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Exogeneity in a small open economy: Canada
Economics Letters 5 (1980) 301-304 0 North-Holland Publishing Company
EXOGENEITY
IN A SMALL OPEN ECONOMY: Canada *
Jack SELODY Bank of Canada, Ottawa, Ont., Canada KIA OG9 Received
21 April 1980
The results of conducting omy data set are reported
pairwise &anger-Sims and assessed.
exogeneity
tests on a typical
small open econ-
This paper reports the results of using Granger-Sims type methodology to identify those economic aggregates which can be adequately characterized as exogenous in small macroeconomic models. The purpose is to provide direction to the specification of descriptive models of the open economy. The need for such direction is evidenced by the proliferation of alternative small open economy models, each with a slightly different specification as to which macro-aggregates are exogenous. The particular test used is that suggested by Hsiao (1979). Consider the bivariate econometric model:
where x and y are jointly covariance stationary and br r (0) = bzz(0) = 1. This model displays a Granger causal ordering (x is statistically exogenous in the first equation) if b2 r (15) = 0 and VI (t) and V2(s) are uncorrelated for all time period t and s [Sims (1977)]. The novelty of Hsiao’s approach is that (1) IS estimated by a full information maximum likelihood technique and that the choice of the order of bii(Z,) is not arbitrary; it is chosen according to Akaike’s (1969) minimum final prediction error criterion, a procedure which balances the bias resulting from an adequately short lag against the increased variance of an unnecessarily long lag. An appropriate choice of * This paper draws on my doctoral dissertation at the University of Western Ontario. I am indebted to my advisors J.M. Parkin, D.E.W. Laidler, and R. Boyer. The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. 301
302
J. Selody / Exogeneity in a small open economy
the order of the lag polynomial is important since exogeneity tests tend to be sensitive to this choice. As Hsiao’s test for exogeneity requires stationary data all series are transformed by logarithms and then first differenced. In addition it appeared necessary to transform the U.S. monetary base, and the Canadian and U.S. inflation rates further by the prefilters (1 - 0.68 I,), (1 - 0.82 L), and (1 - 0.51 L) respectively. These filters were obtained by fitting a first-order autoregressive process. The period of study is 1961 : 3 to 1977 : 3. Complete details of data construction are available in Selody (1979). The pairwise nature of the test procedure suggests that a test of model adequacy is useful. Towards this end the estimates of the residuals were checked for evidence of cross correlation: a significant cross correlation (measured against the approximate two standard deviation benchmark of 2/n”’ where n is the number of observations) at any lead or lag within 12 quarters of zero is interpreted as an indication of model inadequacy. Model inadequacy may originate either from (i) instantaneous Granger causality - the restriction b r2 = hzI = 0 is imposed and hence any within quarter simultaneity should show up in the residuals - or from (ii) excluded Granger causal influences - any excluded influence which is not adequately captured by the model of the past behavior of x andy will show up in the residuals and can distort the test results. The results of pairwise likelihood ratio exogeneity tests are summarized in tables 1 and 2, along with some typical hypothesized relationships between the variables. A number of points emerge: (1) Approximately half of the likelihood ratio tests are free from significant residual cross correlations; in these cases a bivariate test appears adequate. For the other cases, those series most typically identified as endogenous appear to suffer most from residual cross correlation. This tends to support the contention that excluded innovations are pervasive. Furthermore, tests involving U.S. variables which clearly exhibit internal Granger causal relationships also suffer from pervasive residual cross correlations. In these cases the adequacy of bivariate tests is clearly in doubt. (2) On the basis of these tests no series can be shown to be exogenous to all other series considered. This finding has important implications for interpreting the identifying restrictions placed on econometric models. It also suggests that ordering variables by relative exogeneity may be an important concept, that is, the phrase ‘x is less endogenous than y’ may be meaningful. (3) There appears to be a number of counterintuitive results, at least if interpreted within the context of a typical small open economy model. However, virtually all of the counterintuitive results are associated with model inadequacy as indicated by the presence of significant residual cross correlations. (4) Although difficult to tell because of excluded innovations, the Canadian economy appears not to be completely insulated from U.S. economic events: this
YC
3-3 3-3 2-3 3-3* 3-2 2-o* 2-3* 3-2* 2-o* 2-o* 2-3* 2-3*
PC
3-3* 3-3* 3-l* 2-3* 3-3 3-2 2-o 2-3* 3-o 2-1* 2-1* 2-o* 221*
Y-series
hypothesis
3-3* 2-3 3-3 3-3* 2-2 2-2 3-o* 2-o 2-1* 2-3* 2-3*
m
from a pairwise
2-3* 3-3 3-3 2-o* 2-2 3-2* 2-o 2-l=+ 2-o 2-2
exch
likelihood
I-3 3-2* o-3 o-2 l-2* o-o o-1* o-o o-o*
ef
3-3 2-o* 2-3 3-2 2-1* 2-3* 2-o 2-2*
rc
ratio exogeneity
2-2* 2-2 3-3* 2-o* 2-o 2-2* 2-2
res
test. a
o-o 1-O o-2* o-2* o-o O-2”
rexp
1-o* o-o* o-1 * o-o O-3”
rtY
2-o 2-o 2-o 2-o
de
a 0 (X - Y) mutual exogeneity. 2 (Y + X) X endogenous Y exogenous. 2 (X + Y) X exogenous Y endogenous. asterisk denotes evidence of significant residual cross correlation. The first number is the typical hypothesized the test result.
