A stylized fact of global upward trend in domestic-world output ratio for major small open economies is recognized in comparison with Australia’s dichotomous experience with the ratio. This fact is used to shed light on the importance of country-specific shocks for small open economies using a simple real business cycle model. While it has been previously found that country-specific shocks are more significant source of business cycle fluctuations than worldwide shocks for Australia before the 1990s, this article suggests that the country-specific shocks may have become an important driver of output growth only in the early 1990s for Australia. Keywords: worldwide shocks; country-specific shocks; international business cycle; half-life JEL Classification: E32; C32; F43
I. Introduction There has been a growing literature that seeks to extend standard closed economy Real Business Cycle (RBC) models to the open economy with the objective of explaining key features of international business cycles (Mendoza, 1991; Backus and Kehoe, 1992; Backus et al., 1992, 1995; Baxter and Crucini, 1993, 1995; Ravn, 1997). These authors have achieved some success in accounting for a number of anomalies that closed economy models fail to elucidate. Subsequent studies in this literature have emerged and brought interesting findings on international business cycle. One such discovery was on a variety of factors that affect the dynamics of business cycle fluctuations. For instance, multiple previous studies have attempted to address the issue of relative importance of worldwide shocks versus countryspecific shocks (Gregory et al., 1997; Canova and
Marrinan, 1998; Hoffmaister et al., 1998; Kwark, 1999; Kose and Riezman, 2001; Kose, 2002; Kose et al., 2003). However, despite the sizeable volume of the findings on the relative importance, no conclusive evidence has been formed. Also just as the real business cycle researchers did in the closed economy models, most of the open economy research followed the tradition of using either calibration or a structural Vector Autoregressive (VAR) model where identifying restrictions are derived from long-run implications in the spirit of Blanchard and Quah (1989), who used the identification that supply shocks have a permanent effect but demand shocks do not. Gregory et al. (1997) somewhat uniquely entertain Kalman filtering and a dynamic factor model for the Group of Seven (G7) economies to utilize the methodological advantage of accommodating a large number of countries without running into the degree of
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Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online ß 2013 Taylor & Francis http://www.tandfonline.com DOI: 10.1080/00036846.2011.610753
730 freedom problems. These authors find that worldwide and country-specific shocks can have different impacts depending on a particular business cycle episode. Another early work of the structural VAR model is Hoffmaister et al.’s (1998), who argue that domestic shocks are the main source of macroeconomic fluctuations for sub-Saharan African countries. Canova and Marrinan (1998) suggest that worldwide shocks are more important than transmission of country-specific shocks in a three-country (US, Germany and Japan) real business cycle model for the period of 1960 : 01 to 1994 : 04. Kose (2002) uses a calibrated dynamic stochastic general equilibrium model of a small open economy and finds that world price shocks account for a significant fraction of business cycle variability in developing countries. However, Kwark (1999) presents findings that country-specific US shocks are more important than world-wide shocks in explaining the US and foreign output for six Organization for Economic Cooperation and Development (OECD) countries in the long-run. The author employs structural VAR methods in a two-country open economy model in which the USA is adopted as the domestic country, and an aggregate of Canada, France, Germany, Italy, Japan and the UK is used as the foreign country. In contrast to several preceding studies (Shapiro and Watson, 1988; Blanchard and Quah, 1989; King, 1991) which use long-run identifying restrictions in the structural VAR models, three permanent shocks are identified by both short-run and long-run restrictions – a world-wide shock, a domestic country-specific shock, and a foreign country-specific shock. Kwark (1999) concludes that it is the US country-specific shocks that are the most important source of US and foreign output variability. Kose and Riezman (2001) take the calibration approach for African countries. The evidence from these authors suggests that trade shocks play an important role in driving the aggregate output fluctuations but the world interest rate does not. The present article succeeds the methodological practice of utilizing long-run implications from a small open economy model to provide enlightening evidence on the importance of country-specific shocks, although the structural VAR model is not explicitly pursued. Also while standard unit root and cointegration tests are conducted, the article attempts to offer methodological contributions by examining the implications in terms of persistence in the data. Hence, given the mixed evidence on the importance of the shocks in the literature, the findings from the present study may be largely due to the methodological approach. Business cycle shocks accounting and Australia
