# Asymmetric Price Transmission: A Case of Wheat in India

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Data and Methodology

#### 3.1. Johansen’s Approach to Cointegration

_{t}be n × 1 set of I(1) variables (if the series is integrated to order d, it is denoted as I(d)). Usually, any linear combination ${\mathrm{a}}^{\prime}{\mathrm{y}}_{\mathrm{t}}$ will be I(1) for a ≠ 0. However, if there exists an n × 1 vector α

_{i}such that ${\mathsf{\alpha}}_{\mathrm{i}}^{\prime}{\mathrm{y}}_{\mathrm{t}}$ is $\left(0\right)$, ${\mathsf{\alpha}}_{\mathrm{i}}\ne 0$, then it is said that the components in y

_{t}are cointegrated of order one, denoted CI(1) with the cointegrating vector as α

_{i}. It can be noted that if α

_{i}is a cointegrating vector, then so is the kα

_{i}for any k ≠ 0, since ${\mathrm{k}\mathsf{\alpha}}_{\mathrm{i}}^{\prime}{\mathrm{y}}_{\mathrm{t}}~\mathrm{I}\left(0\right)$.

#### 3.2. Error Correction Models (ECM)

_{t}.

#### 3.3. Asymmetric Cointegration

_{1}${\widehat{\mathsf{\epsilon}}}_{\mathrm{t}-1}$, if deviations from the long-run equilibrium are positive, and ρ

_{2}${\widehat{\mathsf{\epsilon}}}_{\mathrm{t}-1}$otherwise.

_{1}and ρ

_{2}are adjustment coefficients; ${\mathsf{\beta}}_{\mathrm{i}}$indicates the coefficient(s) of lagged changes; and ω

_{t}is the identically independently distrusted (i.i.d.) stochastic term. The necessary and sufficient conditions for stationarity of ${\widehat{\mathsf{\epsilon}}}_{\mathrm{t}}$ are ρ

_{1}< 0, ρ

_{2}< 0, and (1 + ρ

_{1}) (1 + ρ

_{2}) < 1 for any values of ${\mathrm{a}}_{0}$[18,19]. Tong [37] showed that the least square estimates of ρ

_{1}and ρ

_{2}had an asymptotic multivariate normal distribution under the condition that ${\widehat{\mathsf{\epsilon}}}_{\mathrm{t}}$ is stationary. The M-TAR model was applied in this paper to examine the long-run relationship among the pairs of wholesale and retail prices of wheat assuming asymmetric adjustment. For threshold cointegration with M-TAR adjustment, the five-step procedure reported in [19] was followed. First, a long-run relationship between the pairs of markets was estimated as follows:

_{1,t}and y

_{2,t}are the logarithm of wholesale and retail prices of wheat at time t; ${\mathsf{\gamma}}_{0}$is a constant term; ${\mathsf{\gamma}}_{1}$ is th elasticity of price transmission; and ε

_{t}is the error term that may be serially correlated. In the second step, following [38], consistent estimates of threshold values for M-TAR models were obtained. Equations (3) and (4) were estimated for each of the possible threshold values. Finally, the threshold (${\mathrm{a}}_{0}$) was estimated by minimizing the sum of squared residuals from the fitted model. In the third step, the null hypothesis of no cointegration, that is, ρ

_{1}= ρ

_{2}= 0, was tested for each of the M-TAR models. Fourth, the null hypothesis of no asymmetric adjustment, that is, ρ

_{1}= ρ

_{2}, was tested for each of the M-TAR models using the standard F-test under the condition that the null hypothesis of no cointegration is rejected. In the last step, the Ljung–Box Q-statistic was applied to test for the white noise process of the estimated residuals from the M-TAR models. Once the presence of cointegration was established among the markets, the dynamics of price transmission among them were analyzed using asymmetric vector error correction models (AVECMs) with threshold (M-TAR) adjustment. On application of the TAR model, it revealed that asymmetric cointegration was present in the wholesale and retail prices of wheat in the markets, namely Ahmedabad, Bengaluru, Bhubaneswar, Hyderabad, Patna and the all India minimum price. On the other hand, using the MTAR model, it was seen that asymmetric cointegration was present in most markets.

