Exports and economic growth in India: cointegration, causality and error-correction modeling: a note.Abstract
This paper uses stationarity, cointegration, and Granger causality Granger causality is a technique for determining whether one time series is useful in forecasting another. Ordinarily, regressions reflect "mere" correlations, but Clive Granger, who won a Nobel Prize in Economics, argued that there is an interpretation of a set of tests as tests to analyze the relationship between exports and economic growth in India over the preliberalization period 1960-92. The analysis is conducted within a rigorous econometric framework that accounts for optimal lag selection and simultaneity bias. We find strong support for uni-directional causality causality, in philosophy, the relationship between cause and effect. A distinction is often made between a cause that produces something new (e.g., a moth from a caterpillar) and one that produces a change in an existing substance (e.g. from exports to economic growth using Granger causality regressions based on stationary variables, with and without an error-correction term. Unlike previous studies which ignore such fundamental issues as export-economic growth simultaneity, we use a Seemingly Unrelated Regression In econometrics, seemingly unrelated regression (SUR), model developed in Zellner (1962), is a technique for analyzing a system of multiple equations with cross-equation parameter restrictions and correlated error terms. (SUR Sur, Lebanon: see Tyre. ) procedure to account for possible simultaneity bias between exports and economic growth.
The causal relationship between exports and economic growth pertains to a fundamental question in economics what factors determine economic growth? From the viewpoint of economic policy, this is an important issue because if exports cause growth [export led growth (ELG ELG Early Learning Goals (education)
ELG Export-Led Growth
ELG Endoluminal Graft
ELG Effluent Limitation Guideline
ELG European Liaison Group
ELG Executive Level Group
ELG Engineering Log Generator ) hypothesis], export promotion through policies such as export subsidies or exchange rate depreciation will increase growth. The substance of the neoclassical arguments underlying the export led growth hypothesis is that competition in international markets promotes scale economies and increases efficiency by concentrating resources in sectors in which the country has a comparative advantage. These positive externalities externalities
side-effects, either harmful or beneficial, borne by those not directly involved in the production of a commodity. promote economic growth [see, for instance, Bhagwati (1978), Balassa (1978), Krueger (1978), Feder (1982)]. The reverse side of this argument that economic growth promotes export growth relies on the notion that gains in productivity give rise to comparative advantages in certain sectors that lead naturally to export growth. Also, countries with high growth rates Growth Rates
The compounded annualized rate of growth of a company's revenues, earnings, dividends, or other figures.
Remember, historically high growth rates don't always mean a high rate of growth looking into the future. and relatively low absorption rates must necessarily export the excess output.
India is an interesting case study of the export economic growth relationship. It is difficult from the Indian experience to a priori a priori
In epistemology, knowledge that is independent of all particular experiences, as opposed to a posteriori (or empirical) knowledge, which derives from experience. assess the nature of this causal relationship. The trade sector constitutes a small section of the Indian economy and this seems to indicate a minor role for exports in economic development. However, it is important to recognize that the size of the export sector in India does not by itself exclude the possibility of export-led growth. Little, et al. (1993; p. 118) in a discussion of the development experience of LDCs point out that "The relationship between export performance and growth does not arise merely because exports are part of GDP GDP (guanosine diphosphate): see guanine. . Except for a handful of countries, the value of exports was not a very high proportion of GDP even in 1988.... In the main, it appears that rapid export growth relieves a country in balance of payments difficulties from having to compress imports by import restrictions or deflationary action. It permits a more liberal trade regime with all the benefits associated with the exploitation of comparative advantage..... It also makes a country more creditworthy cred·it·wor·thy
Having an acceptable credit rating.
credit·wor , while relief from a dominating concern with debt and the balance of payments permits authorities to pursue economic reforms outside the field of trade and payments".
Up to the 1960s, India had followed an import substitution policy. However, the failure of import substitution as a viable industrial policy and the rapid escalation of import bills and balance of payments deficits in the late 1960s forced India to shift to an export oriented strategy. Recent economic reforms in India Economic reform in India is something which is under close study. The phrase is commonly used to describe post-1991 events. The country however has seen a number of distinct eras, which had definite differences from the economic practices of the previous eras. have largely accentuated this export orientation.