P. I. Ji
Australia has been a subject matter of the research on the relative importance of common shocks versus country-specific shocks. Kose et al. (2003) point out that prior studies pay limited attention to a group of countries, or ad hoc world aggregates. The authors have attempted to address this issue by using a Bayesian dynamic latent factor model to investigate the common dynamic properties of business cycle fluctuations across countries, regions and the world. The dataset consists of 60 countries covering seven regions of the world for the period of 1960–1990. Macroeconomic aggregates (i.e. output, consumption and investment) are decomposed into fractions according to the world, region, country and idiosyncratic components. The results indicate that the world factor is an important source of volatility in most countries, providing evidence for a world economic cycle. In addition, it appears that world and regional factors together account for a larger part of fluctuations in output than in consumption. On the other hand, country-specific and idiosyncratic components play a larger role in explaining investment variability. Their findings for Australia are summarized in Table 1. The country factor weighs 65% of the output variability. The variance decomposition estimates show that from 1960 to 1990 the country-specific component (country factor) edges out the world-wide or regional components in explaining fluctuations in consumption, investment and output. It is true that the estimates from Kose et al. (2003) and the present article are not directly comparable because the methodological approaches are substantially different. Also the scope of the sample in this article is limited to the industrial countries, whereas Kose et al. (2003) ascertain their findings for the world by accommodating a large data set in the model. However, the overall findings from the present article show that the country-specific shocks may not have been of such significance for Australia in the decades of 1960 to 1990. In establishing this conclusion, the present analysis uses an updated annual world and domestic output data from 1960 to 2006 and tests long-run implications based on a theoretical model which differentiates the analysis from that of Kose et al. (2003). In passing, it is stated that the contrasting results between Kose et al. (2003) and the present article may be methodological because Kose et al. (2003) do not base themselves on a theoretical model as business cycle studies including this article often do. Although the data period is longer in the present study, only 47 annual observations of world and domestic output
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Do country-specific shocks matter?
Table 1. Variance decompositions for Australia (percent) World Regional Country factor factor factor Idiosyncratic 3.8 4.6 4.6 65.0 39.9 72.9 9.9 38.5 7.4
731 foreign direction investment, privatization of public enterprises and inflation targeting, all of which foster a transition to a more competitive, flexible and innovative economic environment. As a result of the reforms, Australia’s productivity growth was remarkably strong in the 1990s. Australia performed well above the OECD average on labour productivity (Gross Domestic Product (GDP) per hours worked ) and labour utilization (annual hours worked per capita) after an arguably poor record in the preceding decades (see Table 2). This article ascertains that the productivity dichotomy may be manifested in the domestic-world output ratio for Australia. To link the role of the country-specific shocks with these facts, a standard international RBC model is constructed. The model consists of a small country (Australia) and a large country (the rest of the world ) with world productivity as only transmissible shocks. This specification has the advantage of delivering a simple testable implication of relative importance of country-specific productivity shocks in terms of stationarity and persistence. The organization of the article is as follows: Section II presents the small open economy model and derives a testable implication. Section III discusses the empirical findings. Section IV summarizes the results and concludes the article.
Aggregates
Output 19.3 Consumption 18.6 Investment 12.8
Source: Kose et al. (2003). Notes: The estimates are the medians of posterior quantiles. Sample period is from 1960 to 1990.