## 4. Results and Discussion

#### Cointegration in Price Series

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Grid search to find the optimum value of the threshold parameter and cointegration parameter in TVECM.

**Table 1.**Descriptive statistics for the wholesale and retail prices (INR per quintal) of the individual markets.

Markets | Wholesale Price | Retail Price | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | Median | Max | Min | SD | CV(%) | Mean | Median | Max | Min | SD | CV(%) | |

Ahmedabad | 1647.75 | 1650.00 | 2000.00 | 1100.00 | 302.89 | 18.38 | 1851.49 | 1900.00 | 2300.00 | 1200 | 318.11 | 17.18 |

Amritsar | 1491.28 | 1500.00 | 1900.00 | 1050.00 | 229.44 | 15.39 | 1688.93 | 1800.00 | 2200.00 | 1100 | 297.61 | 17.62 |

Bengaluru | 2320.10 | 2500.00 | 2800.00 | 1671.43 | 418.44 | 18.04 | 2582.08 | 2700.00 | 3400.00 | 1800 | 530.42 | 20.54 |

Bhopal | 1457.20 | 1500.00 | 1700.00 | 1050.00 | 170.97 | 11.73 | 1638.73 | 1700.00 | 2000.00 | 1100 | 234.91 | 14.33 |

Bhubaneswar | 1512.65 | 1580.00 | 1580.00 | 1210.00 | 107.36 | 7.10 | 1803.18 | 1800.00 | 2014.29 | 1400 | 222.5 | 12.34 |

Chennai | 2298.40 | 2342.86 | 2814.29 | 1800.00 | 204.42 | 8.89 | 2794.45 | 3000.00 | 3500.00 | 2000 | 439.36 | 15.72 |

Dehradun | 1511.74 | 1512.86 | 1880.00 | 1120.00 | 218.85 | 14.48 | 1709.16 | 1600.00 | 2200.00 | 1200 | 310.24 | 18.15 |

Delhi | 1590.37 | 1671.43 | 2227.86 | 1138.57 | 244.90 | 15.40 | 1800.62 | 1900.00 | 2414.29 | 1300 | 234.88 | 13.04 |

Hyderabad | 2359.37 | 2400.00 | 2700.00 | 1490.71 | 356.55 | 15.11 | 2581.75 | 2700.00 | 2900.00 | 1700 | 353.88 | 13.71 |

Jaipur | 1570.16 | 1600.00 | 2250.00 | 1150.00 | 233.97 | 14.90 | 1709.90 | 1700.00 | 2600.00 | 1300 | 256.55 | 15.00 |

Jammu | 1562.63 | 1617.14 | 2560.00 | 1000.00 | 253.82 | 16.24 | 1698.18 | 1700.00 | 2200.00 | 1100 | 259.59 | 15.29 |

Lucknow | 1445.64 | 1450.00 | 1900.00 | 1035.71 | 215.18 | 14.88 | 1576.59 | 1600.00 | 2000.00 | 1100 | 213.26 | 13.53 |

Ludhiana | 1489.15 | 1350.00 | 1900.00 | 1114.29 | 242.65 | 16.29 | 1601.62 | 1592.86 | 2000.00 | 1200 | 243.15 | 15.18 |

Mumbai | 2102.12 | 2200.00 | 2628.57 | 1453.57 | 313.44 | 14.91 | 2614.76 | 2700.00 | 3514.29 | 1700 | 447.64 | 17.12 |

Patna | 1518.12 | 1600.00 | 2200.00 | 1100.00 | 238.40 | 15.70 | 1730.36 | 1800.00 | 2400.00 | 1200 | 292.66 | 16.91 |

Thiruvananthapuram | 2331.98 | 2400.00 | 3200.00 | 1500.00 | 405.95 | 17.41 | 2557.70 | 2600.00 | 3500.00 | 1700 | 413.19 | 16.15 |

Maximum Price | 2833.35 | 2850.00 | 4021.43 | 1833.00 | 546.88 | 19.30 | 3109.81 | 3100.00 | 4428.57 | 2100 | 632.25 | 20.33 |

