We can use several methods to test whether there is a unit root for panel data in our study, and we used the (Breitung & Im, Pesaran, & Shin) tests, employing a unit root test for panel data. Moreover, this test provides t-test statistics that follow the normal distribution of residuals, with each cross-section receiving a separate estimate, allowing for the specification of parameter values, residual variance, and lag length. Furthermore, the test can be conducted using high power, with little distortion, as well as for small samples. The Augmented Dickey-Fuller (ADF) test is as follows ( Pedroni 2004): ∆ Y it = ai + piYt − 1 + ∑ £ jYt − 1 + βit + ϵt (1)

We can determine whether there is a long-term joint integration relationship between electronic payments and the market value of agricultural companies listed on the Iraq Stock Exchange by applying the Pedroni cointegration test, after ensuring that there is no unit root in the panel data ( Muhammed and Alhiyali 2018). The cointegration test allows for multiple regression and estimates the residuals from the cointegration regressions, providing seven statistical tests. It permits joint integration to vary across the existing sections in the panel, in addition to the heterogeneity between cross-sectional units (panel data). The estimated residuals from the long-term regression are as follows ( Fahad, Battal, and Yaseen 2023): Y it = ai + πi + ∑ m = 1 m βmt . Xmit + μti (2)

The intersection and regression transactions differ according to the cross-sectional units. Pedroni used critical values to test the seven statistics using a Monte Carlo simulation, suggesting that if the values of the statistics exceed the critical values, the null hypothesis should be rejected and the alternative hypothesis accepted, indicating the absence of cointegration ( Al-Anezi et al. 2025b).

Pesaran and Smith (1995) introduced the mean group (MG) as a simple estimator for panel data with a set of observations for time series across several groups (N). When considering the estimation of the (ARDL p, q) model, which relies on a panel data set with time series (i = 1,2 …. N) and time periods (t = 1, … T), T contains a sufficient number of observations to estimate the model and determine the degree of effect ( Asteriou and Hall 2006). Y it = ∑ j = 1 p ⋋ ij ∗ Y i , t − j + ∑ j = 0 q Ҩ ij ∗ X i + y 1 dt + ϵit (3)

Since xit and dt are (k × 1) and (s × 1) rebound factors, while ⋋ij∗s represents the residuals and Ҩij∗s and (ϵi∗ s are (k × 1)) and (s × 1) vectors of unspecified parameters to be estimated. As in the following equation ( KAMACI, CEYHAN, and PEÇE 2019). ∆ Y it = ∑ k = 1 p − 1 ⋋ ik ∆ Y i , t − 1 + ∑ k = 0 q − 1 ∗ ⋋ ik ∆ Y i , t − 1 + Ҩ i ( Y i , t − 1 + βiXit ) + ωi + ϵit (4)

Hiaso tests are one of the essential stages in determining the appropriate methodology for estimating panel data. In the case of complete homogeneity of intercepts and slopes, the panel data method is rejected in favor of the Ordinary Least Squares (OLS) method for estimating a pooled model. However, if the slopes are only homogeneous, the most suitable estimation model would be fixed or random effects, respectively. In the case of complete heterogeneity of intercepts and slopes, one must rely on one of the dynamic models for estimation.

Most electronic payment methods in the financial sector in Iraq witnessed significant development after 2020. This is due to the government’s approach to reform the Iraqi banking sector and improve its poor reality, leading to structural improvements and amendments to the banking law and the financial sector in general. Amendments were made to the operational mechanism in the Iraqi stock market to enable it to keep pace with developments in emerging financial markets ( Dawood et al. 2025). The advancements in electronic payment methods have significantly contributed to improving the market value index of agricultural companies listed in the market. This is reflected in customers' desire to use ATM cards or online payments or the massive expansion in mobile phone usage, which has impacted financial and real investment methods and improved the financial results of agricultural companies. Consequently, their profits increased, leading to a rise in the closing prices of their shares, which resulted in an increase in the number of traded shares, indicating a rise in the market value index of the agricultural companies listed in the market. The annual statistical bulletins issued by the Central Bank for electronic payment variables for the monthly period 2021-2024 were relied upon, while the stock price data of agricultural companies were obtained from the annual reports of the Iraq Stock Exchange for the monthly period 2021-2024.