A large empirical literature has re-examined the ELG hypothesis with mixed findings [see, for instance, Jung and Marshall (1985), Chow (1987), Hsiao (1987), Kwan and Cotsomitis (1991), Ahmad and Kwan (1991), Marin (1992), Oxley (1993), Fung et aI. (1994), Shan and Sun (1998) and Moosa (1999)]. The ELG hypothesis, as it pertains to India, has been examined by Nandi and Biswas (1991), Sharma and Dhakal (1994), Mallick (1996), and more recently by Dhawan and Biswal (1999), Nidugala (2000), and Anwer and Sampath (2001). The empirical evidence offered by these papers is, however, mixed. Dhawan and Biswal (1999) examine the period between 1961-93 and find that growth in GDP causes growth in exports while causality from exports to GDP appears to be a short run phenomenon. Nidugala (2000) finds that exports had a crucial role in influencing GDP growth in the 1980s. Anwer and Sampath (2000) examine the export-economic growth nexus for a wide cross section of developing countries over the 1960-92 period. They find that exports and economic growth in India are cointegrated but do not find any strong evidence of causality from exports to economic growth or vice versa VICE VERSA. On the contrary; on opposite sides. .
In much of the ELG literature as it pertains to India, there is little recognition of the importance of issues such as stationarity and cointegration in empirical testing. Nandi and Biswas (1991) and Sharma and Dhakal (1994) offer some evidence of the ELG hypothesis for India but the empirical evidence offered by both papers is unreliable. Nandi and Biswas (1991) do not test for stationarity and conduct Sims causality tests on the levels of the income and export variables. Given that the levels of the income and export variables are usually non stationary, Nandi and Biswas' results are unreliable. Sharma and Dhakal (1994) conclude that the income and export series for India are non stationary using the Phillips Perron Per´ron
n. 1. (Arch.) An out-of-door flight of steps, as in a garden, leading to a terrace or to an upper story; - usually applied to mediævel or later structures of some architectural pretensions. test. They test for causality but do not test for cointegration. However, the correct application of Granger tests requires the identification of a possible cointegrating relationship. If the levels of the export and income series have a unit root (i.e. the series are non stationary) and are cointegrated, the appropriate Granger causality tests must be constructed either on levels or on the stationary differenced series with an error correction term derived from the cointegrating relationship. Our paper corrects problems in previous empirical studies Empirical studies in social sciences are when the research ends are based on evidence and not just theory. This is done to comply with the scientific method that asserts the objective discovery of knowledge based on verifiable facts of evidence. on the ELG hypothesis in India by not only adjusting for issues such as stationarity, cointegration and error-correction but also applying these tests within the context of a more rigorous and sophisticated econometric framework. For instance, evidence of cointegration between exports and economic growth by itself implies the existence of at least uni-directional causality. Another important aspect of causality testing involves determining the optimal number of lags in the Granger regressions. These lags are usually chosen in an ad-hoe manner resulting in a mis-specification of the autoregressive process. Akaike's Final Prediction Error (FPE FPE Final Prediction Error
FPE Floating Point Exception (a computer math error)
FPE Fokker-Planck Equation
FPE Fire Protection Engineering
FPE Free Primary Education (Africa) ) criterion provides a robust method of determining the order of the bi-variate autoregressive process. Combining the FPE method with the Granger definition of causality provides an econometrically rigorous method of testing causality.
One further issue that is almost invariably in·var·i·a·ble
Not changing or subject to change; constant.
in·vari·a·bil ignored but is fundamental to any study of the ELG hypothesis is the simultaneity problem. Since exports and economic growth are jointly determined, application of single equation ordinary least squares (OLS OLS Ordinary Least Squares
OLS Online Library System
OLS Ottawa Linux Symposium
OLS Operation Lifeline Sudan
OLS Operational Linescan System
OLS Online Service
OLS Organizational Leadership and Supervision
OLS On Line Support
OLS Online System ) will result in both inconsistent and inefficient estimates. The simultaneity problem can, however, be eliminated by using the SUR (Seemingly Unrelated Regression) procedure--a procedure that we apply in our paper.
Our paper thus overcomes some of the shortcomings of previous empirical studies on the ELG hypothesis in India by adjusting for stationarity, cointegration and error correction within a more robust econometric framework than used in other similar work in this area.
In this section, we discuss the methods of testing for stationarity, cointegration and causality. Our first objective is to determine the time series properties of real exports and real GDP before testing for the presence of causal relationship between these variables.