Minimum Price | 1276.89 | 1337.14 | 1471.43 | 100.00 | 169.09 | 13.24 | 1401.84 | 1500.00 | 1671.43 | 1000 | 177.20 | 12.64 |

Modal Price | 1717.69 | 1667.86 | 2714.29 | 1100.00 | 395.82 | 23.04 | 1712.87 | 1797.64 | 2478.57 | 1200 | 267.59 | 15.62 |

Markets | Original Series | Differenced Series | ||||
---|---|---|---|---|---|---|

Wholesale Price | ||||||

ADF Test Statistic | PP Test Statistic | KPSS Test Statistic | ADF Test Statistic | PP Test Statistic | KPSS Test Statistic | |

Ahmedabad | −1.43 | −1.44 | 114.11 * | −15.56 * | −15.74 * | 0.89 |

Amritsar | −0.46 | −0.49 | 136.34 * | −14.92 * | −14.77 * | 1.46 |

Bengaluru | −0.70 | −0.55 | 116.30 * | −15.37 * | −16.64 * | 0.99 |

Bhopal | −0.71 | −0.82 | 178.78 * | −15.13 * | −14.31 * | 0.88 |

Bhubaneswar | −1.89 | −1.77 | 295.55 * | −14.00 * | −13.90 * | 0.29 |

Chennai | −2.48 | −2.78 | 235.84 * | −17.01 * | −14.80 * | 0.46 |

Dehradun | −0.90 | −0.69 | 144.90 * | −13.66 * | −13.28 * | 1.16 |

Delhi | −1.56 | −1.46 | 136.22 * | −15.00 * | −15.04 * | 0.75 |

Hyderabad | −2.13 | −2.10 | 138.80 * | −18.50 * | −18.50 * | 1.22 |

Jaipur | −1.71 | −1.66 | 140.77 * | −14.26 * | −14.27 * | 0.89 |

Jammu | −1.80 | −2.45 | 129.14 * | −15.21 * | −21.69 * | 0.33 |

Lucknow | −1.75 | −1.50 | 140.92 * | −13.14 * | −13.86 * | 1.02 |

Ludhiana | −0.15 | −0.19 | 128.73 * | −15.79 * | −21.58 * | 1.31 |

Maximum Price | −0.82 | −1.58 | 108.68 * | −18.52 * | −77.21 * | 0.71 |

Minimum Price | −2.89 | −3.14 | 158.40 * | −20.26 * | −22.65 * | -0.01 |

Modal Price | −2.64 | −3.95 | 91.03 * | −12.85 * | −41.55 * | 0.03 |

Mumbai | −1.37 | −1.02 | 140.68 * | −14.51 * | −15.25 * | 0.89 |

Patna | −2.01 | −2.06 | 133.58 * | −23.90 * | −24.12 * | 0.33 |

Thiruvananthapuram | −1.97 | −2.10 | 120.50 * | −17.09 * | −16.53 * | 0.31 |

Retail Price | ||||||

Ahmedabad | −1.32 | −1.24 | 122.09 * | −14.47 * | −17.00 * | 0.31 |

Amritsar | −1.43 | −1.23 | 119.04 * | −14.73 * | −14.08 * | 0.98 |

Bengaluru | −0.32 | −0.26 | 102.11 * | −15.56 * | −15.52 * | 1.53 |

Bhopal | −0.94 | −1.02 | 146.33 * | −10.61 * | −14.20 * | 0.91 |

Bhubaneswar | −0.84 | −0.83 | 170.00 * | −13.44 * | −13.33 * | 0.89 |

Chennai | −1.59 | −1.58 | 133.41 * | −15.52 * | −14.54 * | 1.08 |

