In this section we present the results of the unit root tests. The idea is to avoid estimating the per worker production function with possible non-stationary variables without accounting for the non-stationarity. Such a flaw leads to misleading inferences as the estimates would be inconsistent. In doing so we use the homogenous class of tests as well as the heterogeneous class of tests for panel unit root. While the former assumes that all the countries have a common unit root process or do not have unit root, the latter assumes that the countries have different unit root processes, implying that while some of them may have unit root others do not have unit root. The Levin-Lin-Chu (LLC), Breitung and Hadri tests, which are the homogenous panel tests, are applied and under the heterogenous panel tests the Im-Pesaran and Shin (IPS), Maddala-Wu and Choi tests are applied. It is also important to note that while the LLC and the Breitung tests have the null hypothesis as 'the variable has unit root' the null hypothesis under the Hadri test is 'the variable is stationarity'. In addition, while the IPS test and the homogenous panel tests are individual test, the Maddala-Wu and Choi tests are Fisher type tests in the sense that they involve application of unit root tests to each country followed by combining the results through an F-test of joint existence of unit root in the variable for all the countries.

Table 2 shows the results of the unit root tests. The results show that while output

per worker is stationary after first differencing capital per worker is stationary after second differencing. It is also necessary to mention that among the homogenous panel unit root methods applied, while the LLC and the Breitung tests suggests output per worker is stationary in first difference form, the Hadri test suggests that it is not stationary even after first differencing. However, all the heterogenous panel tests reveal that output per worker is stationary in level. Hence, we support the option that output per worker is stationary after firs differencing. It is thus said to be I(1). In the case of capital per worker, apart from the results of the Breitung and Hadri tests which suggests non-stationarity, all the other tests reveals stationarity in level. However, the tests for the stationarity of the variable in first difference form reveals that it is not stationary in the first difference form, according to all the test types. Given that when a variable is stationary in level its first difference must be stationary, which is not the case here we tested the second difference of the variable for stationarity. The result reveals that by all the test types, capital per worker is stationary after second differencing. Hence, it is said to be I(2).

Table 2 Results of the panel unit root tests

LLC

Breitung

Hadri

IPS

Maddala-Wu

Choi

Conclusion

Lny

0.9057

0.9947

0.0000

0.9908

0.3884

0.9845

Lny is I(1)

ΔLnY

0.0000*

0.0003*

0.0000

0.0000*

0.0000*

0.0000*

Lnk

0.0000*

0.9956

0.0000

0.0402*

0.0001*

0.0427*

Lnk is I(2)

ΔLnK

0.4331

0.7365

0.0000

0.2194

0.2560

0.2247

Δ2Lnk

0.0000*

0.0000*

0.0429*

0.0000*

0.0000*

0.0000*

Note: The figures in the table are the probability of failing to reject the null. Hence, a p-value that is higher than 0.05 implies that we fail to reject the null hypothesis of the existence of unit root (the null of stationarity—in the case of the Breitung test). Asterisks have been placed on cases of rejection of the null hypothesis

3.2 Panel Cointegration and Panel Error Correction Model Test Results

To the extent that the model variables are not stationary we proceed to the test for cointegration, which tests for the existence of a long run relationship between output per worker and capital per worker in the ECOWAS countries. We use the Pedroni, Kao, Johansen Fisher type and the Westerlund test. It is also necessary to mention that the null hypothesis of the Pedroni and Kao tests is that there is no cointegration, the null hypothesis of the Johansen Fisher type test is that these are at most k cointegrating vector (for k ¼ 0, 1 as there are only two variables in the model), the null hypothesis for the Westerlund test is that there is no panel error correction model (PECM) underlying the two variables. It is worthy to note that the existence of panel error correction implies the existence of cointegration, as it is only under the existence of cointegration that there can be a panel error correction model. In addition, while the Pedroni, Kao and the Johansen Fisher type tests are tests for homogenous panels, the Westerlund test is a test for heterogenous panel. Tables 3, 4, 5 and 6 show the results of the various panel cointegration tests Table 7 is the country Johansen cointegration test from which the Johansen Fisher type panel cointegration test is obtained. Apart from the result of the Johansen Fisher panel test, the null hypothesis of no cointegration is not rejected by all the panel test types.