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are available. This may have been a discouraging factor for the business cycle researchers from working with the data. To overcome this, this article adopts a bootstrap procedure in the persistence estimation. The stylized fact and Australia The article presents its findings on the importance of country-specific shocks from the observation of a stylized fact that high income countries experience an upward trend in domestic-world output ratios but Australia shows a unique dichotomous feature in the ratio. It should be first noted that the evidence from this article does not consolidate the importance of country-specific shocks relative to the world-wide shocks and the interpretation of the evidence is limited to the suggestion that the country-specific shocks warrant renewed attention. Data plots in Fig. 1 illustrate the stylized fact and the Australia’s distinctive experience. While the stylized fact of global upward trend exists for industrialized small open economies from 1960 to 2006, Australia experiences stability until the late 1980s and joins other members of high income economies in exhibiting the upward trend in the early 1990s.1 In addition, the emergence of Australia’s high productivity growth in the 1990s (unseen in other industrialized small open economies) presents a useful contrast of a dichotomy of high and low productivity periods. It has been often documented that the national productivity surge for Australia in the 1990s was largely due to major reforms that started in the mid-1980s (see Parham, 2002a,b,c, 2004; Parham and Zheng, 2006). These reforms include financial deregulation, adoption of a floating exchange rate, reductions in barriers to trade and
1
II. The Model The model consists of two countries, a small domestic country and the rest of the world (world ). Yd ¼ Aw FðKd Þ t t t Yw ¼ Aw FðKw Þ t t t ð1Þ ð2Þ
where Yd is domestic output, Yw world output, Kd t t t domestic capital, Kw world capital, Aw world prot t ductivity and FðKÞ ¼ K (0 5 5 1). The stochastic process for world productivity follows random walk with drift; w logðAw Þ ¼ w þ logðAw Þ þ t t tÀ1
ð3Þ
w 2 where t $ iid (0, w ). These equations depict the case where worldwide shocks are the sole source of economic growth and
This stylized fact begs another question as to which countries’ ratios are shrinking. Although plots are not presented to conserve space, many low income countries’ ratios (for instance, Bangladesh, Ghana, India, Madagascar, Mali, Morocco and Nicaragua) are downward trending. Because it is unlikely that successive negative shocks hit poor countries only, the contrasting phenomenon between high and low incomes economics means that developed countries are growing faster than less developed countries. A new literature ought to open up and suggest a different type of model to examine the divergent phenomenon for small open economies.
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4.2 4.1 4.0 3.9 3.8 3.8 3.7 3.6 3.5 3.4 65 70 75 80 85 90 95 00 05 3.6 3.4 3.2 3.0 60 65 70 75 80 85 Belgium 4.4 4.2 4.0 3.8 4.2 4.1 4.0 3.9 3.8 60 65 70 75 80 85 Canada 90 95 00 05 3.6 3.4 3.2 3.0 60 65 70 75 80 85 France 3.8 3.6 3.4 3.2 3.5 3.0 3.0 2.5 2.0 60 65 70 75 80 85 Ireland 90 95 00 05 2.4 60 65 70 75 80 85 90 95 00 2.8 2.6 90 95 00 90 95 00 4.4 4.2 4.0
P. I. Ji
05
Australia 4.6
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4.5 4.4 4.3
05
5.5 5.0 4.5 4.0
05
Italy
Fig. 1. Domestic-world per capita GDP ratios
business cycle fluctuations in the domestic country. This specification captures the reality of small open economies such as Australia that trades with multiple international partner economies. It is hard to think that Australian
productivity is propagated to the rest of the world or at least an aggregate economy of major trading partners, whereas it is a fair conjecture that the aggregate world productivity affects Australia.
Do country-specific shocks matter?
4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 60 65 70 75 80 85 90 95 00 05 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 60 65 70 75 80 85 Portugal 5.0 90 95 00
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05
The Netherlands 3.0
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2.8 4.8 2.6 2.4 2.2 4.4 2.0 1.8 1.6 1.4 60 65 70 75 80 85 Spain 90 95 00 05 3.8 60 65 70 75 80 85 90 95 00 05 4.0 4.2 4.6
United Kingdom
Fig. 1. Continued.