Dehradun | −0.69 | −0.79 | 115.56 * | −12.12 * | −13.87 * | 1.02 |

Delhi | −2.02 | −1.43 | 160.81 * | −13.96 * | −13.72 * | 0.70 |

Hyderabad | −2.55 | −2.49 | 153.03 * | −13.80 * | −13.09 * | 1.44 |

Jaipur | −2.07 | −2.27 | 139.81 * | −15.30 * | −18.30 * | 0.51 |

Jammu | −1.38 | −1.27 | 137.22 * | −9.34 * | −15.40 * | 0.70 |

Lucknow | −1.45 | −1.45 | 155.07 * | −16.67 * | −15.30 * | 0.79 |

Ludhiana | −0.92 | −0.66 | 138.17 * | −16.03 * | −18.52 * | 0.95 |

Maximum Price | −0.30 | −0.09 | 103.17 * | −19.55 * | −31.50 * | 0.99 |

Minimum Price | −1.83 | −1.69 | 165.94 * | −20.83 * | −20.98 * | 0.22 |

Modal Price | −2.27 | −3.24 | 134.27 * | −21.57 * | −62.84 * | 0.20 |

Mumbai | −1.37 | −1.23 | 122.53 * | −12.47 * | −17.59 * | 0.85 |

Patna | −1.55 | −1.42 | 124.02 * | −10.28 * | −16.48 * | 1.24 |

Thiruvananthapuram | −1.80 | −1.85 | 129.85 * | −16.67 * | −18.33 * | 0.13 |

No. of Cointegrating Equations | Retail Price | |||
---|---|---|---|---|

Test Statistics (Trace) | 5% Critical Value | Test Statistics (Eigen) | 5% Critical Value | |

None | 392.86 | 277.39 | 95.04 | 68.27 |

At most 1 | 297.82 | 232.49 | 75.47 | 62.42 |

At most 2 | 222.35 | 192.84 | 53.70 | 57.00 |

At most 3 | 168.65 | 157.11 | 40.3 | 51.07 |

At most 4 | 128.35 | 124.25 | 37.76 | 44.91 |

At most 5 | 90.59 | 90.39 | 33.95 | 39.43 |

At most 6 | 56.64 | 70.60 | 23.41 | 33.32 |

At most 7 | 33.23 | 48.28 | 14.69 | 27.14 |

At most 8 | 18.54 | 31.52 | 11.45 | 21.07 |

At most 9 | 7.09 | 17.95 | 6.91 | 14.90 |

At most 10 | 0.18 | 8.18 | 0.18 | 8.18 |

Wholesale Price | ||||

None | 438.07 | 277.39 | 126.4 | 68.27 |

At most 1 | 311.67 | 232.49 | 79.39 | 62.42 |

At most 2 | 232.28 | 192.84 | 73.67 | 57.00 |

At most 3 | 158.61 | 157.11 | 50.88 | 51.07 |

At most 4 | 107.73 | 124.25 | 34.12 | 44.91 |

At most 5 | 73.61 | 90.39 | 25.90 | 39.43 |

At most 6 | 47.71 | 70.60 | 17.71 | 33.32 |

At most 7 | 30.00 | 48.28 | 14.84 | 27.14 |

At most 8 | 15.16 | 31.52 | 8.71 | 21.07 |

At most 9 | 6.45 | 17.95 | 6.34 | 14.90 |

At most 10 | 0.11 | 8.18 | 0.11 | 8.18 |

No. of Cointegrating Equations | Eigen Value | Test Statistics (Eigen) | 5% Critical Value | Test Statistics (Trace) | 5% Critical Value |
---|---|---|---|---|---|