Table 3 Result of Pedroni residual test for cointegration

The Johansen Fisher panel test however shows that there is one cointegrating

relationship at the 5 % level of significance by both the trace and maximum-Eigen versions of the test. Because of the fact that this test is a combination of individual p-values from various country Johansen cointegration tests, we therefore tested the robustness of this result by examining the individual country result, given in Table 7. This reveals that the null hypothesis of no cointegration is rejected only in Benin and Ghana at the 5 % level of significance while it is not rejected for all the other countries. Hence, it is more robust to conclude the existence of no cointegration between output per worker and capital per worker in the ECOWAS countries than concluding on the existence of cointegration. This is confirmed by the fact that the Pedroni and Kao tests for cointegration and the Weterlund test for the existence of panel error correction model (an indirect way of testing for cointegration) all reject the null hypothesis of cointegration between the two variables.

Table 4 Result of Kao residual test for cointegration

Table 5 The Westerlund panel error correction test

Table 6 The Johansen Fisher cointegration test

aProbabilities are computed using asymptotic Chi-square distribution

3.3 The Output per Worker Model

Inasmuch as output per worker is integrated of order one and capital per worker is integrated of order two and the two variables are not cointegrated, the relationship between the two model is estimated by transforming the variables to ensure stationarity. In this regard, the first difference of output per worker and the second difference of capital per worker are used to estimate the output per worker production function. This is estimated without incorporating an error correction term in the model as there is no cointegration between the two variables. The model is estimated by assuming that the country specific heterogeneity is fixed and then assuming that it is random. The two models are then tested for choice of the appropriate form, though with large time dimension in panel the fixed effect result is the same as the random effect result. However, the Hausman test is also used to choose the appropriate model from the two.

Table 7 The individual country results of the Johansen cointegration test

Cross section

Trace test

Max-Eigen test

Statistics

Prob.a

Statistics

Prob.a

Hypothesis of no cointegration

Benin

30.7597

0.0001

30.7547

0.0001

Burkina

10.4108

0.2505

7.8171

0.3976

Cape Verde

11.6677

0.1736

10.2201

0.1979

Cote d'Ivoire

21.6956

0.0051

16.5315

0.0215

The Gambia

10.7822

0.2252

7.6804

0.4121

Ghana

18.4396

0.0175

15.2366

0.0350

Guinea

5.8062

0.7183

5.6737

0.6554

G Bissau

9.7633

0.2994

7.3836

0.4448

Mali

6.4809

0.6387

6.4506

0.5561

Niger

15.1709

0.0559

13.2782

0.0711

Nigeria

12.3855

0.1394

12.2782

0.1006

Senegal

8.8930

0.3754

8.6798

0.3138

Sierra Leone

6.6096

0.6234

6.0035

0.6128

Togo

10.5315

0.2420

9.2886

0.2629

Hypothesis of at most one cointegration relationship

Benin

0.0050

0.9428

0.0050

0.9428

Burkina

2.5937

0.1073

2.5937

0.1073

Cape Verde

1.4476

0.2289

1.4476

0.2289

Cote d'Ivoire

5.1640

0.0231

5.1640

0.0231

The Gambia

3.1018

0.0782

3.1018

0.0782

Ghana

3.2030

0.0735

3.2030

0.0735

Guinea

0.1325

0.7159

0.1325

0.7159

G Bissau

2.3797

0.1229

2.3797

0.1229

Mali

0.0303

0.8618

0.0303

0.8618

Niger

1.8926

0.1689

1.8926

0.1689

Nigeria

0.1073

0.7433

0.1073

0.7433

Senegal

0.2132

0.6442

0.2132

0.6442

Sierra Leone

0.6061

0.4363

0.6061

0.4363

Togo

1.2429

0.2649

1.2429

0.2649

aMacKinnon-Haug-Michelis (1999) p-values

Tables 8 and 9 show the results of the fixed effect and random effect models respectively. The former is estimated using the within estimator while the latter is estimated using the GLS. Both fixed effect and random effect models show that, the share of capital in production is 0.95 in the ECOWAS countries. Implying that the share of capital in the output of ECOWAS was 95 % and that of labour was 5 % during the period 1980–2012. Table 10 shows the result of the Hausman test, which reveals that the null hypothesis of random effect specification cannot be rejected based on the p-value (0.6221). It is important to note that under the alternative hypothesis of random effect, the random estimators are consistent and efficient but the fixed effect estimator is inconsistent and inefficient. In addition however, when the time dimension T is large, the random effect coefficient and the fixed effect coefficient are the same. This is observed here as our T is large (from 1980 to 2012) with the coefficient in the fixed effect model being 0.948 and the random effect coefficient being 0.947. Table 11 shows the tests for random versus pool model, which uses the Breausch-Pagan test. The result shows that the null hypothesis that the pool model is the same as the random effect model is rejected in favour of the alternative that the random effect is the appropriate model.