A variable [x.sub.t] is said to be integrated of order d, I(d), if it becomes integrated of order 0, I(0) (i.e., stationary) after being differenced d times (Engle and Granger, 1987). The order of integration of [x.sub.t] can be tested using the following regression:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] (1)
The test statistics [??]/[sigma]([??]) is referred to as the Dickey-Fuller (DF) test when [[delta].sub.i] = 0, [[for all].sub.i] and is referred to as the Augmented Dickey-Fuller (ADF (1) (Application Development Facility) An IBM programmer-oriented mainframe application generator that runs under IMS.
(2) (Automatic Document Feeder) A paper stacker that feeds one sheet of paper at a time into the unit. ) test when [[delta].sub.i] [not equal to] 0, [[for all].sub.i]. The optimal lag length, p, is chosen such that the error term et is white noise (1). The optimal lag length can be determined using the Ljung-Box statistic (Ljung and Box, 1978). If [beta] is negative and significantly different from zero, the null hypothesis null hypothesis,
n theoretical assumption that a given therapy will have results not statistically different from another treatment.
n of a unit root ([H.sub.0]: [beta] = 0) or nonstationarity is rejected. Failure to reject the null implies that [x.sub.t] is non-stationary and has a unit root. Under the null hypothesis, the DF test statistic does not have a standard t distribution. However, the critical values for this test are tabulated by Engle and Yoo (1987).
Now consider two variables [x.sub.t] and [y.sub.t], both of which are integrated of order d. The series [x.sub.t] and [y.sub.t] are said to be cointegrated, if there exists the linear combination, [z.sub.t] = [x.sub.t] - [alpha][y.sub.t]. such that [z.sub.t] is integrated of order d-b, I(d-b), b>0 (see Engle and Granger, 1987). The cointegrating regression is then given by:
[y.sub.t] = [alpha] + [[beta][x.sub.t] + [z.sub.t] (2)
If [x.sub.t] and [y.sub.t] are both integrated of order one, I(1) and the error term [z.sub.t] in (2) is stationary then [x.sub.t] and [y.sub.t] are "cointegrated". The null hypothesis in this test [z.sub.t] is that is nonstationary (i.e. non-cointegration). There are two fundamental implications of cointegration. First, cointegration among two variables can be interpreted as the presence of long-run equilibrium relationship between the variables and as a result they will not drift far apart in the long run. Second, cointegration between [x.sub.t] and [y.sub.t] by itself implies the existence of at least, unidirectional Granger causality between the two variables.
The Granger Representation Theorem In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to a concrete structure.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
where [z.sub.t-1] and [z.sub.t-1], are the error-correction terms that represent the extent to which [x.sub.t] and [y.sub.t] deviate from their equilibrium values (2). This result has important implications for testing the export-led growth hypothesis. According to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. the Granger Representation Theorem, if two variables are I(1) and cointegrated, then the VAR can be estimated either in levels or in first differences with an error-correction term included. On the other hand, if two variables are I(1) but not cointegrated, then the vector autoregressive (VAR) model must be constructed in terms of stationary variables (i.e., first differences).
A. Empirical Results
To test the ELG hypothesis in India, we use the log of real exports (LREXP) and the log of real GDP (LRGDP). Nominal exports and nominal GDP Nominal GDP
A gross domestic product (GDP) figure that has not been adjusted for inflation.
It can be misleading when inflation is not accounted for in the GDP figure because the GDP will appear higher than it actually is. were deflated by an export price index and a GDP deflator GDP deflator
A price index used to adjust gross domestic product for changes in prices of goods and services included in the GDP. The GDP deflator is a more broadly based and, many economists argue, a better measure of inflation than the consumer price index series. The data consists of annual observations between 1960-92 collected from various issues of International Financial Statistics (IFS). We focus on the 1960-92 period because the period after 1992 may be structurally different in view of the liberalization lib·er·al·ize
v. lib·er·al·ized, lib·er·al·iz·ing, lib·er·al·iz·es
To make liberal or more liberal: "Our standards of private conduct have been greatly liberalized . . . reforms undertaken by the Indian government.