Delhi | |||||

None | 0.0054 | 22.43 | 14.90 | 24.85 | 17.95 |

At most 1 | 0.0499 | 2.41 | 8.18 | 2.41 | 8.18 |

Ahmedabad | |||||

None | 0.0061 | 43.77 | 14.90 | 46.48 | 17.95 |

At most 1 | 0.0951 | 2.71 | 8.18 | 2.71 | 8.18 |

Amritsar | |||||

None | 0.0023 | 9.54 | 14.90 | 10.58 | 17.95 |

At most 1 | 0.0215 | 1.04 | 8.18 | 1.04 | 8.18 |

Bengaluru | |||||

None | 0.0016 | 8.75 | 14.90 | 9.47 | 17.95 |

At most 1 | 0.0197 | 0.72 | 8.18 | 0.72 | 8.18 |

Bhopal | |||||

None | 0.0030 | 42.07 | 14.90 | 43.40 | 17.95 |

At most 1 | 0.0915 | 1.33 | 8.18 | 1.33 | 8.18 |

Bhubaneswar | |||||

None | 0.0025 | 14.63 | 14.90 | 15.73 | 17.95 |

At most 1 | 0.0328 | 1.10 | 8.18 | 1.10 | 8.18 |

Chennai | |||||

None | 0.0070 | 25.69 | 14.90 | 28.77 | 17.95 |

At most 1 | 0.0569 | 3.09 | 8.18 | 3.09 | 8.18 |

Dehradun | |||||

None | 0.0026 | 13.67 | 14.90 | 14.84 | 17.95 |

At most 1 | 0.0307 | 1.16 | 8.18 | 1.16 | 8.18 |

Hyderabad | |||||

None | 0.0089 | 37.59 | 14.90 | 41.53 | 17.95 |

At most 1 | 0.0822 | 4.00 | 8.18 | 4.00 | 8.18 |

Jaipur | |||||

None | 0.0055 | 58.65 | 14.90 | 61.09 | 17.95 |

At most 1 | 0.1253 | 2.44 | 8.18 | 2.44 | 8.18 |

Jammu | |||||

None | 0.0064 | 134.00 | 14.90 | 136.80 | 17.95 |

At most 1 | 0.2634 | 2.84 | 8.18 | 2.84 | 8.18 |

Lucknow | |||||

None | 0.0068 | 52.58 | 14.90 | 55.61 | 17.95 |

At most 1 | 0.1131 | 3.03 | 8.18 | 3.03 | 8.18 |

Ludhiana | |||||

None | 0.0015 | 31.19 | 14.90 | 31.88 | 17.95 |

At most 1 | 0.0687 | 0.69 | 8.18 | 0.69 | 8.18 |

Mumbai | |||||

None | 0.0049 | 33.22 | 14.90 | 35.40 | 17.95 |

At most 1 | 0.0730 | 2.18 | 8.18 | 2.18 | 8.18 |

Patna | |||||

None | 0.0061 | 21.00 | 14.90 | 23.67 | 17.95 |

At most 1 | 0.0467 | 2.69 | 8.18 | 2.69 | 8.18 |

Thiruvananthapuram | |||||

None | 0.0101 | 52.46 | 14.90 | 56.95 | 17.95 |

At most 1 | 0.1128 | 4.49 | 8.18 | 4.49 | 8.18 |

Markets | Dimension | Epsilon (1) | Epsilon (2) | Epsilon (3) | Epsilon (4) |
---|---|---|---|---|---|