The domestic and world representative agents maximize the Constant Relative Risk Aversion (CRRA ) utility functions 1 X C1À ð4Þ Ud ¼ Et i uðCd Þ, uðCÞ ¼ t tþi 1À i¼0 Uw ¼ E t t
1 X i¼0
i uðCw Þ, uðCÞ ¼ tþi
C1À 1À
ð5Þ
subject to their respective resource constraints; Kd ¼ ð1 À ÞKd þ Yd À Cd þ Bd À ð1 þ rtÀ1 ÞBd tþ1 t t t tþ1 t ð6Þ Kw ¼ ð1 À ÞKw þ Yw À Cw þ Bw À ð1 þ rtÀ1 ÞBw tþ1 t t t tþ1 t ð7Þ
2 3
where Cd is domestic consumption, Cw world cont t sumption, Bd domestic net bond holding, Bw world t t net bond holding, the coefficient of relative risk aversion, depreciation rate and rt interest rate on noncontingent bond.2 The growth rate of output, consumption, w investment and capital in steady state is 1À and w they all share the common stochastic trend of logðAt Þ where w is the growth rate of world 1À technology.3 Hence, dividing all variables (output, consumption, investment and capital) by the 1 trend component ðAw Þ1À leaves the transformed t stationary variables. Since this is true for both domestic and world, domestic–world ratios of all variables should be stationary and I(0) in the steady state. All variables share the common stochastic trend
Following Kwark (1999), it is assumed that the only internationally traded asset is a noncontingent risk-free bond. Due to the resource constraint, the growth rate of investment is equal to that of output and capital. For full proof, see Kwark (1999).
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Table 2. Labour productivity and labour utilization growth (percent) 1950–1973 Labour productivity OECD 4.0 Australia 2.5 Labour utilization OECD À0.5 Australia À0.2 Source: Parham (2002b). 1973–1990 2.0 1.5 0.6 0.2 1990–2001 1.8 2.3 À0.3 0.2
P. I. Ji
World Tables.4 10 small open economies (Australia, Belgium, Canada, France, Italy, the Netherlands, Norway, Portugal, Spain and the UK) are chosen for comparison. The choice of countries is based on the fact that they are major small open economies of the OECD members which are likely to be affected by world-wide productivity shocks propagated from the rest of the world, whereas their own productivity shocks are likely to have limited (in some cases close to zero) effects on world productivity. All per capita outputs are measured in 2000 prices and evaluated in the US dollars.5 Figure 1 shows the domestic–world per capita GDP ratio in log for the 11 economies. As a clear indication of departure from stationarity, a commonly observed phenomenon is the global upward trend. Interestingly it is only in the early 1990s when Australia starts to show the upward trend in its world output share. Because of the notable increase in the domestic– world output ratio after a steady path before 1990, Australia serves as a useful case for measuring the importance of country-specific shocks. The countryspecific shocks in the model appear to be associated with the remarkable productivity growth witnessed in the 1990s for Australia. The observation that the Australia–world output ratio is more stable than other countries until the high productivity period hints that the low level of domestic productivity growth may be the explanation for the weak Australian output growth relative to the world before the early 1990s. Tables 2 and 3 evidence the catch-up of Australia with other OECD members. Table 2 reports labour productivity growth and labour utilization growth, which shows that Australia was behind the OECD averages until the 1990s. The same is true for multifactor productivity growth in Table 3 where Australia suffered the low productivity compared to its OECD peers until 1990. Unit root test and persistence
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of log Aw =ð1 À Þ whose growth rate is t w ðw þ t Þ=ð1 À Þ. However, if domestic productivity participates in driving the domestic economy, the domestic production function changes to Yd ¼ Ad Aw FðKd Þ t t t t where Ad is the domestic productivity following t d logðAd Þ ¼ d þ logðAd Þ þ t t tÀ1 d 2 d w t $ iid ð0, d Þ and Eðt t Þ ¼ 0:
ð8Þ
ð9Þ
Then, the ratio of domestic to world output should display a significant departure from stationarity w because domestic output grows at ðw þ t þ d d þ t Þ=ð1 À Þ while world output grows at w ðw þ t Þ=ð1 À Þ. That is, the domestic–world d output ratio grows at ðd þ t Þ=ð1 À Þ, which has a stochastic trend and becomes an I(1) variable. The present article pays attention to this implication that the ratio is testable for stationarity and persistence when the domestic shocks are given importance, which no previous work has noted in the literature.
