.001 (0.09) lap -E~p 0.001 (0.57)
- 0.022 (0.16) 0.011 (0.53)
0.112 (0.91) 0.018 (0,91)
0.396 (1.32) 0.946 (!9.63)
Ap -EAp
]
A Apd-EApd
Ap -EAD
Z
q
-0.013
0.073
(0.52) (0.32) 0.011 -0.097 (1.35)(1.24)
APd-EAPd - 0,026 (1.88) Ap - ~ p - 0.0006 (0,18)
0.109 (0.51) 0,001 (0.03)
0.722
0.466
(3.42) 0.275 (3.79)
(1.42) 0.500 14.44)
0.148 (1.10) 0.043 (1.34)
1.059 12.40) 0,773 17.40)
I
I I
0.038 (0.44) - 0.005 (0.39) 0.012
(0.08) -0.094 (1.77) 0,308 (2.92) 0.021 (0.85)
I
0.10]0.021 1.91
I
0.96{i0.003 2.59 ~).62[ D.036
1.38
I
3.691D.013 1.99
/
3.42[ 9.024 1.47
/
3.72 [ 9.005 1.62
I
Note: See Table 1.
ed rates of inflation. The model explains a large fraction of the latter variable. In sum, our evidence is consistent with the notion that the larger portion of the rate of inflation is unanticipated which can be traced back to unanticipated changes in foreign prices, exports and nontraded goods prices. Unanticipated m o n e y has a tenuous impact on the unanticipated inflation rate. This does not rule out that unexpected m o n e y growth influences APd and Ap through Apo. 2. E s t i m a t e s
for Output
Having estimates for Ap - EAp and Pd we are n o w in a position to fit the data to (7') so as to simultaneously incorporate the formation of rational
46
Michele Fratianni and Mustapha Nabli
expectations and the endogeneity of Pd" The estimates using (7') in level are shown in Table 3. We have also estimated output equations in growth rates but since their results were generally inferior to their level counterparts they are not reported here. From Table 3 we can see that the coefficient of the Table 3 - Supply of Output Equations (2 SLS and Rational Expectations) 1959-1980 Country
C - 147.09 (8.15)
Ap-EAp
0.076 (8.40) ]
0.028
0.096
(0.38) 0.579 (2.45)
-
0,0341 0.765 (2.72) { (1.36)
62.58 (2.53)
- 95.75 (7.80)
0.050{ (8.20) {
1.200 (2.05)
- 74.29
0.0391 (4.53) I
1.688 (1.66)
(3.32) See Table
1.
-
0.141
(0.39) - 0.321
SE
p
DW
P0-Pd
0.088 (4.27)
- 1.207 (2.92)
0.99{0.031[4.421 1.80
0.130 (4.84)
-0.180 (0.83)
0.99[0.031[4.390 1.75
-0.116 (3.76)
1.029 (2.34)
0.98]0.043]4.364 1.67
0.033 (0.42)
0.834 (2.70)
0.9810.04814.407{1.36
0.104 (1.92)
0.480 (1.02)
0.9710.04314.441
-
-
(0.80) 0.305 (1.12)
~2
Ph-Pf
l~d-Pf
(0.03)
114.81 0.0601 1.346 (10.10) (10.51) I (2.01)
-
Note:
A
t
-
1 . 7 0
t is a time trend (t = 1959, ..., 1980).
rate of inflation comes out highly significant for France and Italy, but marginally significant for Germany and the Netherlands. It is not statistically different from zero for Belgium, a country with virtually complete indexation. Italy apart, both the final goods and indermediate goods terms of trade exert the impact predicted by theory. The evidence concerning the internal terms of trade is more mixed: strong and conforming to theory for Belgium, zero for France and opposed to what theory predicts for Germany and the Netherlands. Despite the noted weaknesses of specific empirical results, we assess that for four countries the overall evidence is favorable towards an hypothesis which has stressed the primary role of relative prices, including the unexpected rate of inflation, in explaining the cycle of manufacturing output. It follows that the traditional Lucas-supply equation does not do as well as a model that, in addition to misperceptions of the price level, includes internal and external relative prices as well as wage indexation. The results of Table 3 bear on this ' Pd = AP-"f'~E6Pd + EAp""~+ Pd-1 Notice that we actually carry out the estimation in two steps, instead of a one-step instrumental variable procedure. Therefore, standard errors of estimates are not strictly correct.
