metadata: authors: 0: author: Sinha,Rishabh
count: India
docna: 0: docna: Crop Yield Convergence across Districts in
            India&#39;s Poorest State
docty: Policy Research Working Paper
subtopic: Climate Change and Agriculture,Crops and Crop Management Systems,Agricultural Economics,Food Security,Fertilizers,Banks & Banking Reform
teratopic: Agriculture,Finance and Financial Sector Development
abstracts: cdata!: Bihar, India's poorest state,
            witnessed impressive yield growth in each of its three
            principal crops over 2005–17. This paper examines whether a
            convergence in district yields accompanied the improvement
            in yields at the state level, thereby reducing regional
            inequalities in land productivity. The convergence test
            allows the idiosyncratic element of productivity to be
            time-varying, thus allowing yields to diverge in some
            interim phases. District rice yields appear to be converging
            towards a common growth path, but wheat and maize yields
            have been diverging. The sub-period analysis shows a trend
            of divergence for all crops going forward. The analysis also
            identifies district clubs, which are converging to similar
            steady states. The club classification transcends
            agro-climatic boundaries, indicating a need for policy
            action to aid yield growth in lagging districts. Finally,
            there is no evidence that the divergence in yields was
            driven by a divergence in credit allocation, highlighting
            the limitations of a macro credit-driven policy. Credit
            supply might not be enough when there are structural snags
            in the availability of direct agricultural inputs.
geo_reg_key: 517198,517191,517212
repnme: repnme: Crop Yield Convergence across Districts in
            India's Poorest State
display_title: Crop Yield Convergence across
            Districts in India's Poorest State : Crop Yield
            Convergence across Districts in India's Poorest State
listing_relative_url: /research/2020/07/32278017/crop-yield-convergence-across-districts-indias-poorest-state-crop-yield-convergence-across-districts-indias-poorest-state
topicv3: Commercial Banking m1326069 1236,Agriculture and Food Security m1326205 435,Crop Production m1326627 174,Fertilizers m1327354 175,Agricultural Credit m1327605 1962
publishtoextweb_dt: 2020-07-27T00:00:00Z
historic_topic: Agriculture,Finance and Financial Sector Development
origu: DECRG: Macroeconomics & Growth (DECMG)
no_of_pages: 42
author_keys: 0: author_key: 1411342
model_extractions: any WORLD BANK GROUP
Policy Research Working Paper 9339

# **Abstract**

Bihar, India’s poorest state, witnessed impressive yield growth in each of its three principal crops over 2005–17. This paper examines whether a convergence in district yields accompanied the improvement in yields at the state level, thereby reducing regional inequalities in land productivity. The convergence test allows the idiosyncratic element of productivity to be time-varying, thus allowing yields to diverge in some interim phases. District rice yields appear to be converging towards a common growth path, but wheat and maize yields have been diverging. The sub-period analysis shows a trend of divergence for all crops going forward. The analysis also identifies district clubs, which are converging to similar steady states. The club classification transcends agro-climatic boundaries, indicating a need for policy action to aid yield growth in lagging districts. Finally, there is no evidence that the divergence in yields was driven by a divergence in credit allocation, highlighting the limitations of a macro credit-driven policy. Credit supply might not be enough when there are structural snags in the availability of direct agricultural inputs.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at rishabhsinha@worldbank.org. .

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Crop Yield Convergence across Districts in India’s Poorest State

# Rishabh Sinha<sup>1</sup> The World Bank _Updated November 2020_

## **JEL classification:** O13; Q14; R11

**Keywords:** Crop yield convergence; Time-varying idiosyncratic productivity; India; Bihar districts; Rice; Wheat; Maize

1 Contact: 1818 H St NW, Washington, DC 20433, USA (rishabhsinha@worldbank.org). Thanks to two anonymous referees and the associate editor for their comments and suggestions which led to significant improvements. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Most recent version available here.
# **1   Introduction**

Beginning with Solow (1956), the convergence hypothesis has been a key feature of several neoclassical and endogenous growth models. Not surprisingly, an extensive and growing empirical body of research investigates the convergence of incomes and labor productivity across regional and national economies (Barro _et al._ , 1991; Barro and Sala-i-Martin, 1992 etc.). As sectoral convergence is directly related to aggregate convergence, few studies have undertaken analysis at a sectoral level, with a handful of them focusing on agriculture (Ball _et al._ , 2001; Ball _et al._ , 2004; Rezitis, 2010 etc.). Nonetheless, these tests of convergence do not allow for the idiosyncratic element of productivity to vary over time. Thus, there is no room for productivities to diverge in some phases even when convergence is achieved for the entire period. Such a test of convergence requires stricter conditions in which the convergence process is somewhat uniform.

In this paper, I follow the econometric specification developed in Phillips and Sul (2007), which allows the idiosyncratic element of productivity to evolve over time, thus supporting a scenario in which long-term convergence occurs even when inequality rises in some interim intervals. To the best of my knowledge, this paper is the first to employ the time-variant idiosyncratic specification to test convergence in agricultural productivity. Moreover, there exists a gap in the literature when it comes to examining agricultural productivity convergence in the context of developing countries. This is particularly alarming given the enormous role the sector plays in developing economies. I seek to contribute to this small literature by studying convergence in agricultural yields across districts of Bihar – India’s poorest state which has realized massive growth in yields during the period under study. It is vital to note, at the very outset, that crop yields are only a partial measure of productivity. Unfortunately, data constraints do not allow me to perform a multi-factor productivity (TFP) analysis. Hence, an examination of TFP trends may potentially yield different results. I return to the issue in the concluding section and reflect on how the convergence results may play out if TFPs are used as a measure of productivity.

To give some background, Bihar is India’s third most populous state and is home to more than 100 million people. It is also the nation’s poorest state with a per capita net state domestic product (NSDP) that is a third of the national average. In contrast, the situation in much better in Uttar Pradesh (UP) – India’s second-poorest state, where per capita NSDP is almost 50 percent higher (Reserve Bank of India, 2019). The state economy is still principally agrarian. More than 70 percent of the workforce derives its livelihood from agricultural activities (Census of India, 2011). Many observers believe that such an extreme dependence on agriculture together with low yields of cereal crops is the primary cause of the state’s economic woes and widespread poverty (Bansil, 2011). The low agricultural yields in Bihar are a long-standing issue and comparing the evolution of agricultural yields across neighboring states over time reveals its miserable position.

After a long period of stagnation, the eastern states of UP and West Bengal (WB) embarked on a path of agricultural yield expansion that began in the early 1980s. In contrast, the yield gain in Bihar was much weaker and short-lived even though coming off a low base (Pandey and Pal, 2000; Kishore, 2004). For instance, Bihar and UP had similar rice yields in 1980, but the latter produced 50 percent more output per hectare by the turn of the century (Kishore, 2004). Moreover, the rich endowment of agronomic resources makes the prevalence of low yields even more a cause of concern. Rice yield in WB is almost twice that of Bihar despite the former having less fertile land and lower irrigation facilities (Bandyopadhyay, 2009). Previous research highlights the role of various factors in explaining the 2
productivity deadlock in the state, including its colonial history (Banerjee, 2004; Banerjee and Iyer, 2005) and the incumbent land tenure system (Bhaduri, 1973; Prasad, 1974).