Before testing the order of integration of LREXP and LRGDP, we need to determine the optimal value of p required to ensure that the error term in equation (1) is white noise. This can be determined through the Box-Pierce Q statistic or the Ljung-Box statistic. We choose to use the Ljung-Box (LB)statistic because of its better small sample properties. The LB statistic is given by (Ljung and Box, 1978):
LB = n(n + 2)[m.summation over (j=1)([[??]sup.2.sub.j]/n x j]) (5)
where n is the sample size. The test statistic is distributed as chi-square with m*k degrees of freedom, where m is the number of autocorrelations and k is the number of estimated parameters in (1). The null hypothesis in this test is that the [[rho].sub.j] autocorrelation Autocorrelation
The correlation of a variable with itself over successive time intervals. Sometimes called serial correlation. coefficients are jointly equal to zero (i.e. the error term is white noise). Rejection of the null implies that the autoregressive process is not white noise.
The DF and ADF test results for LREXP and LRGDP are reported in Table 1. These results imply that the null hypothesis that exports and GDP in log levels are I(1) cannot be rejected. However, the hypothesis that exports and GDP are I(1) in first differences is rejected. Thus, LREXP and LRGDP are non-stationary in levels but stationary in first differences.
To determine if exports and GDP are cointegrated, we use the cointegrating regression with LRGDP as the dependent variable. Thus:
LRGDP = 9.94 + 0.857 LREXP
N = 33, [R.sup.2]= .95, D.W. = 1.10, DF = -3.37, SE in parentheses
The null hypothesis is that the error term in the above regression has a unit root (i.e. noncointegration). The critical values for this test at the 5% and 10% level are -3.54 and -3.18. Thus, the null cannot be rejected at the 5% level but is rejected at the 10% level. Based on the above results, we conclude that LRGDP and LREXP are 'weakly' cointegrated.
It is now well-known that cointegration tests have relatively low power of rejecting the null hypothesis of noncointegration. Hakkio and Rush (1991, p.579) point out that "... much of the recent work that has accepted the hypothesis of noncointegration (less formally, rejected cointegration) may be simply the result of very low power. On the other hand, the lack of power suggests that rejecting noncointegration (that is 'accepting cointegration') may be a fairly strong conclusion." Given the small sample size, our results provide some, though not conclusive, evidence of cointegration.
B. Causality Testing and Results
Given that LRGDP and LREXP are 'weakly' cointegrated, we test Granger causality using first differenced variables with and without an error-correction term.
The Granger definition of causality essentially equates causality with predictability. In terms of the export-led growth hypothesis, if GDP growth can be better predicted using past information on both GDP growth and export growth than with just past information on GDP growth alone, then export growth is said to "cause" GDP growth.
An important issue in the empirical implementation of Granger causality is the determination of the optimal lag length of past information. In most of the previous studies on Granger causality, these lags are determined arbitrarily. (3) Akaike's Final Prediction Error (FPE) criterion, however, provides an econometric criterion for determining optimal lag lengths.
In estimating (3) and (4), the lag lengths of p, q, r and s are determined using Akaike's Final Prediction Error (FPE) criterion. The optimal values of p and q in (3) are chosen using a two-stage search procedure. In the first stage, we set q = 0 and search for the optimal value of p ([p.sup.*]) which minimizes:
FPE= n+k/n-k SSR (Scalable Sampling Rate) See AAC.
SSR - Scalable Sampling Rate (p)/n
where n is the sample size, SSR(p) is the sum of squared residuals, and k is equal to p + 2 or p + 1 depending upon whether an error-correction term is included or not in (3). In the second stage, we set p = [p.sup.*] and search to find the optimal value of q (q') that minimizes:
FPE([p.sup.*], q) = n + m / n - m SSR([p.sup.*], q) / n
where m =[p.sup.*]+q+2 if an error correction term is included in (3); otherwise, m = [p.sup.*]+ q + 1. (4) Apart from enabling the choice of optimal lag lengths in (3) and (4), the FPE criterion also provides an additional test to determine the direction of causality between exports and GDP growth. Specifically, if FPE([p.sup.*], [q.sup.*]) < FPE([p.sup.*]) then we can infer that x causes y (Giles et al., 1993). Thus, an added advantage of using the FPE method is that it enables us to double-check the Granger causality results.