PUS Yus hus rus
rv dc
rc res rexp
ef
Yc m exch
X-series
Table 1 Most acceptable
2-o* 3-3
YUs
l-3
hus
3 (X ++ Y) mutual endogeneity. An relationship, the second number is
3-1* 2-2 3-2*
Pus
z
2
S 3 2
i
;;; : % 2 . . G s
Fa 3 8
S
J. Selody / Exogeneity in a small open economy
304 Table 2 Classification
of variables
on basis of exogeneity.
Test results.
Relatively endogenous Canadian real income @c) Canadian price level (pc) Canadian 90 day interest rate (YC) Canadian-U.S. exchange rate (exch) Canadian money supply - narrowly defined (m) Canadian holdings of international reserves (res) Forward exchange rate - 90 days (efl Canadian domestic credit component of monetary
base (dc)
Relatively exogenous Canadian real government expenditure Canadian real tax receipts (rt) U.S. real income @us) U.S. price level (pus) U.S. monetary base @us) U.S. 90 day interest rate @us)
(rexp)
evidence supports the contention that the Canadian economy is ‘open’. There also appears to be some evidence that Canadian economic fluctuations feedback onto U.S. fluctuations (although it should be re-iterated that excluded innovations may be distorting these results). (5) The money supply, the exchange rate, and international reserves are endogenous to virtually every variable considered. Macroeconomic models of the Canadian economy that treat these variables as exogenous are making identifying restrictions that are not supported by this evidence. (6) Fiscal policy instruments tend to be among the ‘most exogenous’ of those variables tested. It appears that if any of the variables tested must be exogenous (to help identify a small model), exogenizing these variables appears to be a good place to start.
References Akaike, Hirotugu, 1969, Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics 21, 243-247. Hsiao, Cheng, 1979, Autoregressive modeling of Canadian money and income data, Journal of the American Statistical Association 74, 553-560. Selody, Jack, 1979, A monetary model of Canadian price and output fluctuations, Unpublished Ph.D. thesis (University of Western Ontario, London, Ont.). Sims, C.A., 1977, Exogeneity and causal ordering in macroeconomic models, in: New methods in business cycle research: Proceedings from a Conference (Federal Reserve Bank of Minneapolis, Minneapolis, MN).
EXOGENEITY
IN A SMALL OPEN ECONOMY: Canada *
Jack SELODY Bank of Canada, Ottawa, Ont., Canada KIA OG9 Received
21 April 1980
The results of conducting omy data set are reported
pairwise &anger-Sims and assessed.
exogeneity
tests on a typical
small open econ-
This paper reports the results of using Granger-Sims type methodology to identify those economic aggregates which can be adequately characterized as exogenous in small macroeconomic models. The purpose is to provide direction to the specification of descriptive models of the open economy. The need for such direction is evidenced by the proliferation of alternative small open economy models, each with a slightly different specification as to which macro-aggregates are exogenous. The particular test used is that suggested by Hsiao (1979). Consider the bivariate econometric model:
where x and y are jointly covariance stationary and br r (0) = bzz(0) = 1. This model displays a Granger causal ordering (x is statistically exogenous in the first equation) if b2 r (15) = 0 and VI (t) and V2(s) are uncorrelated for all time period t and s [Sims (1977)]. The novelty of Hsiao’s approach is that (1) IS estimated by a full information maximum likelihood technique and that the choice of the order of bii(Z,) is not arbitrary; it is chosen according to Akaike’s (1969) minimum final prediction error criterion, a procedure which balances the bias resulting from an adequately short lag against the increased variance of an unnecessarily long lag. An appropriate choice of * This paper draws on my doctoral dissertation at the University of Western Ontario. I am indebted to my advisors J.M. Parkin, D.E.W. Laidler, and R. Boyer. The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. 301
302
J. Selody / Exogeneity in a small open economy
the order of the lag polynomial is important since exogeneity tests tend to be sensitive to this choice. As Hsiao’s test for exogeneity requires stationary data all series are transformed by logarithms and then first differenced. In addition it appeared necessary to transform the U.S. monetary base, and the Canadian and U.S. inflation rates further by the prefilters (1 - 0.68 I,), (1 - 0.82 L), and (1 - 0.51 L) respectively. These filters were obtained by fitting a first-order autoregressive process. The period of study is 1961 : 3 to 1977 : 3. Complete details of data construction are available in Selody (1979). The pairwise nature of the test procedure suggests that a test of model adequacy is useful. Towards this end the estimates of the residuals were checked for evidence of cross correlation: a significant cross correlation (measured against the approximate two standard deviation benchmark of 2/n”’ where n is the number of observations) at any lead or lag within 12 quarters of zero is interpreted as an indication