While yield levels remain low in Bihar, there has been an uptick in productivity growth over the last 15 years or so. The yields of all three major crops – rice, wheat, and maize, have doubled during the 2005-2017 period. The main objective of the paper is to examine whether these impressive gains observed at the state level have been widespread and have helped in reducing disparities in land productivities across the districts. Analyzing regional inequality in yields is important for several reasons. First, the crossdistrict differences are significant. For rice and wheat, the yield in most productive district was 7–8 times that of the least productive district in 2005 (Government of Bihar, 2010). Hence, the burden of low yields is felt differently, with the situation being more concerning in some districts than others. Second, the districts lie in different agro-ecological zones with variations in agronomic endowments. As such, the principal drivers of low productivity might vary across districts, and policies that contribute to productivity growth in some may fail to address the challenges faced by others. Thus, a convergence result will support continuing the ongoing efforts as far as regional aspects of agricultural policy are concerned. On the other hand, the absence of convergence will call for fine-tuning the policy to correct the situation in laggard districts. With this motivation, I test whether a convergence in district yields accompanies the aggregate yield improvement. To test the convergence hypothesis, I collate a district-level database of both annual production and area under cultivation for the main crops using information from multiple annual surveys. A valuable feature of this study is that I examine convergence in yields for the three main crops, which usually account for more than 90 percent of the gross own area at the district level. This crop-specific approach provides further richness to policy guidance. If inequality persists for a particular crop only, policy makers can focus narrowly on the crop-specific factors which are likely to be the cause relative to the more generic ones.

The econometric test of convergence developed in Phillips and Sul (2007) admits three outcomes – convergence occurs at the yield levels (absolute), convergence occurs at the yield growth rates (conditional), or a convergence does not occur. Absence of absolute convergence indicates a rise in the cross-district disparity in yields. As mentioned previously, the convergence test relaxes the assumption of time-invariant idiosyncratic effect. This opens the possibility of transitional cross-sectional divergence. I find evidence of conditional convergence in rice yields during 2005–2017.<sup>2</sup> In contrast, the convergence hypothesis is rejected with statistical certainty for wheat and maize.

The period under analysis is long enough to make a further inquiry which helps discern whether the divergence results are transitory or not. I divide the entire sample into two periods – 2005–2011 and 2012–2017, to see whether the patterns of convergence differ across the two sub-periods. The exercise presents interesting insights when considered with the results for the entire period. The overall convergence result for rice depends crucially on the developments in the 2005–11 period. There is no evidence of convergence happening in the second sub-period. Wheat yields were also converging during 2005–11 but started diverging in the later years, which was strong enough to reject divergence for the entire period. Inequalities in maize productivity across districts grew in both sub-periods. Yet, the pace of divergence has increased over the years. Thus, the district-level behavior for the entire period masks

> 2 The choice of 2005 as the initial year of analysis is incumbent on data availability as it is the earliest year for which such information is obtainable.

3
recent shifts in trends in each of the three principal crops. Neither of three crop yields exhibit a move towards convergence going forward.

Another advantage of adopting the convergence test proposed in Phillips and Sul (2007) is that it allows to ascertain whether overall non-convergence happens in the presence of club convergence (Baumol, 1986). Specifically, the rejection of the null does not preclude the possibility of club convergence. Certain subsets of districts may form a club, with the possibility of multiple clubs existing. Districts within a club can then converge either on an absolute or conditional basis.

In the context of Bihar, it means testing whether districts are forming clubs and converging at different levels of yields. Moreover, the identification of which districts constitute clubs is contingent on statistical properties of the data rather than an ad-hoc and ex-post taxonomy (De Long, 1988). The statistical identification has important implications for policy design, and I discuss this in detail later when presenting results. Given the lack of evidence of any convergence happening yields during 2012-2017, I examine if there is evidence of club convergence. For rice, I find that the southern districts form a fastgrowing club that is increasingly gaining ground over the north. Wheat and maize yields paint a different picture. Districts from all three zones (two from the northeast, three from the northwest, five from the south) make up the leading wheat club, which towers over others. The northeastern zone outpaces districts elsewhere in maize yields that align themselves in various lagging clusters.

A critical question that the analysis poses is what factors drive the divergence in rice and maize yields in the second sub-period. While a rigorous investigation of this query is outside the scope of this paper, I take a first step towards ruling out an important factor – supply of agricultural credit. Though not a control for the universe of inputs, credit holds a special status as it is closely tied to the usage of more direct inputs like seeds, fertilizers, machinery, etc. Moreover, multiple studies have found that agricultural credit has enabled the use of purchased inputs and has affected the input mix in India (Bhalla and Singh, 2010; Narayanan, 2016).<sup>3</sup> Thus, productivity growth might be lagging in some districts due to relatively lower credit allocation.

Using the credit data, I ask whether the supply of credit in the districts forming the lagging clubs has declined during 2012–17 relative to the districts in the leading clubs using a difference-in-difference approach. I do not find any evidence of the credit supply shrinking in the former relative to the latter. Credit expansion – both in absolute value and share, is higher in lagging rice clubs relative to the most productive club. The test also does not lend support to the credit hypothesis for the other two crops, and its presence can be reasonably rejected. The finding does not imply that productivity is unresponsive to credit, especially given the evidence that it encourages the use of inputs. Instead, in line with Das _et al._ (2009) – who find a positive but variable impact across states, the analysis here suggests that a similar phenomenon holds at the district level in Bihar. Credit might be more efficient in some districts and future research should focus on explaining the heterogenous impact as it has crucial policy implications.

This paper is most closely related to papers that study agricultural productivity convergence in the context of developing economies. For instance, McErlean and Wu (2003) and Wu (1995) test for regional convergence in agricultural productivity in China. Martin and Mitra (2001) consider cross-country

> 3 Yet, the evidence on the credit-growth relationship is varied. For instance, Binswanger and Khandkher (1995) and Subbarao (2012) estimate a positive effect, while Burgess and Pande (2005) and Narayanan (2016) find a negligible to weak impact.

4
convergence using a panel data set which consists of many developing countries. Mukherjee and Kuroda (2003) investigate convergence in productivity across Indian states during 1973–1993 and find no evidence of unconditional convergence. More recently, Mukhhopadhyay and Sarkar (2019) explore the convergence in agricultural productivity across Indian states during 2000-13 and find evidence of convergence in growth rates. Compared to these papers, I show that yields differ considerably across much narrower geographical regions (districts). In this light, the divergence results appear starker as these districts are closer in terms of exogenous agronomic endowment and are subject to similar institutional and policy environments. Finally, as reported earlier, the test of convergence that I employ is general enough to allow for idiosyncratic district-level productivity to be time-varying.

The rest of the paper observes the following order. The next section details the methodology succeeded by a discussion of the data used in the analysis. Section 4 reports the findings with Section 5 providing robustness checks on them. Finally, I conclude the paper by outlining the policy relevance of the study's learnings that apply more generally, and by discussing how the convergence patterns may change for multi-factor measures of productivity.

# **2   Methodology**

I employ the convergence test developed in Phillips and Sul (2007) to examine if the yields at the district level have been moving closer over time. The model features both common- and district-specific components. Specifically, the yield i of district in production period is given by i i (1)yy ii tt where i is the time-varying idiosyncratic element and ii is the common growth component. The log yy = bb μμ common growth component captures the effect of technology which is common across districts. For ii instance, all districts benefit from the availability of better-quality seeds. In contrast, bb μμ i denotes the ii relative share of district in μμ in period . bb Convergence of yields across districts can be expressed in terms of their ratios ii μμii tt i lim log yy ii→∞ jjii = 1 ∀ ii, jj (2) The condition in equation (2) is equivalent to a convergence of factor loading coefficients log yy lim<sup>= bb ∀ii (3)</sup> The number of observations in the panel is less than the number of unknowns as per equation (1). ii→∞<sup>bbi</sup> 5
(h g g( log Uu <u>x ‘)</u>
than an ad-hoc and ex-post taxonomy. Let me briefly sketch the procedure of identifying convergence clubs.<sup>6</sup> First, sort the districts decreasingly according to their yields in the last third fraction of the time sample. The second step is to identify a core group of districts. To do this, the -test statistic from the regression for all highest yield districts in step 1 are obtained. The subsequent step is to kk tt tt add districts to the core conditional on preserving convergence. The core group size is chosen by log tt maximizing subject to kk∈[2, NN]≥−1.65 . If no such exists, there is no evidence of club convergence. Conditional on existence of , the third step is to sieve districts for club membership. Let kk<sup>∗</sup> and ∗ kk kk denote the set of districts in the core group and its complement respectively. Taking a district from tt tt kk<sup>∗</sup> cc∗ kk<sup>∗</sup> kk one at a time and adding it to the core group, run the kk<sup>∗</sup> regression again. Filter the districts for whom GG GGcc kk the -test statistic exceeds 0.<sup>7</sup> Starting with the district with the highest -statistic, keep adding districts GG one at a time to the group till the -statistic for each subsequent enlarged group exceeds the log tt asymptotic tt 5% critical value of −1.65 . The fourth step follows the recursion of the above three steps with tt kk<sup>∗</sup> GG tt the left-over districts not getting included in the most recent club. The final step is to merge the identified clubs, if possible. The process follows iteratively beginning with the first two clubs. For example, test for convergence among members of club 1 and 2. If the test shows convergence, then merge them together and test for convergence between the merged club and club 3. Else, proceed to test convergence between club 2 and 3.<sup>8</sup> The next section discusses the data that I use to test convergence. log tt