Table 8 Fixed effect estimates of the production function

3.4 Estimating the Productivity of Labour and Capital

Having obtained the share of capital and labour in output, we present in this sub-section the estimates of their productivity and determine whether the growth of the ECOWAS countries was more of factor-quantity growth or factor productivity growth. In doing this we give recourse to the production function and then decompose the growth of output into the contribution of capital accumulation, the contribution of labour growth and the contribution of total factor productivity.

Table 9 Random effect estimates of the production function

Table 10 The Hauseman tests for fixed versus random effect model

Test cross-section random effects

Test summary

Chi-Sq. statistic

Chi-Sq. d.f.

Prob.

Cross-section random

0.242965

1

0.6221

Cross-section random effects test comparisons

Variable

Fixed

Random

Var (Diff.)

Prob.

DDLNKPW

0.948601

0.946777

0.000014

0.6221

Table 11 Breusch-Pagan LM test for random effects versus pool model

Table 12 Contributions of capital, labour and TFP to growth in ECOWAS

Country

Contribution of capital to growth

Contribution of labour to growth

Contribution of TFP to growth

Actual GDP

growth

Actual growth of capital

Actual growth of labour

Benin

2.2

0.2

1.6

4.0

2.4

3.2

Burkina

6.6

0.1

-1.6

5.1

6.9

2.8

Cape Verde

7.8

0.1

-0.4

7.5

8.2

1.6

Cote d'Ivoire

-1.9

0.1

3.2

1.5

-2.0

2.8

Gambia

1.7

0.2

1.5

3.5

1.8

3.5

Ghana

8.9

0.1

-4.7

4.4

9.4

2.7

Guinea

6.9

0.1

-3.6

3.4

7.3

3.0

Guinea Bissau

1.3

0.1

1.3

2.7

1.4

2.2

Mali

4.3

0.1

-0.9

3.5

4.5

2.5

Niger

3.0

0.2

-0.6

2.5

3.1

3.4

Nigeria

-2.7

0.1

6.3

3.7

-2.8

2.6

Senegal

4.9

0.1

-1.8

3.3

5.1

2.9

Sierra Leone

1.4

0.1

0.8

2.3

1.5

2.0

Togo

1.9

0.1

0.1

2.2

2.0

2.8

Table 12 shows the contributions of capital accumulation, labour growth and total factor productivity to growth in the ECOWAS countries during the period 1982–2012.

The table shows that in seven (7) of the 14 ECOWAS countries in the Sample, total factor productivity made a negative contribution to growth. These are Burkina Faso, Mali, Niger and Senegal among the UEMOA countries (with TFP growth of -1.6 %, -0.9 %, -0.6 % and -1.8 % respectively) and Ghana, Guinea and Cape Verde in the non-UEMOA countries (with -4.7 %, -3.6 % and -0.4 % respectively). While in the rest of the countries TFP contributed to growth, the contribution to growth was strong in Nigeria and Cote d'Ivoire with a growth contributions of 6.3 % and 3.2 % respectively. Another observation is that the countries that had high contribution of capital accumulation, which are Cape Verde (7.8 %), Ghana (8.9 %), Guinea (6.9 %), Mali (4.3 %) and Senegal (4.9 %) are the countries with negative contribution of total factor productivity. This suggests that while capital accumulation was evident in these countries, its productivity was not an opportunity to the countries, implying there was decay in capital quality rather than increase in its quality or productivity. It was in Nigeria and Cote d'Ivoire that TFP growth was strong, contributing 6.3 and 3.2 % to growth of output. However, in both countries real capital accumulation was negative. Suggesting that capital declined in real terms but its productivity however increased. It is also observed that from all the countries that had higher than 3 % growth rate during the period 1980–2012, which are Benin (4.0 %), Burkina Faso (5.1 %), Cape Verde (7.5 %), Gambia (3.5 %), Ghana (4.4 %), Guinea (3.4 %), Mali (3.5 %), Nigeria (3.7 %), Senegal (3.3 %) it was only Gambia and Nigeria that experienced positive contribution of TFP growth to growth of output. This also suggests that higher growing economies in ECOWAS are not factor-productive bias. This is a reflection of poor standard of leaving since it is increased in the productivity of factors of production, including labour that has a long term welfare impact on the economy.

Another observation from the table is that in spite of differences in real GDP growth among the countries, the contribution of labour growth in all the countries is 0.1 % with the exception of Benin, Gambia and Niger where it was 0.2. This suggests a limit to the contribution of growth of labour to output growth in the region and it also suggests that there is no relationship between labour growth and its productivity. That is, in spite of growth in the number of workers, for which the labour force is the proxy here, the contribution of its growth to growth of output is very limited.

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