A second critical issue in testing the ELG hypothesis involves selecting an appropriate regression procedure to estimate equations (3) and (4). Since the focus of this hypothesis is on the simultaneous determination of export growth and economic growth, the issue of a simultaneous equation bias cannot be easily dismissed. When LRGDP and LREXP are I(1) and cointegrated, the OLS estimates of the error-correction model may suffer from a simultaneity bias (Serletis (1992, p. 139)). However, with the exception of Giles et al. (1993), virtually all studies on the export-led growth hypothesis have used Ordinary Least Squares (OLS). One way of overcoming this simultaneity bias is to estimate (3) and (4) simultaneously using the Seemingly Unrelated Regression (SUR) procedure. Table 2 below reports Granger causality test results based on three alternative testing methods: OLS (F statistics), SUR ([chi square chi square (kī),
n a nonparametric statistic used with discrete data in the form of frequency count (nominal data) or percentages or proportions that can be reduced to frequencies. ] statistics), and Akaike's FPE. The null hypothesis in the F and [chi square] tests is:
a.[d.sub.j] = 0 for j= 1, ... [q.sup.*]
b. [[gamma].sub.j] = 0 for j = 1, ... [s.sup.*]
If both (a) and (b) above are rejected, there is a feedback (y [left and right arrow] x) effect. If (a) is rejected but (b) is not, then x causes y(x [right arrow] y). However, if (a) is not rejected but (b) is rejected, then y causes x(y [right arrow] x). Results for the three methods are reported with and without the inclusion of an error-correction term.
The causality results based on both OLS and SUR estimates indicate that exports ([x.sub.t]) cause economic growth ([y.sub.t]), irrespective of irrespective of
Without consideration of; regardless of.
preposition despite whether we include the error-correction term or not. These results are further reinforced by the fact that FPE([p.sup.*]) > FPE([p.sup.*], [q.sup.*]) and FPE([r.sup.*]) < FPE([r.sup.*], [s.sup.*]). On the other hand, there is little support for the opposite view that economic growth leads to export growth. The invariance in·var·i·ant
1. Not varying; constant.
2. Mathematics Unaffected by a designated operation, as a transformation of coordinates.
An invariant quantity, function, configuration, or system. of these results across different estimation procedures and across different model specifications suggest that there is strong causality running from exports to economic growth in India.
Using annual data on India's exports and GDP over the 1960-92 pre liberalization period, we analyze the time series properties of these variables in order to determine the appropriate functional form for testing the ELG hypothesis. Since we find that exports and GDP are 'weakly' cointegrated, we test Granger causality using stationary variables with and without an error-correction term. Using three alternative test procedures, we find strong support for uni-directional causality running from exports to economic growth. Furthermore, we find that these results are robust across alternative functional forms (i.e. whether the model includes an error-correction term or not).
Our finding that export performance was an important cause of growth does not by itself explain how exports could have contributed to economic growth in India. There are several possible explanations. Exports may have contributed to economic growth in India directly by relieving severe import constraints, especially in vital capital goods Capital Goods
Any goods used by an organization to produce other goods.
Examples of capital goods include office buildings, equipment, and machinery.
See also: Capital Expenditure, Disinvestment
Capital goods industries. Indirectly, exports may have eased the balance of payments situation and relieved the Indian government of the necessity of pursuing deflationary policies and undertaking difficult structural adjustment programmes such as those undertaken by many developing countries in response to the trade shocks of the seventies and eighties. Another possible explanation involves the existence of strong forward and backward linkages in Indian industries. The dynamic spillover spill·o·ver
1. The act or an instance of spilling over.
2. An amount or quantity spilled over.
3. A side effect arising from or as if from an unpredicted source: effects from the export sector may have lead to an overall increase in productivity. An interesting avenue for further research is to study the exporteconomic growth relationship at the industry level. An industry level study may provide further insights into the factors that link export expansion to economic growth.
Ahmad, J. and A.C.C. Kwan (1991), "Causality Between Exports and Economic Growth", Economics Letters Economics Letters is a scholarly peer-reviewed journal of economics that publishes concise communications (letters) that provide a means of rapid and efficient dissemination of new results, models and methods in all fields of economic research. Published by Elsevier. , Vol. 37, pp. 243-248.
Anwer, M.S. and R.K. Sampath (2001), "Exports and Economic Growth", Indian Economic Journal, Vol. 47, No. 3, pp. 79-88.