Inflation a n d O u t p u t
47
point: two out of three relative prices are highly significant for Belgium, France and the Netherlands, whereas one out of three is significant for Germany. The evidence for Italy, on the other hand, is more consistent with a fixed-wage hypothesis than with the modified Lucas-supply curve 1. V. Conclusions
This paper has developed a model of the real sector of a small open economy. Domestically produced output, domestic prices and the overall price level are explained in terms of foreign prices, money, the fiscal impulse, exports, and the exchange rate. The model incorporates rational expectations and derives a modified Lucas-type supply function which depends not only on the unexpected rate of change of the overall price level, but also on the final goods, intermediate goods and internal terms of trade. We used annual data from 1957 to 1980 for five European countries to test the major implications of the model. Our findings indicate that a large component of the inflation rate has not been anticipated and that unanticipated rates of inflation can be traced back to unanticipated changes in exports, foreign prices in dollars and changes in the exchange rate which are altogether unpredictable. These outcomes are in contrast with earlier evidence which found a larger expected component in the rate of change of the overall price level. In this sense our findings about the rate of inflation come close to our understanding of changes in the exchange rate. For four out of the five countries investigated the behavior of output supports the hypothesis that internal and external relative prices play a significant role, in addition to the traditional Lucas price-level misperception term.
Eqs. (1), (3), (4) a n d (6') yield the fixed-wage output e q u a t i o n Y = a0 + al (P - ~ ) + (a1~'2 + a2) (Pd - Pf) - a2 (PI~ - Pi~) - al~'3(P0 - Pd) 2 SLS estimates for the period 1957-1980 yield for Italy: rio = - 276.9 (5.17); time t r e n d = 0.142 (5.26); 0"1 = 1.46 (3.72); a 1 ~ 2 = 0.59 (1.22); "~2 = 0.254 (1.95); a - ~ 3 = 0.92 (1.36); SE = 0.045; p = 4.338; D W = 1.27.
Michele Fratianni and Mustapha Nabli
48
Appendix 1 List of Variables and Sources Used in the Empirical Work (Yearly Data) C o u n t r i e s covered: B e l g i u m (B), F r a n c e (F), G e r m a n y (G), Italy (I), N e t h e r l a n d s (N) Symbol Period Y
Pd
Description
Source
57-80
Index of industrial production
IMF, International Financial Statistics (IFS), Country Tables, :~: 66
57-80
Index of industrial productionmanufacturing
OECD, Main Economic Indicators
61-79
Value added in manufacturing
OECD, National Accounts of OECD Countries, 1950-1979, Table 2b
57-80
Wholesale price index (F, I, N)
IMF, IFS, Country Tables, :~z 63
57-80
Domestic goods prices (B, G)
UN, Monthly Bulletin
61-79
Value added in manuf., deflator
OECD, National Accounts of OECD Countries, Tables 2a, 2b
P
57-80
Consumer price index
IMF, IFS, Country Tables, : ~ 64
Pm
57-80
CPI: goods less food
Po
!57-80
P~
57-80
World export index for manufactured goods (in U.S. dollars)
UN, Monthly Bulletin, Special Table C
P~
57-80
Saudi Arabia petroleum price (U.S. S/Barrel)
IME IFS, Commodity Prices Table, line 76aa
W
57-80
Wages: hourly earnings
IMF, IFS, Country Tables, :~: 65
E
57-80
Exchange rate, spot, period average
IME IFS, Country Tables, line rf
M
57-80
Exclusive money stock (yearly average)
IMF, IFS, Country Tables, line 34
OECD, Consumer Price Indices: Sources and Methods and 'Historical Series, March 1980; completed when necessary
Food and services consumer price index, calculated as Po = [P - (•lVd + X2 Pf)]/h3 = [P - ~,oPm]/(1-Xo)
Inflation and Output Symbol JPeriod G
57-80
Description
49 Source
Total governmentexpenditures OECD, National Accounts of OECD Countries, Vol. II, Table 9, Lines 12 and 23
T
57-80
Total government revenues
r
57-80
Total transfer payments of general government/ nominal GDP
G. Warren Nutter, Growth of Government in the West. American Enterprise Institute, 1978, Table B-l, period 1950-69 OECD, National Accounts of OECD Countries,
Table 9, period 1970-80 (::~17+ 18+ 19+20+21) X
57-80
GDP 57-80
Value of exports
IMF, IFS, Country Tables, line 70
Gross domestic product at current prices (purchasers' values)
OECD, National Accounts of OECD Countn'es, Vol. I, June 1982
Appendix 2 ARIMA Processes for Forecasting Exogenous Variables Standard Box-Jenkins techniques (using an IBM program) were used to identify and estimate ARIMA models to forecast the exogenous variables. The number of observations was necessarily limited on the basis of annual data, 1957-1980. In all cases first order differencing of the variables (in natural logarithms) was necessary to achieve stationarity of the series. 1. M o n e y S t o c k The variable used is M1, as a yearly average. Through analysis of autocorrelation and partial autocorrelation coefficients it appeared that: - for Germany and the Netherlands, a white-noise process for Am, around a constant growth rate of money, could not be rejected; - for the other three countries some evidence but which was not very strong appeared in favor of an AR(1) process. Fitting AR(1) models for all countries we obtained the following estimates which were used to generate EAm, even though, as expected for Germany and the Netherlands the explanatory power is almost nil: Weltwirtschaftliches Archiv Bd. CXXI.
