Using an error-correction model to test whether endogenous long-run growth exists

Using an error-correction model to test whether endogenous long-run growth exists

by

Sau-Him Paul Lau University of Hong Kong

January 2003

Abstract:

A major empirical interest in growth studies is whether permanent changes in economic fundamentals affect the long-run growth rate. However, a direct time series analysis of this hypothesis may not always be feasible because the permanence of many such changes is rather questionable. This paper explains why examining the long-run effects of temporary changes in investment share on per capita output provides indirectly the answer regarding the effects of (possibly hypothetical) permanent changes in investment share, when per capita output and per capita investment are cointegrated. Applying the proposed method to the post-war data of major industrial countries, it is found that a disturbance to investment share does not produce a positive long-run effect in France, Japan and the UK. The evidence is unfavorable to the class of endogenous growth models.

JEL Classification Numbers: O40; E22

Keywords: error-correction model; presence or absence of endogenous growth

Correspondence to:

S.-H. P. Lau, School of Economics and Finance, University of Hong Kong, Pokfulam Road, Hong Kong

Phone: (852) 2857 8509 Fax: (852) 2548 1152 E-mail: [email protected]

I am grateful to Trevor Breusch, David Harris, John Hutton, Chung-Ming Kuan, Jin-Lung Lin, Nilss Olekalns, Peter Pedroni, Tony Phipps, Bill Russell, Chor-Yiu Sin, the seminar/conference participants at Academia Sinica, Australian Macroeconomics Workshop, Econometric Society Meetings, Hong Kong University of Science and Technology, McGill University, Monash University, National Taiwan University, Reserve Bank of Australia, Sydney University, Universidad de Guanajuato, University of Hawaii, University of Hong Kong, University of Melbourne, University of New South Wales, and Victoria University of Wellington for helpful comments and discussions. I am also thankful to the Australian Research Council for financial support.

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22

Figure 1: France

0 2 4 6 8 10 12 1950 1960 1970 1980 1990 2000 Year Pe r ca pi ta l ou tp u t & i n v est m e n t 16 18 20 22 24 26 28 30 In vest m en t sh ar e (% )

Log of per capita output Log of per capita investment Investment share (right-hand scale)

Figure 2: Japan

0 2 4 6 8 10 12 1950 1960 1970 1980 1990 2000 Year Pe r ca pi ta l ou tp u t & i n v est m e n t 12 14 16 18 20 22 24 26 28 30 32 34 36 38 In vest m e n t sh ar e (% )

Log of per capita output Log of per capita investment Investment share (right-hand scale)

23

Figure 3: UK

0 2 4 6 8 10 12 1950 1960 1970 1980 1990 2000 Year Pe r ca pi ta l ou tp u t & i n v est m e n t 10 12 14 16 18 20 22 In vest m en t sh ar e (% )

Log of per capita output Log of per capita investment Investment share (right-hand scale)

Figure 4: USA

0 2 4 6 8 10 12 1950 1960 1970 1980 1990 2000 Year Pe r ca pi ta l ou tp u t & i n v est m e n t 12 14 16 18 20 22 24 26 In vest m e n t sh ar e (% )

Log of per capita output Log of per capita investment Investment share (right-hand scale)

24 Table 1:

AIC, BIC and Durbin-Watson Statistics

Country Lag length AIC BIC DW(û ly ) DW(û li ) France 1 -9.05 -8.73 1.95 1.97 France 2 -8.92 -8.45 1.94 1.95 France 3 -8.86 -8.22 2.15 2.00 France 4 -8.89 -8.10 2.03 2.01 Japan 1 -8.44 -8.13 2.37 2.03 Japan 2 -8.54 -8.06 2.11 2.09 Japan 3 -8.47 -7.83 2.12 2.08 Japan 4 -8.38 -7.58 2.16 2.08 UK 1 -8.49 -8.17 1.76 1.69 UK 2 -8.56 -8.09 2.03 1.94 UK 3 -8.42 -7.78 1.98 1.92 UK 4 -8.42 -7.63 2.01 1.98 USA 1 -8.23 -7.91 1.76 1.87 USA 2 -8.26 -7.79 1.82 1.91 USA 3 -8.18 -7.55 1.79 1.87 USA 4 -8.12 -7.32 1.77 1.81

Note: AIC represents Akaike Information Criterion, BIC represents Bayesian Information Criterion, DW represents the Durbin-Watson statistic, and ly and li represent log per capita GDP and log per capita investment respectively.