# **3   Data**

The data for the analysis come from Bihar Economic Surveys (BES) (Government of Bihar, 2010– 2019). Since 2010, the BESs started reporting both the annual production and the gross area under cultivation of many crops at the district level. The annual surveys jointly provide data for agricultural production in 13 periods. The first period for which the data are available is 2005-06. Utilizing the two series, I construct the district-wise crop yields. Hereafter, I refer to the production period overlapping two calendar years by the initial year for the sake of exposition (for example, the year 2007 represents the production period 2007-08). There are 38 districts in the state. Barring Arwal, the surveys have no gaps in data. Hence, I drop Arwal from my analysis. There are three major agro-climatic zones (ACZ) in Bihar - northwest alluvial plain (NW), northeast alluvial plain (NE), and south alluvial plain (South). The Himalayan rivers feed the northern zones which are flood prone whereas the southern zone is adversely affected by the onslaught of droughts. Figure 1 shows the districts and their ACZ classification.

The district-wise data on production and cultivated area for the three major crops – rice, wheat and maize, are available starting in 2005. In recent years, the surveys have also started reporting such figures for other crops like pulses, oilseeds, sugarcane etc. Nonetheless, the three cereal crops account for the bulk of the area under cultivation. The gross area under cultivation dedicated to rice, wheat or

> 6Refer to Phillips and Sul (2007) and Phillips and Sul (2009) for details on the clustering procedure.

> 7It is possible to aim for more clubs by increasing the threshold for -test statistic. I restrict my choice of the critical value to 0 in order to target the most conservative number of convergence clubs. 8 The club identification follows a slightly different algorithm relative to Phillips and Sul (2007, 2009). Specifically, I tt follow the revision suggested in Schnurbus, Haupt and Meier (2017) which makes the manual interventions in the former procedure redundant. The analysis makes use of STATA's psecta package (Du, 2018).

7
maize ranged from about 75 percent in Patna to almost 100 percent in Gopalganj during 2017. A total of 30 districts report a share in excess of 90 percent. Among the three, rice and wheat are the dominant crops and account for 50 and 30 percent respectively. Another 10 percent of the state’s sown area is used for maize production with districts in the north leading the charge. Table 1 reports the descriptive statistics of the data. Yields in Panel A corresponds to the entire balanced panel consisting of 37 districts and 13 years. As the analysis also focusses on convergence over time, Panels B and C provide statistics by splitting the time-series into two sub-periods (2005-2011 and 2012-2017).

At the state level, all crops report an expansion in yields. The magnitude of gain is also similar across crops with yield in the last period being just over twice the initial level. Nevertheless, there are variations in yield improvements across the ACZs. Figure 2 plots the crop-wise mean ACZ yields. Rice productivity was highest in the southern zone in 2005. Thereafter, the productivity surge in the region outpaced the gains in northern zones. As a result, the north-south yield gap broadened. In wheat production, the largest percentage expansion in yield occurred in the northeastern districts. The ACZ had the lowest mean yield initially. The southern zone continues to be the most productive region. However, its below average increment in yield has led to a closing of the gap across ACZs. Trends in maize productivity resemble that of rice production. The percentage yield gain has been largest in the northeastern zone which led other zones to begin with. Yields in the northwest zone and the south zone mostly remain close to each other. Though in some intermediate years, productivity in the latter outperforms the former by a distance. In summary, the yield trends at the ACZ-level suggest divergence in rice and maize yields and possible convergence in wheat productivity.

Another metric to gauge regional disparities is the yield differences between the 90<sup>th</sup> and 10<sup>th</sup> percentiles. In 2005, the productivity of the district at the 90<sup>th</sup> percentile was 5.4 and 3.0 times that of the district at 10<sup>th</sup> percentile for rice and maize respectively. The corresponding figures in 2017 declined to 2.3 and 1.5 respectively. The absolute gap in rice yield, though, presents an opposite trend. The yield gap in rice increased from 1,740 to 2,000 kilograms per hectare over the same period. I observe an expansion of both relative and absolute yield gaps in the case of maize production. There exists an ambiguity when determining the existence of convergence using the above metrics which makes it essential to formally test the hypothesis.

In the next section, I conduct the formal test of convergence using district-level data and employing the methodology outlined in section 2. In the formal analysis, I smoothen the actual annual yield series by HP filtering them using a parameter of 40 to remove the cyclical component from the actual series. The procedure also allows me to consider convergence at a sub-group or club level. Thus, it is possible to identify clusters that are converging to lower levels of yield. A feature is that there are no restrictions on club formation ex-ante. As such, districts from different ACZs can lie in the same club. The quantitative analysis indeed finds evidence of club formation that cuts across boundaries dictated by agroclimatic zones.

# **4   Results**

The following two sections discuss the results of the convergence tests. I begin with testing for convergence in yields during 2005-17 and in two sub-periods of the panel. Following, I investigate if there is evidence of club convergence given the evidence of divergence in yields more recently.

8
# **4.1   Overall convergence: Log t-test containing all districts**

Table 2 reports the test results for the overall convergence. Recall that the null hypothesis is that district yields converge over the 13 years. The estimate of the convergence parameter = 1.724) for rice lies firmly in the positive territory with a reasonably small standard error. Hence, the null of rriiccrr γγ (γγ� convergence cannot be rejected. However, the point estimate being less than 2 indicates only conditional convergence, i.e., convergence in yield growth rate and not levels. Evidence of convergence of any sort is absent for wheat and maize. The point estimates of for both crops are negative. Moreover, the precision is high enough to reject the null at 5 and 1 percent level of significance for wheat and maize respectively. γγ Figure 2 suggests a difference in convergence behavior over the years. For rice and maize, the yields across ACZs move together in a narrower band initially. The southern region pulls ahead in the later years in rice productivity. Similarly, the northeastern zone realizes substantially higher yield gains in maize production after 2015. In contrast, wheat yields display no notable behavior with productivity differences across zones being small in several years.

I formally test for such time-varying behavior at the district level by dividing the time series into two periods. Sub-period I ranges from 2005 to 2011 and Sub-period II from 2012 to 2017. Table 2 also contains the convergence statistics for the two sub-periods.

There is evidence of conditional convergence in rice yields for the entire period. The sub-period analysis shows that the convergence during the entire period is driven primarily by the developments in Sub-period I. The -test finds evidence of a stronger convergence in the first sub-period = 2.864) in which districts were converging in yields. However, such strong convergence in rice yields does rriiccrr,05−11 log tt (γγ� not hold in the second sub-period = −0.959) . The negative coefficient suggests divergence and a low standard error implies that convergence can be ruled out with considerable certainty (1 percent rriiccrr,12−17 (γγ� level of significance).