III. Empirical Analysis Data 47 observations of the annual data for the period 1960 to 2006 are collected from World Bank
4
Unit root test. A portfolio of econometric methodologies is applied in this section to examine the transition from I(0) to I(1) for Australia and the
Unlike other small open economies, data availability for Australia is limited to the period of 1965 to 2006. Shaded in the plot (Fig. 1) is for the period from 1991 to 2006 during which the upward trend appears. 5 Per capita data are conventionally used in the literature (see Kwark, 1999). There is an issue with the output data of whether to use Purchasing Power Parity (PPP) output. Although the PPP seems most appropriate for cross-country comparisons of GDP in wealth term, the interest here is in measuring domestic–world output dynamics inherent in an economy. Ideally, however, a proxy for real exchange rate, if available, can be used to isolate nominal exchange rate fluctuations. Kwark (1999) uses an implied real exchange rate from the Penn World Table Data. Also separation of data period over exchange rate regime difference is not considered here for the same reasons as Kose et al. (2003) quote. First is the data availability that disallows for such split. Second, As Baxter and Stockman (1989), Baxter (1991), and Ahmed (1993) show, there is little conclusive evidence that macroeconomic variables behave differently in a significant way across different exchange rate regimes.
Do country-specific shocks matter?
Table 3. Multifactor productivity growth (percent)
1985–1990 1990–1995 1995–2000 2001–2007 Australia À0.1 Belgium 1.6 Canada À0.5 France 1.8 Italy 1.2 The Netherlands 1.4 Portugal – Spain – United Kingdom 0.8 1.5 1.4 0.5 1.1 0.9 1.7 – 1.1 1.2 1.7 1.4 1.5 1.4 0.1 1.2 2.3 À0.2 1.4 0.3 – 0.3 0.3 À0.6 – – – –
735 domestic–world output ratios. That is, the stronger Ad is in generating fluctuations, the more persistent t the ratio ought to be. Or if Ad is a negligible portion t of technology propagated into home country, the ratio should display a relatively low degree of persistence. Persistence of time series is typically measured by half life, formally defined as the number of periods required for the impulse response to a unit shock to a time series to dissipate by half. This has emerged as a popular measure of persistence in PPP literature (Rogoff, 1996). Half-life is measured from Autoregressive (AR) coefficients. For instance, in AR(1) model h ¼ logð0:5Þ= logðÞ where h is half-life and is the AR coefficient. In the higher order of AR models Xt ¼ c þ 1 XtÀ1 þ Á Á Á þ p XtÀp þ ut ð11Þ ð10Þ
Source: OECD.
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permanent I(1) behaviour of the other countries. Results from the Augmented Dickey–Fuller (ADF) test are presented in Tables 4 and 5. There is evidence suggestive of such transition from I(0) to I(1) for Australia and the absence of the transition for other countries. The output ratio is I(0) in low productivity period (1965–1989) but I(1) in high productivity period (1990–2006) for Australia.6 For the others, the ratio appears to be I(1) in both periods.7 Persistence Half-life and bootstrap. One may be cautious to interpret results from the small sample size of 17 observations for the high productivity period. As a remedy for this, amongst others, bootstrap can be a resort. This section examines persistence in the ratios and attempts to supplement the unit root test results and circumvent the small sample deficiency by using a bootstrap procedure in persistence estimation. While unit root tests can indicate if a particular time series is I(0) or I(1), it is also possible to measure the strength of driving force, Ad , by estimating directly the t persistence (the degree of mean-reversion) of the
The error term ut is assumed to be independent and identically distributed (i.i.d.) with zero mean and fixed variance. The AR model given in Equation 11 can be expressed as an MA(1) model with the È É1 coefficients i i¼0 where 0 ¼ 1 and i represents the impulse response of Xtþi to a unit shock in ut at time t, i.e. i ¼ @Xtþi/@ut , for i ¼ 0, 1, 2, . . . . The half-life h is calculated as the largest value j which satisfies | jÀ1| ! 0.5 and | j |50.5. Unlike the case of the closed form solution (10) for the AR(1), the value of h in the AR(p) model with p41 can be obtained from È Ém 8 i i¼0 . When j is a number between i À 1 and i, linear interpolation is used to determine the value of h. As for the estimation of h, the Least Square (LS) estimator of can be readily used. However, this
