## _Robustness to subjective bias_

We applied both classical statistical modeling and algorithmic modeling to the classification of the sample based on the pooled classification. This exercise led to high consistency of predictions regardless of the specific approach used. Overall the random forests method is the best performer, followed closely by the Logit model. But a relevant question is whether the prediction performance would have been similar had the sample classifications based on individual rounds of assessments been used instead.

We showed above that assessor characteristics and the nature of the protocol followed only had a modest impact on the classification of places in the sample, but their impact could potentially become significant when predicting the urban status for out-of-sample units. To evaluate this potential bias, we first trained the model on each of the eight classifications, including the pooled classification and the seven classifications based on individual rounds of assessments. To this effect we used the random forests method, given its higher prediction accuracy. We then generated a predicted classification and computed the percentage of agreement between this predicted classification and each of the other classifications.

The prediction model performs well regardless of which subjective classification is used for training and regardless of the subjective classification used for validation (table 7). The average prediction accuracy is between 84.8 and 88.4. Standard deviations are small in all cases. This confirms our previous finding on the high consistence between classifications.

# **5. How urban is India?**

Our proposed methodology can be used to shed light on the ongoing debate about India’s “true” urbanization rate. This can be done by applying the trained models from the sample to predict the urban status of all administrative units in our universe of places in 2011 and then estimating the population living in those administrative units we deem urban. This prediction can be compared with official estimates, with the outcomes of other studies and with recent global products that estimate land use.

## _The urbanization rate in 2011_

We chose as the benchmark to estimate India’s urbanization rate the pooled classification of places in the sample. Also, because of its higher prediction accuracy, we relied on the random forests method with the full set of covariates (key indicators, NDVI, NDWI, quadratic terms and interactive terms) as our preferred approach. If the predicted likelihood of being urban was above 0.5, we classified the place as urban; otherwise we considered it rural.

According to the census, 31.2 percent of the population lived in urban areas in 2011. But this figure corresponds to the entire country, whereas our universe of places excludes small states as well as villages for which information is missing. If only the 564,052 places considered in our analyses were retained, the census would yield an urbanization rate of 31.6 percent. This is only slightly higher than the 29.9 percent rate predicted by the random forests method with the full set of covariates.<sup>8</sup>

> 8     Predictions also fall within a close range of the official estimate when the Logit model or the LASSO method are used or when smaller sets of covariates based on both types of data are considered. The results are available upon request.

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