The behavior of wheat yields is also dissimilar across the two sub-periods and resembles the preceding finding. There is weak evidence of convergence in growth rates in the initial period, which is opposite of what I find for the entire period. Divergence in wheat yields is more acute in the later years as the convergence parameter moves further into the negative territory = −1.610) . Moreover, the point estimate is identified with a lot more precision. wwhrreeii,12−17 (γγ� Maize yields have diverged over the last 13 years. In contrast to the other crops, I find evidence of divergence in maize productivity in both sub-periods. Still, the divergence is more prominent in the latter subperiod = −1.696) . The convergence parameter not only moves firmly into negative territory during the 2012-17 period, it is more precisely estimated. mmeeiimmrr,05−11 mmeeiimmrr,12−17 (γγ� = −0.382;γγ� In summary, changes over the last 13 years hide critical trends in yield convergence. Over time, rice and wheat yields have moved from a regime of conditional convergence towards a regime of divergence. Inequalities in maize productivity across districts grew in both sub-periods. Yet, the pace of divergence is increasing given the overtime change in the point estimate of . Conditional that there is role of policy in addressing unbalanced yield growth, the obvious implication of the crop-specific nature γγ of convergence is that the policies need to be designed at the level of individual crops. The results for the initial sub-period show that convergence and divergence may happen concurrently depending on the crop 9
in question. Therefore, a general approach towards boosting agricultural productivity in lagging districts may not help in reducing cross-district inequalities in yields.

# **4.2   Club convergence during 2012-2017**

The overall convergence test poses a strict benchmark in which all districts converge to a common level of yield or yield growth rate. The rejection of the null does not preclude the possibility of club convergence. Certain subsets of districts may form clubs and convergence can happen at a disaggregated level. Hence, it is worthwhile to check if the divergence in crop yields in the later period occurs in the presence of convergence at the club level in which clubs achieve different steady states. To identify the clubs, I restrict my attention on the later sub-period (2012-17) as there is definite evidence of divergence for each crop.

To reiterate, the identification of clubs is not incumbent on any observable characteristics of the districts except how they differ in terms of crop yields. For example, it is possible to group districts into clubs based on their ACZ classification and test whether cross-club convergence is evident. However, it is not straightforward to interpret divergence at the club level in which clubs converge to different levels as inefficient and demanding policy action. It is possible that an ACZ-based classification captures differences in agronomic endowment of districts. As such, the club-level divergence can be a result of such variations in which districts with better natural endowment move towards higher yields. In this context, a club identification which is independent of such classification rules offers insights on whether the patterns suggest some inefficiencies. For instance, it will be difficult to rule out efficiency if club formation follows ACZ taxonomy. Districts lying in the same ACZ have similar natural endowments and should have yields that are close to each other. Therefore, a distribution of districts across clubs which cuts across ACZ boundaries will signal inefficiency.

Table 3 presents the results of the exercise and Figure 3 maps the distribution of districts across the different clubs. Club NC represents districts that do not fall in any of the converging clubs.<sup>9</sup>

## **4.2.1   Rice**

There is a noticeable pattern of club convergence in rice yields during 2012-2017. The estimates of (column (1)) for each club correspond to the convergence happening across districts in the respective club. The evidence of club convergence contrasts with divergence for the sub-period reported in Table 2. γγ All coefficients are positive, and the one-tailed tests of convergence are not rejected. The clustering methodology classifies 35 districts into three clubs that experience conditional convergence while failing to assign two (Kaimur and West Champaran) in any. As mentioned previously, the method of assigning districts to clubs treats the yields in the final years as an input to guide hierarchy. Districts in club 1 are likely to have higher yields in 2017 relative to members of club 2, and so on. The leading club consists of 16 districts and all of them except one (Begusarai) lie in the southern ACZ. Additionally, Kaimur is the only southern district which is not a member. The finding is consistent with the pattern observed in Figure 2 which showed that the southern region was on a faster growth path. The remaining 19 districts fall into two lagging clubs with 8 districts constituting the club with lowest yields in 2017. The distribution of

> 9 Table A.1 in the appendix lists the districts according to their club classification for each crop.

10
districts across the two lagging clubs does not align with ACZ boundaries. A large share of northwestern districts lies in club 2 whereas the northwestern districts are almost equally split between clubs 2 and 3.

Comparing mean yields of different clubs provides additional insights. Figure 4(a) plots the mean yields (in logs) for the three clubs. There exist marginal differences in the growth rates in the initial years as the slope varies little across clubs. Nonetheless, the paths diverge in the later years. Club 1 grew much faster than club 2. Yield growth in club 3 stagnated and its yield is reasonably lower than club 2 in 2017. In 2005, the club stood slightly ahead of club 2. Contrasting Figure 4(a) with Figure 2(a) highlights the importance of the clustering procedure. The latter shows that the yields in the two northern zones remain close to each other with no clear evidence of divergence. On the other hand, the clustering method identifies two diverging clubs consisting of leading and lagging districts in the north. Barring Saharsa and Supaul, all districts in the northeast are members of club 2. Five districts in the northwest zone – Darbhanga, Samastipur, Sitamarhi, Siwan, and Vaishali, also fall in club 2 and have performed substantially better compared to the six lagging districts of the region. Finally, the mean yields of clubs varied over a much narrower range in 2005 but have grown apart over the years.

In summary, there is evidence of club formation in the later years. Southern districts comprise a fast-growing club that is increasingly gaining ground over the north. The northern districts fall into two lagging clubs in which one experiences modest growth while the other faces stagnation. The formation of the two lagging clubs transcends the ACZ classification.

# **4.2.2   Wheat**

In sharp contrast to rice yields, the full panel test in Table 2 finds divergence in wheat yields. Yet, the sub-period tests for the two crops are similar. After converging conditionally in Sub-period I, the inequalities in yields of both crops increased in Sub-period II. The club convergence tests identify the formation of five converging clubs for wheat. Table 3 shows that the point estimate for the leading club is negative. Still, the standard error is not low enough to allow for rejection of the null. The evidence of conditional convergence is stronger for the non-leading clubs.

Figure 4(b) plots the mean yields of the wheat clubs. Till 2011, the yields remain close in line with the evidence of sub-period convergence. The paths branch out in the later years. The identified clubs do not line up with ACZ boundaries. ACZ representation in clubs is even more diverse relative to that of rice clubs. Districts from all three zones (two from the northeast, three from the northwest, five from the south) are present in the leading club which experienced exceptional yield growth since 2005. The club towers over the rest even though it was at the median initially. The next three clubs also consist of districts across zones. East and West Champaran make up the lagging club and experience loss of yield bucking the trend elsewhere. The club yield in 2017 is not very different from 2005, making the situation even more concerning. The loss of relative position also reflects this as the club led most districts initially.

# **4.2.3   Maize**

Results in Table 2 attest that maize yields started diverging at a higher pace in the second subperiod. Still, there is evidence that such extreme divergence occurred in presence of club convergence (Table 3). Thirty-four districts map into four converging clubs while three (Katihar, Lakhisarai, Sheikhpura) fail getting associated to any. The evidence of conditional convergence is stronger for the two leading 11
clubs. Though the evidence is weaker for the latter two given the negative estimate of , the null of convergence is not rejected at 10 percent level of significance. γγ Figure 4(c) tracks the mean yields of the clubs over the years. The yield growth rate varies over a tight range initially but diverges in the later period. The growth in the leading club outpaces growth elsewhere, effectively creating a massive yield gap. The next two clubs do not see any marked difference in growth rates over the two periods. However, a higher growth rate for club 2 leads to a rise in the gap between the two clubs. The lagging club 4 fails to maintain even the modest growth of the first period and records a falling yield. Looking at the ACZs, it is no surprise that the northeastern zone has performed better given the evidence in Figure 2(c). The leading club exclusively consists of districts from the region with the remaining regional districts falling in club 2. However, club 2 does not entirely consist of northeastern districts. Of the 13 districts in club 2, seven and four districts lie in the southern and northwestern zones respectively. Like in the case of rice yields, the formation of non-leading clubs does not follow ACZ classification more generally. The other two regions have a balanced representation in clubs 3 and 4. The figure also shows the vast difference in the fortunes of the clubs. The mean log yield in the leading club increased by more than 75 percent during 2005–17. Yet, the mean log yields in clubs 3 and 4 in the most recent year are lower than that of the leading club in 2005.