Figure 1 shows Most electronic payment methods in the financial sector witnessed a remarkable development after the year 2020 in Iraq. This is due to the government’s approach to reforming the Iraqi banking sector and improving its declining reality. It worked to introduce structural improvements and amend the banking law and the financial sector in general, and made amendments to the mechanism of work in the Iraqi Stock Exchange. In a way that enables it to keep pace with developments taking place in emerging financial markets.

The PMG-ARDL model was applied to the data of agricultural companies listed on the Iraq Stock Exchange, and the estimation results of the relationship are as follows:

7-2-1: Results of the panel data stationarity test

Table 3 shows the results of the panel data stationarity test as indicated below.

It is evident from Table 3 that the time series of variable X1 is unstable at its original level according to various stationarity tests for panel data at the 5% level, as is variable Y, which necessitated taking the first differences, making it stationary at the first difference. Meanwhile, variable X2 is stationary at the original level. Therefore, it is necessary to employ the Panel ARDL Model for the panel data due to the differences in the degrees of stationarity of the variables.

7-2-2: Hiaso test for homogeneity of cross sections

Table 4 shows the results of the Hiaso test for the homogeneity of cross sections as follows:

It is clear from Table 4 that the panel data for the agricultural companies in the study sample lack homogeneity and therefore static models cannot be applied because they give us inefficient estimates, and this does not help us in arriving at solutions to the research problem aimed at measuring the impact of electronic payments on the market value index of agricultural companies listed in Iraq Stock Exchange.

First Hypothesis: Assuming the existence of complete homogeneity of segments and coefficients, and after conducting the estimation process, the following was revealed: F1 = 199.9492 , prob . F1 = 0.001

It is clear from the above results that the calculated value of F1 is greater than its tabulated value at a significance level of less than 5%. Therefore, we reject the null hypothesis and accept the alternative hypothesis which states that there is no homogeneity of the overall data for the panel data model. This leads us to test the second hypothesis as follows:

Second Hypothesis: Assuming the existence of homogeneity of coefficients only, and after the estimation process, the following was revealed: F2 = 9.370854 , Prob . F2 = 0.001

As evident from the above results, the calculated value of F2 is greater than its tabulated value at a significance level of less than 5%. Therefore, we reject the null hypothesis indicating homogeneity of the slope coefficients and accept the alternative hypothesis which states that there is no homogeneity of the overall data for the panel data model. This leads us to test the third hypothesis as follows:

Third Hypothesis: Assuming homogeneity of constants only, and after the estimation process, the following was revealed: F3 = 426.0463 , Prob . F3 = 0.001

It is clear from the above results that the calculated value of F3 is greater than its tabulated value at a significance level of less than 5%. Therefore, we reject the null hypothesis indicating homogeneity of the slope coefficients and accept the alternative hypothesis which states that there is no homogeneity of the overall data for the panel data model.

Table 4 shows that the panel data for the agricultural companies in the sample study lacks homogeneity; therefore, static models cannot be applied as they provide us with inefficient estimators, which does not help us in reaching solutions to the research problem aimed at measuring the impact of electronic payments on the market value index of agricultural companies listed on the Iraq Stock Exchange.

7-2-3: Cointegration test for panel data

Table 5 shows the results of the (Pedroni) test, and based on the extracted results, it was found that there are (6) statistically significant statistics out of (8) statistics. Therefore, the null hypothesis was rejected and the alternative hypothesis was accepted for four tests: (Panel PP-Statistic), (Panel ADF-Statistic), (Group PP Statistic), and (Group ADF-Statistic) at confidence levels of 95% and 99%. Consequently, the results of the different cointegration tests indicate that the variables of electronic payments (retail payment via mobile and electronic checks) are jointly cointegrated with the market value of agricultural companies listed on the Iraq Stock Exchange.

7-2-4: Analysis of Kao residual cointegration test results

Table 6 shows the results of the (Kao) test regarding the extent to which there is a cointegration relationship between electronic payments and market value. This is evident from the Kao value of (-2.217846), which was significant at the significance level (5%).