Ahmedabad_Retail | 2 | 600.67 | 173.78 | 117.59 | 70.00 |

3 | 1129.23 | 215.99 | 133.03 | 70.30 | |

Ahmedabad_Wholesale | 2 | 2173.76 | 319.87 | 108.27 | 72.50 |

3 | 3950.85 | 431.49 | 119.93 | 72.39 | |

Amritsar_Retail | 2 | 93.81 | 117.40 | 91.05 | 69.29 |

3 | 149.09 | 160.84 | 102.21 | 69.63 | |

Amritsar_Wholesale | 2 | 180.06 | 136.23 | 88.66 | 73.80 |

3 | 329.51 | 181.74 | 96.50 | 71.81 | |

Bengaluru_Retail | 2 | 292.59 | 323.93 | 131.92 | 59.34 |

3 | 522.18 | 439.46 | 147.52 | 57.72 | |

Bengaluru_Wholesale | 2 | 244.40 | 1255.52 | 181.84 | 72.96 |

3 | 365.17 | 1663.65 | 217.31 | 73.67 | |

Bhopal_Retail | 2 | 137.42 | 165.38 | 101.25 | 62.23 |

3 | 222.07 | 220.16 | 111.85 | 61.05 | |

Bhopal_Wholesale | 2 | 209.93 | 180.14 | 101.56 | 64.07 |

3 | 421.36 | 247.94 | 111.55 | 62.80 | |

Bhubaneshwar_Retail | 2 | 166.81 | 84.49 | 74.55 | 61.24 |

3 | 277.31 | 100.98 | 81.61 | 62.74 | |

Bhubaneshwar_Wholesale | 2 | 36.89 | 51.99 | 45.93 | 35.62 |

3 | 47.80 | 63.11 | 50.41 | 35.26 | |

Chennai_Retail | 2 | 181.38 | 187.00 | 103.10 | 73.61 |

3 | 295.91 | 241.48 | 116.06 | 74.61 | |

Chennai_Wholesale | 2 | 100.65 | 85.42 | 63.95 | 53.87 |

3 | 156.00 | 103.09 | 67.05 | 51.98 | |

Dehradun_Retail | 2 | 669.71 | 166.61 | 107.52 | 73.71 |

3 | 1230.74 | 210.35 | 121.92 | 72.53 | |

Dehradun_Wholesale | 2 | 539.88 | 199.04 | 90.49 | 75.48 |

3 | 1033.83 | 276.57 | 96.11 | 73.98 | |

Delhi_Retail | 2 | 88.11 | 91.31 | 72.94 | 61.73 |

3 | 135.25 | 115.87 | 80.75 | 61.20 | |

Delhi_Wholesale | 2 | 113.22 | 92.92 | 83.71 | 70.42 |

3 | 177.46 | 118.92 | 95.89 | 70.09 | |

Hyderabad_Retail | 2 | 72.33 | 65.15 | 57.72 | 50.04 |

3 | 118.83 | 80.06 | 62.26 | 49.80 | |

Hyderabad_Wholesale | 2 | 103.98 | 69.05 | 64.85 | 52.94 |

3 | 185.87 | 83.48 | 71.01 | 53.02 | |

Jaipur_Retail | 2 | 158.78 | 97.03 | 65.89 | 52.97 |

3 | 277.57 | 125.27 | 71.73 | 50.48 | |

Jaipur_Wholesale | 2 | 183.13 | 102.85 | 72.85 | 64.64 |

3 | 315.12 | 133.01 | 79.83 | 63.58 | |

Jammu_Retail | 2 | 111.30 | 129.08 | 68.34 | 66.87 |

3 | 194.38 | 173.25 | 76.45 | 63.79 | |

Jammu_Wholesale | 2 | 109.77 | 99.42 | 68.60 | 58.83 |

3 | 191.54 | 129.57 | 74.86 | 56.69 | |

Lucknow_Retail | 2 | 125.41 | 117.73 | 79.20 | 67.49 |

3 | 194.25 | 143.68 | 84.73 | 65.61 | |

Lucknow_Wholesale | 2 | 390.74 | 164.18 | 92.79 | 74.23 |

3 | 741.61 | 216.04 | 100.56 | 73.06 | |

Ludhiana_Retail | 2 | 262.12 | 937.45 | 179.97 | 84.53 |

3 | 397.97 | 1233.07 | 214.37 | 88.56 | |

Ludhiana_Wholesale | 2 | 247.35 | 683.00 | 211.98 | 81.38 |

3 | 360.43 | 901.09 | 260.63 | 85.69 | |

Maximum_Price_Retail | 2 | 493.20 | 175.26 | 96.65 | 71.00 |

3 | 939.21 | 234.04 | 105.91 | 70.88 | |

Maximum_Price_Wholesale | 2 | 677.41 | 189.46 | 92.78 | 70.06 |

3 | 1324.58 | 253.50 | 103.21 | 71.68 | |

Minimum_Price_Retail | 2 | 79.60 | 112.47 | 83.43 | 57.51 |

3 | 141.35 | 146.67 | 92.67 | 57.06 | |

Minimum_Price_Wholesale | 2 | 80.12 | 76.01 | 60.34 | 44.10 |