The key takeaway is that Sub-period II is characterized by increased divergence in maize yields. Still, club convergence materialized at significantly difference levels. While the northeastern region pulled ahead, districts in other regions formed clusters. The worst performing cluster consisting of five districts lying in both the northwestern as well as the southern region experienced not much expansion during 2012-17.

# **4.3   Agricultural credit over the two sub-periods**

The previous two sub-sections show that there is vast heterogeneity in yield progression across districts. Some have seen significantly higher growth while some have also witnessed contraction of late. There exists evidence of club convergence in which districts are converging to yield levels with considerable variation. Both relative and absolute gaps in yields between the leading and the lagging clubs appear to be increasing. More importantly, the results show that the club formation does not align well with the ACZ classification, especially so in the non-leading clubs. Therefore, it is likely that the divergence in yields indicates inefficiency in which districts in the lagging clubs are not able to reap productivity gains.

To address the concern of low gains in lagging districts, it is essential to identify areas that policy could target or where the current policy is lacking. While I am not attempting to address this issue in detail, I check whether the differences in the supply of agricultural credit can explain the divergence patterns observed more recently. Though not a control for the universe of agricultural inputs, credit holds a special status as it is closely tied to the usage of more direct factors such as seeds, fertilizers, machinery, etc.

The government also believes the supply of credit to be a critical policy instrument when it comes to boosting agricultural productivity. Credit allows farmers to make many decisions that are directly related to productivity – adoption of capital-intensive technology, managing risks associated with investments, using yield-enhancing inputs like better seeds and fertilizers etc. Moreover, many observers argue that cooperative credit crowds out borrowing from local moneylenders as they carry a much lower rate of interest. The state economic surveys contain consistent long time-series data on the supply of 12
agricultural credit for each district that goes back to 2007. Agricultural credit is made available via various institutions that include the commercial banks, the regional rural banks and the central co-operatives. Commercial banks account for more than half of the total credit. Though the co-operatives’ share is less than 10 percent, its share has been consistently rising over the years. Agricultural credit has seen exponential growth over the years with aggregate credit in 2017 being 11 times that in 2007. Additionally, agriculture commands around 60 percent of the priority sector lending, illustrating its central role in development policy. In contrast, small and medium enterprises account for approximately 25 percent.

A potential mechanism that can explain the divergence in the latter period might operate via the credit channel. If access to credit only increased for districts in the leading club(s), then it is reasonable that most productivity gains flowed to such districts, leaving the districts in other clubs behind. I test this hypothesis using a difference-in-difference (DiD) approach captured in equation (9): i 1 2 4 5 i (9) where λλ = ββi CC represents the credit flowing to district ii + ββ PPTTPPttii + ββ3CC(CCii × PPTTPPttii) + ββ λλ̅ii(2007−11) in year + ββ . The dummy ZZii + εε in the above equation denotes the club affiliation of district and can be thought of as various groups of a standard DiD approach. ii λλ ii tt CC In this setting, the leading club constitutes the control group while the lagging clubs (Club 2 ii onward) serve as the treatment groups. The hypothesis is that the lagging clubs received lower agricultural credit in the latter period (2012-2017) relative to the leading club. This treatment period is captured by the dummy which equals 1 for years beginning 2012. The DiD coefficients on the interaction of and shed light on the hypothesis. To see this, consider the change in agricultural credit over ii 3ii any years 1 and PPTTPPtt 2 1 2 ∈[2012,2017]) . For a district in leading club, ββ equals 2 . ii ii ii CC PPTTPPtt Δλλ Similarly, the change in credit in district in a non-leading club equals 2 . Hence, the coefficient ii tt tt (tt ∈[2007,2011], tt ii Δλλ ββ captures the marginal difference in flow of credit across districts in the two clubs which occurs over 3CC jj CC ββ + ββ the two sub-periods. A negative value of indicates that districts in the lagging club received lower 3CC ββ credit during 2012–17 relative to districts in the leading club, thus supporting the hypothesis that the 3CC allocation of credit led to divergence in yields. Finally, I add controls for average credit ββ i allocated to districts during 2007–11 to account for size considerations and ACZ-level dummies . λλ̅ Columns (1)–(3) of Table 4 report the results of the DiD regression. The unit of the dependent ZZii variable is 10 million Rupees, which roughly corresponds to US$135,000 under the current exchange rate. Let me begin by considering the credit allocation across rice clubs (column (1)). Recall that the coefficient on dummy equals 1 for years 2012 and later, and 0 otherwise. The coefficient is positive and significant, and the point estimate indicates that the annual supply of agricultural credit in districts of the ii PPTTPPtt leading club expanded by nearly 7.1 billion Rupees in the latter period. However, for the credit channel to explain the divergence, the supply needs to expand by less (or contract) in the lagging clubs. The DiD interaction coefficients in the next two rows capture this effect. The DiD coefficient for club 2, which immediately follows club 1 in terms of yields, is positive. However, the estimate is noisy and insignificant. 3CC ββ Thus, the expansion of credit in club 2 districts during the latter sub-period is not significantly different from that in the leading districts. The DiD coefficient for club 3 – the least productive club, is positive and statistically significant at the 10 percent level. The point estimate suggests that the supply of annual credit in club 3 districts outpaced that of the leading districts by 1.3 billion rupees. These results conclusively reject the hypothesis that a divergence in credit allocation led to a divergence in rice yields across districts.

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Now, let's examine whether the credit channel can explain the divergence in wheat yields by analyzing DiD coefficients in column (2). Like rice, the DiD coefficient on the dummy is positive and significant. The annual supply of credit in the leading districts was higher in the later period by around 8.1 ii PPTTPPtt billion Rupees. The corresponding increase in districts of club 2 was not significantly different. The DiD interaction coefficients on clubs 3 and 4 are negative and significant at 5 and 10 percent level. The point estimates show that credit expansion in clubs 3 and 4 was 2.0 and 1.3 billion Rupees lower than in club 1. Finally, districts in the least productive wheat club – club 5, outmatched their counterparts in the leading club. Credit growth over the two periods in the former outran that in the later by almost 4.5 billion Rupees. Attributing divergence in wheat yields to shifts in agricultural credit is not straightforward, given the evidence. On the one hand, it seems that a milder expansion of credit in clubs 3 and 4 led them to fall behind clubs 1 and 2. Yet, districts in club 5 experience the least rise in yields, despite witnessing the most robust extension in credit.

Lastly, column (3) contains the results for maize yields. Not surprisingly, given the previous results, the supply of credit in the leading club was significantly higher in the later period. On average, credit expansion in districts of club 2 outpaced that of the leading club by around 1 billion Rupees. Nonetheless, the point estimate lacks significance, and the hypothesis of no DiD cannot be rejected. Moving on to the two least productive clubs – 3 and 4, I find the DiD interaction coefficients to be positive and significant. The point estimates show that agricultural credit expansion in the later period in clubs 3 and 4 exceeded that of club 1 by 1.6 and 3.3 billion Rupees. Qualitatively, the estimates are opposite to what one may expect if the credit-based explanation had merit. Instead of being negative and increasing in magnitude, the DiD estimates are positive and rise as clubs fall further behind in yield.

