Skip to main content

Table 3 Johansen cointegration test results

From: Spatial market integration of rice in Bangladesh in the presence of transaction cost

Market pairings Model 2 (no linear trend) Model 3 (linear trend)
Test statistics Critical values Test statistics Critical values
Mymensingh-Dhaka
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 23.88** 19.96 27.59** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.66 9.24 9.09 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 19.22** 15.67 21.50** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.66 9.24 9.09 12.25
Rajshahi-Dhaka
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 24.59** 19.96 28.86** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.37 9.24 7.7 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 20.23** 15.67 23.15** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.37 9.24 7.7 12.25
Khulna-Dhaka
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 29.06** 19.96 37.45** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.92 9.24 9.76 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 27.15** 15.67 27.69** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.91 9.24 9.76 12.25
Chattogram-Dhaka
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 21.42** 19.96 28.78** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.13 9.24 9.29 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 19.29** 15.67 19.46** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.13 9.24 9.29 12.25
Rajshahi-Mymensingh
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 24.92** 19.96 27.54** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.49 9.24 5.36 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 16.43** 15.67 22.18** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.49 9.24 5.36 12.25
Chattogram-Mymensingh
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 24.07** 19.96 26.36** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.34 9.24 9.74 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 18.73** 15.67 20.62** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.34 9.24 9.74 12.25
Khulna-Mymensingh
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 23.20** 19.96 30.41** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.3 9.24 10.33 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 20.89** 15.67 22.08** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.3 9.24 10.33 12.25
Khulna-Rajshahi
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 20.82** 19.96 29.31** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.99 9.24 9.42 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 18.83** 15.67 19.89** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.99 9.24 9.42 12.25
Chattogram-Rajshahi
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 26.90** 19.96 34.81** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.33 9.24 7.41 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 22.57** 15.67 25.40** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 2.33 9.24 7.41 12.25
Chattogram-Khulna
 Trace statistics \(\left( {\lambda_{{{\text{trace}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 25.99** 19.96 35.63** 25.32
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.91 9.24 11.88 12.25
 Maximum eigenvalue statistics \(\left( {\lambda_{{{\text{max}}}} } \right)\)
  \(H_{0} :r = 0\;{\text{vs}}\;H_{1} :r \ge 1\) 24.08** 15.67 23.75** 18.96
  \(H_{0} :r \le 1\;{\text{vs}}\;H_{1} :r \ge 2\) 1.91 9.24 11.88 12.25
  1. **Indicates that the null hypotheses are rejected at 5% level of significant