# **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