6 The choice of 1991 as the break point for the productivity revival is based on results from data-dependent unit root test with structural break (Zivot and Andrews, 1992). Other neighbouring years have been used but the results are qualitatively the same. 7 Although Norway appears to be I(0) from 1990 to 2004 at 10% significance, full-sample period results in preliminary analysis strongly support I(1) regardless of the statistical significance levels. 8 Given the observed time series fXt gn , the LS estimator for ¼ (, 1, . . . , p) in Equation 3 can be obtained by regressing t¼1 ^ ^ ^ t¼pþ1 , respectively. In the Xt on (1, Xt-1, . . . ,Xt-p). The LS estimator and its residuals are denoted as ¼ ð, b1 , . . . , bp Þand fut gn AR(1) case, the half-life is estimated as & ^ ^ ^ ¼ logð0:5Þ= logð1 Þ if 1 5 1 h 1 otherwise
^ For a higher order modelh is obtained from the estimated impulse response function f ^ i gm , where ^ i is the ith coefficient in i¼1 ^ ^ When the model has a characteristic root close to one, h may not be found even the MA(1) representation associated withÈ
. É m with a reasonably large value of m, since ^ i i¼1 declines fairly slowly. In this case, an approximation is used & ^ ^ logð0:5Þ= logðÞ if 5 1 ^ h¼ 1 otherwise ^ ^ where ¼ 1 þ Á Á Á þ p , following Murray and Papell (2002). In this article, m is set to n and the approximation is used if È Én ^ ^i does not reach 0.5 for i n. i¼1
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Table 4. The ADF test for low productivity period (1960–1989) ADF test statistic Intercept only Starting periods Australia Belgium Canada France Italy The Netherlands Norway Portugal Spain 1965–1989 1960–1989 1960–1989 1960–1989 1960–1989 1960–1989 1960–1989 1960–1989 1960–1989 Level À4.01* À0.73 À0.21 À1.10 À0.31 À1.10 À0.44 À1.41 À1.55 (0.00) (0.82) (0.92) (0.69) (0.91) (0.70) (0.88) (0.55) (0.49) First difference À5.86* À5.89* À6.26* À5.05* À5.85* À6.60* À3.29* À3.78* À3.61* (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.02) (0.00) (0.01) ADF test statistic Intercept and trend Level À3.81* (0.04) À1.53 (0.79) À2.96 (0.15) À1.29 (0.86) À3.14 (0.11) À1.77 (0.69) À2.48 (0.33) À1.37 (0.84) À1.97 (0.58) First difference À4.01* À5.81* À6.03* À5.08* À5.77* À6.81* À3.23 À3.89* À3.48 (0.02) (0.00) (0.00) (0.00) (0.00) (0.00) (0.09) (0.02) (0.06)
P. I. Ji
AR lag order 1 2 1 1 1 1 2 5 2
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Notes: The AR lag order has been selected by using specific-to-general approach. The order is increased from zero until serial correlation is removed in residuals. Ljung–Box Q statistic is also referred to ensure no serial correlation. p-values are given in parentheses. * Indicates significance at the 5% level.
Table 5. The ADF test for high productivity period (1990–2006) ADF test statistic Intercept only Starting periods Australia Belgium Canada France Italy The Netherlands Norway Portugal Spain 1990–2006 1990–2006 1990–2006 1990–2006 1990–2006 1990–2006 1990–2006 1990–2006 1990–2006 Level À0.82 À2.47 À1.97 À2.83 À1.25 À1.83 À2.92 À1.75 À1.28 (0.78) (0.13) (0.29) (0.07) (0.62) (0.35) (0.06) (0.38) (0.60) First difference À2.82 À3.03 À1.86 À0.99 À2.10 À1.65 À1.90 À2.01 À1.92 (0.07) (0.05) (0.33) (0.73) (0.24) (0.43) (0.32) (0.27) (0.31) ADF test statistic Intercept and trend Level À1.31 (0.84) À1.09 (0.89) À3.54 (0.06) À4.63* (0.00) À0.38 (0.97) À1.84 (0.63) 0.61 (0.99) À1.32 (0.84) À2.55 (0.29) First difference À2.69 À3.72* À1.63 À1.24 À2.72 À1.98 À3.43 À2.29 À1.97 (0.24) (0.04) (0.73) (0.86) (0.23) (0.56) (0.07) (0.41) (0.57) AR lag order 1 1 2 4 4 2 1 2 2
Notes: The AR lag order has been selected by using specific-to-general approach. The order is increased from zero until serial correlation is removed in residuals. Ljung–Box Q statistic is also referred to ensure no serial correlation. p-values are given in parentheses. * Indicates significance at the 5% level.