3 | 121.74 | 90.87 | 65.72 | 43.64 | |

Modal_Price_Retail | 2 | 118.78 | 118.55 | 66.71 | 47.41 |

3 | 201.10 | 155.97 | 72.70 | 48.17 | |

Modal_Price_Wholesale | 2 | 143.71 | 60.58 | 42.94 | 36.59 |

3 | 236.28 | 73.09 | 45.92 | 36.09 | |

Mumbai_Retail | 2 | 294.76 | 165.60 | 94.41 | 75.08 |

3 | 547.07 | 217.46 | 102.39 | 74.63 | |

Mumbai_Wholesale | 2 | 129.13 | 132.31 | 89.78 | 66.80 |

3 | 205.21 | 166.97 | 100.58 | 67.68 | |

Patna_Retail | 2 | 388.63 | 277.51 | 91.02 | 74.61 |

3 | 733.61 | 396.26 | 98.42 | 74.56 | |

Patna_Wholesale | 2 | 199.47 | 191.24 | 84.96 | 61.60 |

3 | 357.21 | 254.22 | 94.33 | 60.17 | |

Thiruvananthapuram_Retail | 2 | 203.09 | 111.99 | 81.55 | 64.48 |

3 | 349.40 | 141.54 | 88.10 | 63.15 | |

Thiruvananthapuram_Wholesale | 2 | 224.43 | 227.39 | 102.92 | 67.89 |

3 | 387.76 | 290.76 | 113.16 | 66.63 |

Markets | MTAR | |||
---|---|---|---|---|

PHI | APT | |||

F Value | Pr. Value | F Value | Pr. Value | |

Ahmedabad | 14.60 | <0.05 | 3.55 | 0.05 |

Amritsar | 6.03 | <0.05 | 2.43 | 0.11 |

Bengaluru | 3.48 | <0.05 | 3.05 | 0.08 |

Bhopal | 26.91 | <0.05 | 4.88 | <0.05 |

Bhubaneswar | 6.38 | <0.05 | 0.02 | 0.88 |

Chennai | 11.05 | <0.05 | 12.74 | <0.05 |

Dehradun | 4.61 | <0.05 | 1.17 | 0.27 |

Delhi | 13.33 | <0.05 | 4.44 | <0.05 |

Hyderabad | 63.31 | <0.05 | 96.47 | <0.05 |

Jaipur | 42.80 | <0.05 | 47.64 | <0.05 |

Jammu | 49.47 | <0.05 | 38.20 | <0.05 |

Lucknow | 40.52 | <0.05 | 32.62 | <0.05 |

Ludhiana | 41.19 | <0.05 | 54.91 | <0.05 |

Mumbai | 7.80 | <0.05 | 1.93 | 0.16 |

Patna | 43.31 | <0.05 | 51.02 | <0.05 |

Thiruvananthapuram | 17.38 | <0.05 | 1.13 | 0.28 |

Maximum | 31.52 | <0.05 | 23.55 | <0.05 |

Minimum | 35.72 | <0.05 | 41.16 | <0.05 |

Modal | 20.84 | <0.05 | 4.82 | <0.05 |

Markets | Test Statistic | p Value |
---|---|---|

Ahmedabad | 17.27 | 0.03 |

Amritsar | 10.88 | 0.77 |

Bengaluru | 11.30 | 0.49 |

Bhopal | 21.54 | 0.01 |

Bhubaneswar | 14.07 | 0.39 |

Chennai | 10.70 | 0.56 |

Dehradun | 13.72 | 0.35 |

Delhi | 22.66 | 0.01 |

Hyderabad | 18.90 | 0.02 |

Jaipur | 15.69 | 0.29 |

Jammu | 22.91 | 0.01 |

Lucknow | 9.36 | 0.88 |

Ludhiana | 11.55 | 0.75 |

Mumbai | 17.97 | 0.03 |

Patna | 19.00 | 0.02 |

Thiruvananthapuram | 19.17 | 0.02 |

Maximum | 11.29 | 0.81 |

Minimum | 25.77 | 0.01 |

Modal | 35.03 | 0.001 |

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## Share and Cite

**MDPI and ACS Style**

Paul, R.K.; Karak, T.
Asymmetric Price Transmission: A Case of Wheat in India. *Agriculture* **2022**, *12*, 410.
https://doi.org/10.3390/agriculture12030410

**AMA Style**

Paul RK, Karak T.
Asymmetric Price Transmission: A Case of Wheat in India. *Agriculture*. 2022; 12(3):410.
https://doi.org/10.3390/agriculture12030410

**Chicago/Turabian Style**

Paul, Ranjit Kumar, and Tanmoy Karak.
2022. "Asymmetric Price Transmission: A Case of Wheat in India" *Agriculture* 12, no. 3: 410.
https://doi.org/10.3390/agriculture12030410