4
50
Michele Fratianni and Mustapha Nabli
Germany: (t-values)
~"mt =
0.091 - 0.107 Amt_1 (7.04) (0.74)
~2 = _ 0.02
Netherlands:
A~ t :
0.066 + 0.240 Amt_ 1 (3.14) (1.09)
~2=
0.01
France:
Am t =
0.066 + 0.316 Amt_ 1 (3.04) (1.51)
R2 =
0.06
Belgium:
Am-~t=
0.037 + 0.388 AmH (2.40) (1.80)
"~2=
0.10
Italy:
Am"~=
0.103 + 0.322 Amt_1 (3.35) (1.62)
~2=
0.07
2. F o r e i g n P r i c e The foreign price in domestic currency (in logs) is defined as: pf = p~ + e. Attempts to estimate ARIMA models for pf directly did not yield any results. So we decided to model p~' and e separately. For the exchange rate (domestic currency price of the dollar), Ae exhibits the characteristics of white noise; it is constant up to 1971 and highly volatile during the seventies. As for Ap~ an AR(3) model was identified and estimated, using data for the period 1957-1980: Ap~'= 0.012 + 1.118 Ap~_I - 0.819 Ap~_2 +0.552 Ap~_3 (1.26) (5.90) (3.20) (2.80) 3. I n t e r m e d i a t e
~2 = 0.69
Goods Price
The variable used is the dollar price of Saudi oil. The analysis of the autocorrelation and partial autocorrelation coefficients did not suggest any particular model, and the coefficients were not significant. Attempts to fit AR(1) or MA(1) models did not yield positive results, s o Aph is treated as white noise. 4. E x p o r t s As for the price of oil the analysis of the series of export values did not yield any good ARIMA model, so we could not reject a white-noise process. 5. O t h e r G o o d s P r i c e s For the price index of food and services P0, an AR(1) was found satisfactory in general: Germany:
Ap0 =
0.013 + 0.641 Apot_1 (2.10) (3.76)
~2 =
0.38
51
Inflation and Output A
Netherlands: AP0t =
0.017 + 0.699 Ap0t_ 1 (2.01) (4.72)
~2 = 0.50
France:
APot =
0.044 + 0.341 APot_~ (3.27) (2.01)
~ 2 = 0.13
Belgium:
AP0t =
0.010 + 0.829 APot_l (1.48) (7.30)
R 2 = 0.71
Italy:
~Pot =
0.011 + 0.914 APot_l (1.12) (8.24)
R2 = 0.76
References Argy, Victor, "A Comment on the Korteweg, Fratianni and Fourgans Papers". In: Karl Brunner and Allan H. Meltzer (Eds.), The Problem o/Inflation. Carnegie-Rochester Conference Series on Public Policy, Vol. 8. Amsterdam 1978, pp. 181-191. -, and Erich Spitiiiler, "The Joint Determinations of Changes in Output and Prices in the Seven Main Industrial Countries". Weltwirtschaflliches Archiv, Vol. 116, 1980, pp. 87-113.
Bruno, Michael, and Jeffrey Sachs, Macro-Economic Adjustment with Import Price Shocks. Real and Monetary Aspects. Institute for International Economic Studies, Stockholm 1979. Darhy, Michael R,, The Real Price of Oil and the 1970s World Inflation. NBER Working Paper No. 629. New York 1981. F,ourgans, Andre, "Inflation and Output Growth: The French Experience, 1960-1975". In: Karl Brunner and Allan H. Meltzer (Eds.), The Problem of Inflation. Carnegie-Rochester Conference Series on Public Policy, Vol. 8. Amsterdam 1978, pp. 81-140. Fratianni, Michele, "Inflation and Unanticipated Changes in Output in Italy". In" Karl Brunner and Allan H. Meltzer (Eds.), The Problem of Inflation. Carnegie-Rochester Conference Series on Public Policy, Vol. 8. Amsterdam 1978, pp. 141-180. -, "Money, Wages and Prices in Italy". Banca Nazionale del Lavoro Quarterly Review, Vol. 33, 1980, pp. 515-537.