I supplement the above results by considering another dependent variable – the district shares of agricultural credit. As such, i and in equation (9) now refer to the share of the total agricultural credit received by district in year and district ’s average share during 2007–2011. Columns ii(2007−2011) (4)–(6) of Table 4 report the results for the three crops. Recall that the earlier results indicate that credit λλ λλ̅ ii tt ii flow increased across the board, including the leading districts. Given that district shares sum to unity, this is no longer a possibility. Examining the dummy for rice clubs, I find that the share of districts in the leading club declined by 40 basis points in the 2012–17 period and is statistically significant at the 5 percent level. The ii PPTTPPtt decline is quantitatively considerable, given that the average share of districts during the 2007–11 period was 2.9 percentage points. The DiD estimates in the next two rows show that both lagging clubs realized an expansion in their credit shares – 70 and 80 basis points for club 2 and 3. The coefficients are also estimated with precision and are highly significant.

A similar trend applies when analyzing shares across wheat clubs. The leading club realizes a share contraction of 60 basis points. In contrast, all lagging clubs witness a rise in the shares. The magnitude of expansion varies narrowly across the clubs and ranges between 70–90 basis points. Barring the least productive club, the DiD coefficients are always statistically significant.

The change in shares is somewhat different for maize clubs. The coefficient on the dummy is positive and significant at the 10 percent level, and the point estimate suggests a 50-basis points expansion for the leading club. This expansion comes at the expense of districts in club 2 that witness almost a percentage point reduction in the credit share. Although the coefficients on the interaction terms 14
for clubs 3 and 4 are negative, the estimate lacks statistical power. Like in the case of wheat clubs, when examining the absolute value of agricultural credit, the nature of DiD coefficients here fails to establish the link between credit mechanism and the divergence in maize yields.

In summary, the DiD analysis shows that the intertemporal variation in credit cannot explain the divergence in yields across clubs. Credit expansion - both in absolute value and share, is higher in lagging rice clubs relative to the most productive club. The results are not as straightforward for wheat and maize clubs. Still, the support is even weaker for the credit mechanism, and its presence can be reasonably rejected.

# **5   Robustness checks**

This section conducts robustness checks to address two critical concerns surrounding the results presented earlier. First, the club convergence tests in section 4.1 rely on an arbitrary criterion to break time-series into two sub-periods – creating two samples of approximately the same length. Is there a statistical basis to divide the series instead of using the ad-hoc criteria? Second, as the regression equation (8) exploits the cross-sectional variance, it does not allow controlling for district-specific effects, including the ACZ classification of districts. A possibility is that the across-ACZ factors drive the divergence results, even when district yields within an ACZ are converging. To some extent, the club convergence analysis undermines this prospect indirectly as club participation transcends ACZ boundaries. Still, it is possible to investigate the concern more directly. The next two sub-sections discuss the two issues in that order.

## **5.1   Statistical identification of sub-periods**

To see if there is a statistical reason to divide the time-series, I conduct a structural break test for each district-crop pair. The tests make use of the same smoothened series used in the earlier analysis. In the first step, the log of district yield is regressed on its lag and a constant. In the following step, a structural break test with an unknown break date is conducted to determine if there is a considerable shift in the data. The test allows for only a single break and is robust to unknown forms of heteroskedasticity.

Except for a few cases, the test identifies a break for almost all district-crop pairs. Figure 5 plots the distribution of break years for each crop. Just less than 50 percent of the districts report break-in rice yields beginning in 2011. A statistical break happens in 2012 for another sizable share, which maps to the year used arbitrarily in the earlier analysis. The mode of break year for wheat yields is 2013, with several breaks occurring in the prior year as well. Maize shares its modal year with rice. However, a considerable share of breaks take place in other years as well and are somewhat evenly distributed across them. The modal year serves as the support to split the time-series into two samples, i.e., 2005-2010 and 2011-2017 serve as two sub-periods for rice and maize, whereas 2005-2012 and 2013-2017 are the corresponding periods for wheat.

Recall the baseline results presented in Table 2 (row 2). District yields were converging for rice (absolute) and wheat (conditional) in the earlier years (2005-2011) but were diverging for maize. In contrast, all three crop yields were diverging in the later years (2012-2017, row 3). The robustness results reported in Table 5 delivers the same conclusion, which is somewhat expected. The modal year-based approach creates sub-periods that are not very different from those obtained arbitrarily. It decreases the 15
length of Sub-period I by a year for rice and maize and extends that of maize by a year. The point estimates of the convergence parameter alpha across the two approaches are close and often within the 95 percent confidence interval of each other. Finally, there is no difference in the level of significance attached to the estimates in Tables 2 and 5.

The findings related to the credit supply presented in the earlier section are also robust when using the statistical approach of identification. For brevity, these results are relegated to appendix Table A.3.

# **5.2   Convergence results within ACZs**

A second concern with the baseline convergence test is that it is not able to control for ACZ classification of districts. Hence, it is difficult to rule out the possibility of within-ACZ convergence. However, it is straightforward to test this hypothesis by running the convergence tests at the ACZ level.

Table 6 presents these results that complement the ones reported in Table 2. In each panel, the sample is restricted to districts that lie in the corresponding ACZ. Like in the baseline case, Table 6 informs about convergence during the entire period and the two sub-periods. First, let's look at column (1) that tabulates the rice estimates. The baseline results showed that rice yields were converging for the entire period. However, it was primarily driven by trends in the earlier years, as there was definite evidence of divergence in Sub-period II. The estimates from Southern districts (Panel A) do not fit this pattern, as the later period is not characterized by divergence. Still, the finding is not strictly inconsistent. There is definite evidence that the strength of convergence has weakened significantly in Sub-period II. The Southern districts appear to be on divergent paths, and the convergence test may fail in the future as more data come in.

While not entirely matching the baseline results, the estimates from the northwestern (Panel B) and the northeastern (Panel C) districts tell a similar story. Both ACZs report absolute convergence for the entire period, but the point estimates suggest divergence in Sub-period II. The later period estimate for northeastern districts lacks precision, and it is not possible to reject convergence with any statistical power. The robustness test confirms that, as in the baseline, rice yields within ACZ are diverging, often from a path of convergence.

Now, let's consider the wheat estimates reported in column (2). The baseline tests show a divergence for the entire period driven by developments in Sub-period II. There was evidence of conditional convergence in the earlier period. The within-ACZ tests for the southern districts show a similar pattern. It is not possible to reject the convergence hypothesis either in Sub-period I or for the entire period. Yet, the large standard errors around the point estimates highlight the uncertainty around this finding. The 95 percent confidence interval includes estimates that fall in the divergence region. At the same time, the evidence establishing divergence in Sub-period II is compelling. The within-ACZ tests for the two northern ACZs are broadly in line with the baseline findings. The point estimates are below zero for the entire period and the later sub-period, implying divergence. Like in the baseline, the convergence is not rejected in Sub-period I.

Finally, column (3) reports the within-ACZ estimates of the convergence parameter for maize. The baseline results in Table 2 showed that yields were diverging for the entire period and in the two subperiods as well. The point estimates are higher in magnitude in the later period, suggesting that the pace 16
of divergence increased over the years. These findings extend to the two northern zones when I conduct the within-ACZ convergence tests. In contrast, the convergence hypothesis holds for in Sub-period I in the southern zone. Still, the corresponding point estimate is barely in the positive territory and has large standard errors. But like in the baseline, districts in the southern zone exhibit divergent yields for the entire period, which becomes more pronounced in the later sub-period.

In summary, the within-ACZ tests complement the earlier findings. Though there are minute differences in convergence patterns across zones, the principal learnings from the baseline apply to them all. There is definite evidence of divergence in the later period. Furthermore, the divergence represents a weakening of the earlier trend. Either the yields were converging or were diverging at a slower pace in the earlier years. These findings extend to each crop and ACZ.