raises several issues on the undesirable properties of the LS estimator including; the unknown distribution of h, the possible absence of finite sample moments, and small sample bias. In particular, the small sample issue with 17 observations for the high productivity period in the present data ought to be addressed. This study adopts a bias-corrected bootstrap procedure due to Kilian (1998) (see, e.g. Kim et al., 2007). Kilian (1998) finds that the small sample deficiency of the impulse response estimator can render the confidence intervals inaccurate and the bias-corrected procedure that he proposes can address the problem.
A brief description of the bias-corrected bootstrap procedure is as follows. First, the bias-corrected ^ ^ version of ¼ ð, b1 , . . . , , bp Þ is obtained using the nonparametric bootstrap. Generate a pseudo-data set fXà gn as t t¼1 ^ tÀ1 Xà ¼ þ b1 Xà þ Á Á Á þ bp Xà þ eà tÀp t t ð12Þ
using fXt gp as starting values, where eà is a random t t¼1 ^ t¼pþ1 . draw with replacement from fut gn The resampling process repeats so that B1 sets of pseudo-data are produced and B1 sets of bootstrap
Do country-specific shocks matter?
Table 6. Half-life Period I (1960–1989) Point Australia Belgium Canada France Ireland Italy The Netherlands Norway Portugal Spain United Kingdom Mean* Median* 1.31 64.29 1.92 85.97 3.73 1.32 1394.38 6.39 66.97 19.76 206.38 185.11 42.03 95% Interval 0.27 0.55 0.33 0.45 0.42 0.27 0.32 1.56 0.48 1.33 1.43 0.71 0.46 47.57 203.04 86.78 284.26 296.63 81.20 257.80 519.34 387.46 652.99 739.35 350.88 290.44 Point 3.98 278.90 1.93 4.29 4.29 104.11 4.84 65.62 65.62 244.88 14.35 78.88 39.98 Period II ( 1990–2006) 95% Interval 0.27 0.27 0.26 0.77 0.77 0.60 0.31 0.98 0.98 0.27 0.27 0.55 0.46
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166.77 300.36 165.50 193.53 193.53 309.91 170.40 1086.58 1086.58 128.37 219.88 385.46 206.71
Notes: *The figures are in years. Values more than 80 years are indicated as infinity.
parameter estimates for
, denoted as f à ð j ÞgB1 , can j¼1 be obtained.