25 Table 2:

Likelihood Ratio Tests for the Null Hypothesis of No Cointegration Country Lag length L _U L _R LR =2(LU −LR)

France 1 216.1 208.3 15.6***

Japan 2 208.3 199.5 17.6***

UK 2 208.9 204.4 9.0*

USA 2 202.0 201.8 0.4

Note: The number of lags is determined by the Akaike Information Criterion. LR stands for the likelihood ratio test statistic for the hypothesis 1 =2 =0 in Eq. (8). The critical value of the LR test statistic for the null hypothesis of no cointegration is 8.30 at 10% significance level, 10.18 at 5% significance level, and 13.73 at 1% significance level respectively (Horvath and Watson, 1995, Table 1). The symbols *, ** and *** represent statistical significance at 10%, 5%, and 1% respectively.

26 Table 3:

Estimated Coefficients and t-statistics for France, Japan and UK, 1955-2000

Country France Japan UK Left-hand variable û ly_t û lit û lyt û lit û lyt û lit constant -0.09 (-2.43) -0.54 (-3.98) -0.07 (-3.03) -0.25 (-4.28) -0.02 (-0.44) -0.38 (-2.08) 1 ) (li−ly t₋ -0.068 (-2.79) -0.36 (-4.02) -0.056 (-3.42) -0.19 (-4.31) -0.023 (-0.95) -0.24 (-2.34) 1 ûlyt− 0.93 (4.01) 2.82 (3.33) 0.87 (3.54) 2.21 (3.38) 0.49 (1.83) 2.19 (1.93) 2 ûlyt− 0.44 (1.90) 0.46 (0.76) -0.46 (-1.73) -2.07 (-1.84) 1 ûlit− -0.15 (-2.44) -0.53 (-2.36) -0.16 (-1.75) -0.42 (-1.76) -0.02 (-0.38) -0.06 (-0.26) Right-hand variables 2 ûlit− -0.14 (-1.75) -0.35 (-1.61) 0.03 (0.53) 0.03 (0.12) (1) 11 M 0.015 0.027 0.012 (1) 12 M -0.014 -0.035 -0.004

Note: Numbers without parentheses are the estimated coefficients and numbers inside parentheses represent t-statistics.

27

Table 4: Cointegration Tests for Various Models (A) Based on per capita output and per capita investment

Country Lag length L _U L _R LR =2(LU −LR)

Japan 1 202.2 194.4 15.6***

UK 1 203.2 197.0 12.4**

USA 1 197.3 196.7 1.2

(B) Based on output per worker and investment per worker

Country Lag length L _U L R LR =2(LU −LR)

France 1 216.2 209.9 12.6**

Japan 2 209.4 200.4 18.0***

UK 2 209.6 205.0 9.2*

USA 2 198.2 197.7 1.0

28 Table 5:

Estimated Coefficients and Long-run Responses for Various Models (A) Based on per capita output and per capita investment Country Lag length R

1  R 2  M₁₂(1) France 1 -0.068 (-2.79) -0.36 (-4.02) -0.014 France 2 -0.070 (-2.64) -0.36 (-3.70) -0.014 France 3 -0.072 (-2.76) -0.36 (-3.76) -0.018 France 4 -0.072 (-2.71) -0.36 (-3.60) -0.028 Japan 1 -0.052 (-3.17) -0.18 (-4.11) -0.029 Japan 2 -0.056 (-3.42) -0.19 (-4.31) -0.035 Japan 3 -0.060 (-3.51) -0.20 (-4.41) -0.029 Japan 4 -0.066 (-3.76) -0.21 (-4.59) -0.029 UK 1 -0.037 (-1.54) -0.32 (-3.03) -0.007 UK 2 -0.023 (-0.95) -0.24 (-2.34) -0.004 UK 3 -0.019 (-0.75) -0.23 (-2.19) -0.003 UK 4 -0.012 (-0.45) -0.23 (-2.11) -0.001

(B) Based on output per worker and investment per worker Country Lag length R

1  R 2  M12(1) France 1 -0.076 (-3.17) -0.32 (-3.62) -0.022 Japan 2 -0.060 (-3.52) -0.20 (-4.35) -0.036 UK 2 -0.031 (-1.21) -0.25 (-2.40) -0.005

Note: Numbers before parentheses are the estimated coefficients and numbers inside parentheses are t-statistics. The long-run responses M₁₂(1) are obtained under the identifying assumption of m_0,12 =0.