7-2-5: Estimation of panel ARDL model results

Table 7 shows that the error correction coefficient (COINTEQ01) reached (-0.878165) with a negative and significant value at a 10% significance level, indicating the presence of a long-term cointegration relationship. From this, we conclude the following: •

There is a positive effect of the mobile retail payment variable (X2) on the market value index, as a 1% increase in mobile retail payments leads to a 0.032% increase in market value, and this relationship is significant at a 5% significance level.

7-2-6: Choosing the best ARDL model

Table 8 shows the results of the (ACI) test for selecting the best estimated model. After calculating the results, it was found that the best model is (ARDL(7, 4, 4)). This model indicates that seven lag periods were estimated for the dependent variable, four lag periods for the first independent variable (retail payment via mobile), and four lag periods for the second independent variable (electronic check).

7-2-7: Results of the short-term cointegration relationship

7-2-7-1: The short-term relationship of the Modern Animal Production Company (AMAP)

Table 9 shows the results of estimating the short-term relationship between electronic payments indicators and the market value of the Modern Animal Production Company (AMAP) over the study period. The table shows the existence of a short-term cointegration relationship, as evidenced by the value of the error correction coefficient (COINTEQ01), which reached (-0.396620), which was significant at a significance level of (5%).

Table 9 shows the results of estimating the short-term relationship between electronic payment indicators and the market value index of the Modern Animal Production Company (AMAP) during the study period. It is clear from the table that there is a short-run cointegration relationship, and this is evident through the value of the error correction factor (COINTEQ01), which reached (-0.396620), which was significant at the significance level (5%).

7-2-7-2: The short-term relationship of the Middle East Fisheries Company (AMEF)

Table 10 shows the results of estimating the short-term relationship between electronic payments indicators and the market capitalization index of the Middle East Fisheries Company (AMEF) over the study period. The table shows a short-term cointegration relationship, as evidenced by the value of the error correction coefficient (COINTEQ01), which reached (-0.628304), which was significant at a significance level of (5%).

Table 10 shows the results of estimating the short-term relationship between electronic payment indicators and the market value index of the Middle East Fisheries Company (AMEF) during the study period. It is clear from the table that there is a short-run cointegration relationship, and this is evident through the value of the error correction factor (COINTEQ01), which reached (-0.628304), which was significant at the significance level (5%).

7-2-7-3: The short-term relationship of the Iraqi company for meat production and marketing (AIPM)

Table 11 shows the results of estimating the short-term relationship between electronic payments indicators and the market value of the Iraqi Company for Meat Production and Marketing (AIPM) over the study period. The table shows a short-term cointegration relationship, as evidenced by the value of the error correction coefficient (COINTEQ01), which reached (-2.367686), which was significant at a significance level of (5%).

Table 11 shows the results of estimating the short-term relationship between electronic payments indicators and the market value index of the Iraqi Company for Meat Production and Marketing (AIPM) during the study period. It is clear from the table that there is a short-run cointegration relationship, and this is evident through the value of the error correction factor (COINTEQ01), which reached (-2.367686), which was significant at the significance level (5%).

7-2-7-4: Short-term relationship of the Iraqi agricultural products company AIPR

Table 12 shows the results of estimating the short-term relationship between electronic payments indicators and the market value of the Iraqi Company for Meat Production and Marketing (AIPM) over the study period. The table shows a short-term cointegration relationship, as evidenced by the value of the error correction coefficient (COINTEQ01), which reached (-0.120049), which was significant at a significance level of (10%).

Table 12 shows the results of estimating the short-term relationship between electronic payments indicators and the market value index of the Iraqi Company for Meat Production and Marketing (AIPM) during the study period. It is clear from the table that there is a short-run cointegration relationship, and this is evident through the value of the error correction factor (COINTEQ01), which reached (-0.120049), which was significant at the significance level (10%).

Model diagnostic tests are used to assess the validity and verify the underlying assumptions. These tests also help detect issues such as multicollinearity or heteroscedasticity to ensure the accuracy and reliability of the results. The table below shows the results of the heteroscedasticity test.

Table 13 shows that the joint test accepts the null hypothesis that the model does not suffer from the problem of heteroscedasticity instability, whether at the overall level or at the level of the four companies, because the significance is greater than 5%.

As shown in Table 14 and according to the correlation test between cross-sections, the model residuals do not include the problem of correlation between cross-sections, and according to the four tests, the significance level is greater than 5%.