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Pedroni's proposed test for panel cointegration considers heterogeneous intercept and trend coefficient across cross country.
Here, income is a function of the observation year times a trend coefficient plus a constant and error term.
If the trend coefficient is determined to be statistically significant (p value less than 0.05), then ( {widehat{Y}}_{it} ) is used as the predicted farm income for each year.
If the trend coefficient is insignificant, then the mean income level, ( {overline{Y}}_{it} ), is used as the predicted farm income for each year as expressed in Equation 4. {widehat{Y}}_{it}={overline{Y}}_{it} (4).
A positive time trend coefficient suggests that there is an autonomous increase in income inequality over time, with the Gini coefficient increasing by 0.0037 per year, after allowing for the effects of all other predictors in the model.
Fig. 2 Subregional climate changes from 1961 to 2011 in winter a rainfall amount, b rainfall days, and c temperature Table 1 Trend coefficient of precipitation amount (Pa), precipitation days (Pd), and temperature (T) during winter and summer in six subregions.
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Then, the trend coefficients were transformed into gravity perturbation on a regular (1^{circ }times 1^{circ }) grid.
Using a trend regression approach for a dataset covering 1972 to 2015, we find that most analysed trading rule specifications show negative trend coefficients.
The trend coefficients in different subregions are listed in Table 1; red and blue values passed the 0.95 significance test, and yellow values passed the 0.9 significance test.
Linear trend analysis showed that trend coefficients and the spatial patterns of trends were similar across all vegetation estimates and the entire study region, especially for areas where vegetation changed gradually.
Temporal trends include spatially homogenous temporal trend functions scaled by spatially varying trend coefficients.
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