of model inadequacy. Model inadequacy may originate either from (i) instantaneous Granger causality - the restriction b r2 = hzI = 0 is imposed and hence any within quarter simultaneity should show up in the residuals - or from (ii) excluded Granger causal influences - any excluded influence which is not adequately captured by the model of the past behavior of x andy will show up in the residuals and can distort the test results. The results of pairwise likelihood ratio exogeneity tests are summarized in tables 1 and 2, along with some typical hypothesized relationships between the variables. A number of points emerge: (1) Approximately half of the likelihood ratio tests are free from significant residual cross correlations; in these cases a bivariate test appears adequate. For the other cases, those series most typically identified as endogenous appear to suffer most from residual cross correlation. This tends to support the contention that excluded innovations are pervasive. Furthermore, tests involving U.S. variables which clearly exhibit internal Granger causal relationships also suffer from pervasive residual cross correlations. In these cases the adequacy of bivariate tests is clearly in doubt. (2) On the basis of these tests no series can be shown to be exogenous to all other series considered. This finding has important implications for interpreting the identifying restrictions placed on econometric models. It also suggests that ordering variables by relative exogeneity may be an important concept, that is, the phrase ‘x is less endogenous than y’ may be meaningful. (3) There appears to be a number of counterintuitive results, at least if interpreted within the context of a typical small open economy model. However, virtually all of the counterintuitive results are associated with model inadequacy as indicated by the presence of significant residual cross correlations. (4) Although difficult to tell because of excluded innovations, the Canadian economy appears not to be completely insulated from U.S. economic events: this
YC
3-3 3-3 2-3 3-3* 3-2 2-o* 2-3* 3-2* 2-o* 2-o* 2-3* 2-3*
PC
3-3* 3-3* 3-l* 2-3* 3-3 3-2 2-o 2-3* 3-o 2-1* 2-1* 2-o* 221*
Y-series
hypothesis
3-3* 2-3 3-3 3-3* 2-2 2-2 3-o* 2-o 2-1* 2-3* 2-3*
m
from a pairwise
2-3* 3-3 3-3 2-o* 2-2 3-2* 2-o 2-l=+ 2-o 2-2
exch
likelihood
I-3 3-2* o-3 o-2 l-2* o-o o-1* o-o o-o*
ef
3-3 2-o* 2-3 3-2 2-1* 2-3* 2-o 2-2*
rc
ratio exogeneity
2-2* 2-2 3-3* 2-o* 2-o 2-2* 2-2
res
test. a
o-o 1-O o-2* o-2* o-o O-2”
rexp
1-o* o-o* o-1 * o-o O-3”
rtY
2-o 2-o 2-o 2-o
de
a 0 (X - Y) mutual exogeneity. 2 (Y + X) X endogenous Y exogenous. 2 (X + Y) X exogenous Y endogenous. asterisk denotes evidence of significant residual cross correlation. The first number is the typical hypothesized the test result.
PUS Yus hus rus
rv dc
rc res rexp
ef
Yc m exch
X-series
Table 1 Most acceptable
2-o* 3-3
YUs
l-3
hus
3 (X ++ Y) mutual endogeneity. An relationship, the second number is
3-1* 2-2 3-2*
Pus
z
2
S 3 2
i
;;; : % 2 . . G s
Fa 3 8
S
J. Selody / Exogeneity in a small open economy
304 Table 2 Classification
of variables
on basis of exogeneity.
Test results.
Relatively endogenous Canadian real income @c) Canadian price level (pc) Canadian 90 day interest rate (YC) Canadian-U.S. exchange rate (exch) Canadian money supply - narrowly defined (m) Canadian holdings of international reserves (res) Forward exchange rate - 90 days (efl Canadian domestic credit component of monetary
base (dc)
Relatively exogenous Canadian real government expenditure Canadian real tax receipts (rt) U.S. real income @us) U.S. price level (pus) U.S. monetary base @us) U.S. 90 day interest rate @us)
(rexp)
evidence supports the contention that the Canadian economy is ‘open’. There also appears to be some evidence that Canadian economic fluctuations feedback onto U.S. fluctuations (although it should be re-iterated that excluded innovations may be distorting these results). (5) The money supply, the exchange rate, and international reserves are endogenous to virtually every variable considered. Macroeconomic models of the Canadian economy that treat these variables as exogenous are making identifying restrictions that are not supported by this evidence. (6) Fiscal policy instruments tend to be among the ‘most exogenous’ of those variables tested. It appears that if any of the variables tested must be exogenous (to help identify a small model), exogenizing these variables appears to be a good place to start.
References Akaike, Hirotugu, 1969, Fitting autoregressive models for prediction, Annals of the Institute of Statistical Mathematics 21, 243-247. Hsiao, Cheng, 1979, Autoregressive modeling of Canadian money and income data, Journal of the American Statistical Association 74, 553-560. Selody, Jack, 1979, A monetary model of Canadian price and output fluctuations, Unpublished Ph.D. thesis (University of Western Ontario, London, Ont.). Sims, C.A., 1977, Exogeneity and causal ordering in macroeconomic models, in: New methods in business cycle research: Proceedings from a Conference (Federal Reserve Bank of Minneapolis, Minneapolis, MN).