Korteweg, Pieter, "The Economics of Inflation and Output Fluctuations in the Netherlands, 1954-1975: A Test of Some Implications of the Dominant Impulse-cum-Rational Expectations Hypothesis". In: Karl Brunner and Allan H. Meltzer (Eds.), The Problem of Inflation. Carnegie-Rochester Conference Series on Public Policy, Vol. 8. Amsterdam 1978, pp. 17-68. -, "The Economics of Stagflation: Theory and Dutch Evidence". Zeitschrift fiir die Gesamte Staatswissenschaft, Vot. 135, 1979, pp. 553-583. Leiderman, Leonardo, "Monetary Accomodation and the Variability of Output, Prices, and Exchange Rates". In: Karl Brunner and Allan H. Meltzer (Eds.), Monetary Regimes and Protectionism. Carnegie-Rochester Conference Series on Public Policy, Vol. 16. Amsterdam 1982, pp. 47-85. Lucas, Robert E., "Some International Evidence on the Output-Inflation Tradeoffs". The American Economic Review, Vol. 63, 1973, pp. 326-334.
MaeCallum, Bennett T., "Rational Expectations and the Estimation of Econometric Models: An Alternative Procedure". International Economic Review, Vol. 17, 1976, pp. 484-490. Muth, John F., "Rational Expectations and the Theory of Price Movements". Econometrica, ~)ol. 29, 1961, pp. 315-335.
4*
52
Michele Fratianni and Mustapha Nabli Inflation and Output
Romanis Braun, Anne, "Indexation of Wages and Salaries in Developed Economies". IMF Staff Papers, Vol. 23, 1976, pp. 226-271. Wallis, Kenneth E, "Econometric Implications of the Rational Expectations Hypothesis". Econometrica, Vol. 48, 1980, pp. 49-75. Wiekens, Michael R., "The Efficient Estimation of Econometric Models with Rational Expectations.". The Review of Economic Studies, Vol. 49, 1982, pp. 55-67.
Z u s a m m e n f a s s u n g : Inflation und Produktion bei rationalen Erwartungen in offenen Volkswirtschaften. - Der Aufsatz entwickelt ein Modell fiir den Giitersektor einer kleinen offenen Volkswirtschaft, die Fertigwaren exportiert und sowohl Fertigwaren als auch Rohstoffe, die im Produktionsprozeg verwendet werden, importiert. Die L6hne sind in unterschiedlichem Mage indexiert, und die Wirtschaftssubjekte verhalten sich rational im Sinne yon Muth. Das ModeU wird getestet mit Hilfe yon Jahresdaten aus fiinf EG-L~indern fiir den Zeitraum yon 1957 his 1980. Die Hauptergebnisse zeigen, daf~ ein relativ groger Tell der Inflationsrate nicht antizipiert wird und dab die Lucas'sche Fehlwahrnehmung des Preisniveaus flit das Produktionsverhalten eine geringere Rolle spielt als die relativen Preis~inderungen.
R6sum6: Inflation et production aux expectatives rationnelles en 6conomies ouvertes. Dans cet article les auteurs d6veloppent un module du secteur r6el d'une petite 6conomie ouverte qui exporte des biens manufacturiers et importe des biens manufacturiers ainsi que des mati~res premieres utilis6es darts la production. Les salari6s au march6 du travail jouissent des plusieurs degr6s de l'indexation au niveau de prix et les agents 6conomiques se comportent rationnellement au sens de Muth. Le module est test6 avec des donn6es annuelles de cinq pays membres de la CEE pour la p6riode 1957-1980. Les r6sultats principaux d6montrent qu'une relativement grande part du taux d'inflation n'6tait pas anticip6e et que la m6sperception du niveau de prix ~ la Lucas jouait un r61e peu important pour la production en relation aux changements de prix relatif. "
R e s u m e n : Inflaci6n y producci6n con expectativas racionales en economias abiertas. En este trabajo se construye un modelo del sector real de una pequefia economia abierta que exporta bienes manufacturados e importa manufacturas y materias primas, estas tiltimas siendo insumos para la producci6n. En el mercado laboral los trabajadores gozan de un sistema diferenciado de indexaci6n y los agentes econ6micos se comportan racionalmente en el sentido de Muth. El modeto es utilizado en un test empirico con datos de cinco paises miembros de la CEE para el periodo 1957-1980. Los resultados demuestran que una parte relativamente importante de la tasa de inflaci6n no fu6 anticipada y que la percepci6n sesgada del nivel de precios en el sentido de Lucas jug6 un papel menor en el comportamiento de la producci6n que el que jugaron las variaciones de los precios relativos.