Bhagwati, J. (1978), Foreign Trade Regimes and Economic Development: Anatomy and Consequences of Exchange Control Regime, NBER NBER National Bureau of Economic Research (Cambridge, MA)
NBER Nittany and Bald Eagle Railroad Company , New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of .
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Engle, R.F. and B.S. Yoo (1987), "Forecasting and Testing in Co-Integrated Systems", Journal of Econometrics, 35, pp. 143-159.
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Fung, H.G., B. Sawhney, W.C. Lo and E Xiang (1994), "Exports, Imports and Industrial Production: Evidence from Advanced and Newly Industrializing Countries", International Economic Journal, 8 (4), pp. 87-97.
Giles, D.E.A., J. Giles and E. McCann (1993), "Causality, Unit Roots and Export-led Growth: The New Zealand New Zealand (zē`lənd), island country (2005 est. pop. 4,035,000), 104,454 sq mi (270,534 sq km), in the S Pacific Ocean, over 1,000 mi (1,600 km) SE of Australia. The capital is Wellington; the largest city and leading port is Auckland. Experience", Journal of International Trade and Economic Development, pp. 195-218.
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n. (used with a sing. verb)
The study of the overall aspects and workings of a national economy, such as income, output, and the interrelationship among diverse economic sectors. Experience of Developing Countries, Oxford University Press, New York.
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(1.) If the error term in noise when (1) is white [[delta].sub.i] = 0, [[for all].sub.i] it is then unnecessary to conduct the ADF test.
(2.) Note that while [z.sub.t-1] is the lagged error term from (2), [z.sub.t-1] is the lagged error term. in the regression [x.sub.t] = [[alpha].sub.0] + [[beta].sub.0] [y.sub.t] [z'.sub.1]
(3.) See, for example, Jung and Marshall (1985), Chow (1987), Hsiao (1987), and Nandi and Biswas (1991).
(4.) The same procedure is used to obtain the optimal lag lengths, [r.sup.*] and [s.sup.*] in (4).
Sudhakar S. Raju, Rockhurst University This article is about Rockhurst University. For Rockhurst High School, see Rockhurst High School. For the Rockhurst mansion in Newport, Rhode Island, see Rockhurst (Rhode Island). , Helzberg School of Management, 1100 Rockhurst Road, Kansas City Kansas City, two adjacent cities of the same name, one (1990 pop. 149,767), seat of Wyandotte co., NE Kansas (inc. 1859), the other (1990 pop. 435,146), Clay, Jackson, and Platte counties, NW Mo. (inc. 1850). , MO 6411, USA. E-mail: email@example.com
Jacob Kurien, Rockhurst University, Helzberg School of Management, 1100 Rockhurst Road, Kansas City, MO 6411, USA. E-mail: firstname.lastname@example.org
Table 1: Stationarity Test Results for LREXP and LRGDP in India, 1960-92 DF ADF LREXP -0.0703 0.3562 (1) (a) LRGDP 0.6849 nn DLREXP -6.4940 * nn DLRGDP -8.5301 * nn (a) The number in parentheses denotes the optimal value of p required to achieve white noise errors. nn denotes that it was not necessary to include augmented terms to attain white noise errors. The asterisk indicates statistical significance at 5% level. The critical value for n = 50 is -2.93. (Engle and Yoo, 1987). Table 2: Granger Causality Results: F and [chi square] Statistics [DELTA] LRGDP = f ([DELTA] LREXP) 95% Critical F Value [chi square] With ECT (a) 5.26 2.74 19.43 Without ECT 5.38 2.87 21.39 [DELTA] LREXP = f ([DELTA] LRGDP) 95% Critical F Value [chi square] With ECT .1839 4.23 0.2125 Without ECT (b) .0004 4.20 0.0021 95% Critical FPE FPE Value ([p.sup.*]) ([p.sup.*], [q.sup.*]) With ECT (a) 11.07 0.00128 (1) (b) 0.00093 (1,5) Without ECT 11.07 0.00128 (1) 0.00096 (1,5) [DELTA] LREXP = f ([DELTA] LRGDP) s 95% FPE Critical FPE ([r.sup.*], [s.sup.*]) Value ([r.sup.*]) With ECT 3.84 0.00655 (1) 0.00692 (1,1) Without ECT (b) 3.84 0.00713 (1) 0.00761 (1,1) (a) ECT denotes the error-correction term. (b) The numbers in parentheses are the optimal lag lengths.