# **6   Discussion**

In this paper, I test for convergence in crop yields when idiosyncratic element of productivity can vary across time. The specification allows for disparities to rise in the interim phases before an eventual convergence is attained, thus offering a more general test of convergence. I apply this novel technique to examine convergence across districts in India’s poorest state which saw a massive rise in yields during the period of analysis. The analysis offers interesting insights that have important implications for policy.

First, I find that overall convergence holds for rice yields while wheat and maize yields appear to be diverging. The pertinent question is to decipher whether developments over the years signal a move towards convergence given that the econometric model allows for divergence to happen in some initial phases. For example, is the divergence of wheat and maize yields a temporary phenomenon? Dividing the period under analysis into two sub-periods paints a different picture. The divergence pattern is more pronounced in the later period, ruling out convergence going forward, at least in the short-to-medium term. For rice, the signs are even more ominous. The divergence in the later period follows a period of absolute convergence in which districts were moving towards a common yield. The methodology not only relaxes the assumption of time-invariant idiosyncratic element but also allows for inferring future developments given the patterns of convergence in the sub-periods.

Second, the econometric technique identifies convergence clubs independent of any ad-hoc and ex-post classification rule. A valuable outcome is that these clubs can be compared to benchmarks to determine if club-convergence is inefficient, leaving some room for policy intervention. For example, it is reasonable that more fertile districts will converge to a higher steady state. In the case of Bihar, I find that club formation transcends ACZ boundaries which maps to the exogenous agronomic endowment of districts. Hence, there exists an argument for agricultural policy to address lower gains in lagging districts. It is alarming that rice yields in the northeastern region have grown faster than in the northwestern zone despite rice not being a primary crop for the former. On the other hand, yield growth has been robust in the south which receives lower rainfall which is surprising as water is critical for rice production.

Third, the analysis highlights the importance of bringing many crops under investigation when performing convergence tests for agricultural productivity. The results are specific to the crop under study and it will be incorrect to generalize the findings from one to the other. A direct implication is that agricultural policy should also become crop specific. Macro or micro interventions that deliver results for 17
one crop might fail for another. Finally, it is in this context that I test whether the divergence in yields is associated with the allocation of agricultural credit. The results are inconsistent with the credit allocation hypothesis. The key takeaway is that there are limits to following an umbrella policy in which the supply of credit solves all problems. Credit might not be enough when there are structural snags in the availability of more direct agricultural inputs.

The points above summarize the analysis’s three critical policy implications. Let me conclude by raising one final point that I mentioned in the introduction. The convergence tests make use of crop yields, which are only a partial measure of productivity. As such, there is no guarantee that the convergence findings will extend to multi-factor measures of productivity. Of course, lack of data on inputs is the limiting reason why the analysis relies on yields, and hence, a formal test of such concerns remains elusive. But can adjustment be made using the relationship between TFPs and yields observed elsewhere? To make progress, I use TFP measures from Avila and Emerson (2010). The estimates from the study help in adjusting the district yields in Bihar to obtain quantitative guidance on how findings might change if TFPs are used instead of the partial measure.

Before I outline the adjustment, let's first consider why the convergence tests may yield different outcomes for the two productivity measures. One option is to ascertain the relationship between yields and TFPs, and a positive association might seem sufficient to conclude that the convergence tests are robust to the choice of measure. Though reasonable, such reasoning does not suffice. Instead, what matters is whether the _bias_ present in yield (as a proxy for TFP) is systematically correlated with yield or not.

To see this, reflect on the divergence outcome and suppose that as a proxy for TFP growth, yield growth always overestimates it. If the difference between the two rates is uncorrelated with the latter, then the convergence results from one should be a reasonable first-order approximation for the other. On the other hand, divergence obtained using yields may come under threat if the difference becomes systematically correlated. Of interest is the case where the excess of yield growth over TFP growth (bias) is positively correlated with the former. In other words, differences in TFP growth across districts will be smaller than the variations in yield growth. Hence, the divergence in yields may not hold for the multifactor measure if the across district variations reduce sufficiently after adjusting for the bias.

Now let me get back to the case of Bihar. The strategy to correct the bias in district yields is to exploit the yield-TFP relationship from Avila and Emerson (2010). The study calculates annual TFP growth rates for several developing countries using output and input<sup>10</sup> data for two 20-year periods – 1961-1980 and 1981-2001. As it also provides the growth rates of output and inputs separately, it is possible to back out yield growth. Figure 6 plots the bias against the estimates of yield growth and confirms the positive association between the two variables. The coefficient of correlation is modest but also highly significant. Furthermore, note that the bias often lies in the negative zone. Yield growth not only overestimates TFP growth by a larger amount when the former is higher but also underestimates the latter when lower. Hence, in addition to exerting a larger downward force in districts with higher yield growth, a move towards the TFP measure also apply an upward push in the lagging ones, further putting the divergence result under threat.

> 10 Inputs include land, labor, fertilizer, seeds, tractors and combine harvesters.

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I use the bias-yield relationship observed in Figure 6 to estimate district TFPs.<sup>11</sup> The principal assumption is that the dependence continues to hold for districts in Bihar. I also assume that the relative yields in the initial year reflect differences in relative TFPs. Table 7 reports the convergence results after adjusting for the bias. Panels A and B correspond to the two 20-year periods shown in Figure 6. The patterns of convergence remain broadly consistent with the baseline results where rice and wheat productivities are moving from convergence to divergence. Like in the case of yields, the pace of divergence in maize TFPs has been increasing. Therefore, under the above assumptions, the exercise suggests that the baseline results are robust to the choice of productivity measure. Still, future research should try and bring first-hand data on inputs under analysis, which will help establish the yield-TFP relationship at smaller geographical units.

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||**Table 1: D**|**escriptive st**|**atistics**||**No of**|**No of**||
|---|---|---|---|---|---|---|---|
|**Variable**|**Mean**<br>(1)|**Std. Dev**<br>(2)|**Min**<br>(3)|**Max**<br>(4)|**.**<br>**districts**<br>(5)|**.**<br>**years**<br>(6)|**Obs.**<br>(7)|
||||**P**|**anel A: All**|**years**<sup>**1**</sup>|||
|**Yield (tonnes per hectare)**||||||||
|Rice|1.84|0.92|0.08|4.33|37|13|481|
|Wheat|2.32|0.71|0.38|4.05|37|13|481|
|Maize|2.94|1.36|0.27|10.37|37|13|481|
|**Credit**||||||||
|Annual flow (Rupees crores)|590|551|4|2953|37|11|407|
|Share of total flow (%)|2.7|1.8|0.3|20.5|37|11|407|
||||**Pa**|**nel B: Sub-**|**period I**<sup>**1**</sup>|||
|**Yield (tonnes per hectare)**||||||||
|Rice|1.39|0.76|0.08|4.33|37|7|259|
|Wheat|2.13|0.70|0.38|4.05|37|7|259|
|Maize|2.46|1.06|0.27|6.37|37|7|259|
|**Credit**||||||||
|Annual flow (Rupees crores)|173|195|4|1039|37|5|185|
|Share of total flow (%)|2.7|2.2|0.3|20.5|37|5|185|
||||**Pan**|**el C: Sub-p**|**eriod II**<sup>**1**</sup>|||
|**Yield (tonnes per hectare)**||||||||
|Rice|2.36|0.81|0.55|4.27|37|6|222|
|Wheat|2.54|0.65|0.60|3.78|37|6|222|
|Maize|3.50|1.46|0.42|10.37|37|6|222|
|**Credit**||||||||
|Annual flow (Rupees crores)|937|509|76|2953|37|6|222|
|Share of total flow (%)|2.7|1.3|0.4|7.1|37|6|222|

1Yield statistics: All years (2005-2017), Sub-period I (2005-2011), Sub-period II (2012-2017). Credit statistics: All years (2007-2017), Sub-period I (2007-2011), Sub-period II (2012-2017).