* ¼ (m*, 1*, . . . , p*) is acquired by ^ regressing Xt* on (1, XÃ , . . . , XÃ ). The bias of tÀ1 tÀp ^ ^ can be estimated as Bias(
) ¼ Ã À
, where à is the sample mean of f à ð j ÞgB1 . The bias-corrected j¼1 ^c ^ 1 p estimator
B ¼ ðc , bc , . . . , bc Þ for can be calculated ^ ^ ^c as À Biasð
Þ and the residuals associated with
B is c n denoted as fut gt¼pþ1 . To obtain the bias-corrected point and interval estimators for half-life, the second-stage bootstrap is conducted using the bias-corrected parameter estimators obtained above, following the bootstrap-afterbootstrap of Kilian (1998). Generate the pseudo-data set fXà gn recursively as t t¼1 ^ Xà ¼ c þ bc Xà þ Á Á Á þ bc Xà þ và 1 tÀ1 p tÀp t t ð13Þ
using fXt gp as starting values, where và is a random t t¼1 à n draw with replacement from fuc gn t t¼pþ1 . Using fXt gt¼1 , the parameters of the AR(p) model can finally arrive with bias-correction to obtain ðcà , cà , . . . , , cà Þ. The p 1 associated half-life estimate is denoted as h*. Repeat (13) and estimation of h* many times, say B2, to obtain the bootstrap-based distribution of the halfÈ ÉB2 life estimates hà i¼1 : i Table 6 reports the half-life estimates. In low productivity period Australia shows much lower point estimate than other countries. The mean and median of the other high income members are 185.11 and 42.03 in years, whereas the Australian counterpart is 1.31. Also the half-life increases to 3.98 years from 1.31 for Australia after the break point of 1990. Other countries maintain large (practically infinite) half-life and upper confidence interval estimates which translate to I(1) for both periods. The interval is markedly
narrow for Australia in low productivity period. The upper interval is 47.57, the lowest of the entire upper interval estimates, but grows to 166.77 in high productivity period. This suggests that the presence of the domestic shocks, Ad , appears to be much stronger t in high productivity period for Australia. Also the lower persistence of the Australian ratio compared to other peers evidences the contrasting experience of the country in low productivity period. The increase in persistence is likely associated with the effects of productivity boom in the early 1990s. These findings warrant careful consideration to what Kose et al. (2003) have documented for Australia. The authors have found that country-specific factors account for a more significant fraction of output growth than common factors for Australia during the same period 1965–1990 as examined in this article. Contrarily, this article finds that there is little dominance of country-specific shocks for Australian output growth until the productivity boom. The absence of common stochastic trends Another testable implication of the model is that each country (except for Australia in low productivity period ) grows in output driven by independent country-specific shocks; hence, no common stochastic trends should exist between countries in output. Johansen’s (1991) method is employed to examine whether such case holds. The trace and maximal eigenvalue tests of Johansen (1991) are used to determine the cointegration rank. Each pair of countries is tested for cointegration in full sample period. The pair-wise cointegration test results are
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Table 7. Number of cointegrating vectors for pairs of countries
P. I. Ji
The United Australia Belgium Canada France Ireland Italy Netherlands Norway Portugal Spain Kingdom Australia Belgium Canada France Ireland Italy The Netherlands Norway Portugal Spain United Kingdom – 0 – 1 0 – 0 0 0 – 0 0 0 0 – 0 0 0 0 0 – 0 0 0 0 1 0 – 1 0 0 0 0 0 0 – 0 0 0 0 0 0 0 0 – 0 0 0 0 0 0 0 0 0 – 0 0 0 0 0 0 0 0 0 0 –
Note: Each cell shows the number of pair-wise cointegrating relations based on the trace statistics and maximal eigenvalues.
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tabulated in Table 7. Each cell in the table indicates number of cointegrating vectors based on trace and maximal eigenvalue statistics for all pairs of countries. Overall, no cointegration is found with a few exceptions of the Australia–Canada, Australia– Norway and Ireland–the Netherlands pairs.9 The cointegration results thus supplement the unit root tests and persistence measure in suggesting the significant role of the country-specific shocks.
external world-wide shocks such as the global financial crisis. The policy makers may gain insight from this study and stay vigilant of the domestic productivity measures (including the labour productivity and multifactor productivity factor) against the external shocks as a sustaining driver of the economic growth.
Acknowledgement The author is grateful to Glenn Otto for his helpful comments. IV. Conclusion A single-country-world model has been used to study the importance of country-specific shocks for small open economy. Only world-wide technology is specified to affect domestic economy to accommodate the reality of small open economies in terms of technology propagation. The model predicts that domestic–world output ratio should be stationary, which does not agree with data as a stylized fact. Unit root tests and persistence measures suggest that the country-specific shocks also participate in driving the system of the domestic and world outputs together with world-wide shocks for major small open economies. In addition, cointegration tests support this claim. In particular, this article finds that country-specific shocks led by productivity reforms may have been a major factor in output growth since the early 1990s for Australia, which conveys a policy implication. For example, the domestic productivity reforms deserve careful consideration as an important policy tool to insulate the economy from negative
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