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**Table 2: Convergence test**<sup>**1**</sup>

|**Period**|**Rice**|**Wheat**|**Maize**|
|---|---|---|---|
||(1)|(2)|(3)|
|2005-2017|1.724|-0.316 **|-0.454***|
||(0.194)|(0.153)|(0.127)|
|2005-2011|2.864|0.452|-0.382***|
||(0.017)|(0.038)|(0.132)|
|2012-2017|-0.959 ***|-1.610 ***|-1.696***|
||(0.042)|(0.016)|(0.013)|

1Standard errors in parentheses. *Rejecting convergence at 10 percent, **Rejecting convergence at 5 percent, ***Rejecting convergence at 1 percent.

**Table 3: Club convergence test: 2012-2017**<sup>**1**</sup>

|**Period**|**Rice**|**Wheat**|**Maize**|
|---|---|---|---|
||(1)|(2)|(3)|
|Club 1|0.882|-0.061|1.468|
|Club 2|0.619|0.040|0.123|
|Club 3|0.625|0.098|-0.072|
|Club 4||0.234|-0.915|
|Club 5||0.094||
|Club NC|-1.526 ***||-2.284 ***|

1*Rejecting convergence at 10 percent, **Rejecting convergence at 5 percent, ***Rejecting convergence at 1 percent.

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**Table 4: Agricultural credit across sub-periods**<sup>**1,2**</sup>

||**Pan**|**el A: Agricultural cre**|**dit**|**P**|**anel B: Credit share**||
|---|---|---|---|---|---|---|
||**Rice**<br>(1)|**Wheat**<br>(2)|**Maize**<br>(3)|**Rice**<br>(1)|**Wheat**<br>(2)|**Maize**<br>(3)|
|Post|707.4 ***|805.2***|661.4 ***|-0.004 **|-0.006***|0.005 *|
||(43.8)|(54.5)|(76.9)|(0.002)|(0.002)|(0.003)|
|Club 2 x Post|28.0|13.3|88.8|0.007 ***|0.007**|-0.009 ***|
||(68.6)|(81.8)|(90.5)|(0.002)|(0.003)|(0.003)|
|Club 3 x Post|130.2 *|-203.5**|158.8 *|0.008 ***|0.008**|-0.003|
||(75.9)|(89.0)|(92.7)|(0.003)|(0.003)|(0.003)|
|Club 4 x Post||-134.7*|328.9 ***||0.009***|-0.003|
|||(77.1)|(108.7)||(0.003)|(0.004)|
|Club 5 x Post||448.1***|||0.007||
|||(133.5)|||(0.005)||
|Club NC x Post|365.8 ***|28.3|-253.8 **|0.004|0.007|-0.005|
||(131.4)|(180.8)|(125.5)|(0.005)|(0.006)|(0.004)|
|Club 2|-48.3|49.3|-78.0|-0.004|-0.001|0.004|
||(88.3)|(60.7)|(82.0)|(0.003)|(0.002)|(0.003)|
|Club 3|-70.7|133.1**|-45.7|-0.004|-0.005*|0.004|
||(89.3)|(67.2)|(88.3)|(0.003)|(0.002)|(0.003)|
|Club 4||104.4*|-139.7||-0.004*|0.006|
|||(57.9)|(98.3)||(0.002)|(0.003)|
|Club 5||-144.6|||0.000||
|||(101.4)|||(0.004)||
|Club NC|-130.0|11.8|111.7|0.000|-0.004|0.001|
||(102.2)|(135.7)|(100.7)|(0.004)|(0.005)|(0.004)|
|Average Pre-period|2.7 ***|2.7***|2.7 ***|0.749 ***|0.749***|0.750 ***|
||(0.2)|(0.2)|(0.2)|(0.027)|(0.029)|(0.027)|
|ACZ controls|Yes|Yes|Yes|Yes|Yes|Yes|
|R<sup>2</sup>|0.73|0.74|0.74|0.69|0.69|0.69|
|Observations|407|407|407|407|407|407|

1Standard errors in parentheses. Level of significance: *10 percent, **5 percent, ***1 percent.

2Post-period (2012-2017), Pre-period (2005-2011).

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**Table 5: Convergence test: Alternative sub-periods**<sup>**1,2**</sup>

|**Period**|**Rice**|**Wheat**|**Maize**|
|---|---|---|---|
|Sub-period I|2.880|0.481|-0.533***|
||(0.021)|(0.042)|(0.138)|
|Sub-period II|-0.725***|-1.733***|-1.558***|
||(0.031)|(0.019)|(0.010)|

1Standard errors in parentheses. *Rejecting convergence at 10 percent, **Rejecting convergence at 5 percent, ***Rejecting convergence at 1 percent.

2Rice and maize: Sub-period I (2005-2010), Sub-period II (2011-2017). Wheat: Sub-period I (20052012), Sub-period II (2013-2017).

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**Table 6: Convergence test: Agro-climatic zones**<sup>**1**</sup>

|**Period**|**Rice**<br>(1)|**Wheat**<br>(2)|**Maize**<br>(3)|
|---|---|---|---|
|||**Panel A: Southern districts**<br>||
|2005-2017|2.698|0.090|-0.348**|
||(0.168)|(0.146)|(0.164)|
|2005-2011|1.077|0.047|0.046|
||(0.158)|(0.154)|(0.149)|
|2012-2017|0.300|-1.554***|-1.674***|
||(0.117)|(0.025)|(0.029)|
|||**Panel B: Northwestern districts**||
|2005-2017|5.465|-1.366***|-0.653**|
||(0.808)|(0.140)|(0.328)|
|2005-2011|-1.763|0.015|-0.127|
||(2.160)|(0.084)|(0.201)|
|2012-2017|-1.447*|**<br>-1.739***|-2.510***|
||(0.064)|(0.047)|(0.052)|
|||**Panel C: Northeastern districts**||
|2005-2017|2.387|-0.036|-1.122***|
||(0.125)|(0.082)|(0.136)|
|2005-2011|1.818|0.733|-1.234***|
||(0.023)|(0.095)|(0.100)|
|2012-2017|-0.057|-1.351***|-1.927***|
||(0.055)|(0.015)|(0.103)|

1Standard errors in parentheses. *Rejecting convergence at 10 percent, **Rejecting convergence at 5 percent, ***Rejecting convergence at 1 percent.

34
|**Table 7: Convergence tes**<br> <br>|**t: Adjusting for bias**<br>|<br>|
|---|---|---|
|**Period**<br>**Rice**|**Wheat**|**Maize**|
|(1)<br>**Panel A: Adju**|(2)<br>**sting using 1961-198**|(3)<br>**0 estimate**|
|2005-2017<br>2.019|-0.128|-0.321***|
|(0.201)|(0.157)|(0.119)|
|2005-2011<br>3.396|0.611|-0.406***|
|(0.088)|(0.046)|(0.138)|
|2012-2017<br>-0.891***|-1.577***|-1.645***|
|(0.040)|(0.019)|(0.008)|
|**Panel B: Adju**|**sting using 1981-200**|**1 estimate**|
|2005-2017<br>1.903|-0.204*|-0.374***|
|(0.199)|(0.156)|(0.122)|
|2005-2011<br>3.186|0.547|-0.395***|
|(0.059)|(0.042)|(0.135)|
|2012-2017<br>-0.918***|-1.591***|-1.666***|
|(0.041)|(0.018)|(0.010)|

Standard errors in parentheses. *Rejecting convergence at 10 percent, **Rejecting convergence at 5 percent, ***Rejecting convergence at 1 percent.

35