Policy Research Working Paper                      10865




       Absentee Landlords and Land Tenancy
                                 Melanie Khamis
                                Annemie Maertens
                                Siddharth Sharma




South Asia Region
Office of the Chief Economist
August 2024
Policy Research Working Paper 10865


  Abstract
  Internal migration and structural transformation are strongly                      Using a shift-share instrument that exploits information on
  interrelated. This paper uses Indian data spanning 2001–13                         bilateral migration flows between districts, the paper shows
  to examine a little-known aspect of this relationship: how                         that migration increased fixed rent tenancy and contract
  migration affects agricultural land rental contracts. Building                     formalization. Given the continued importance of agricul-
  on anecdotal evidence and theory, the paper hypothesizes                           tural land rental markets, these findings have significant
  that as landlords migrate away, their choice of contract for                       implications for rural efficiency and equity in developing
  tenant-cultivators changes from sharecropping to fixed rent.                       countries.




 This paper is a product of the Office of the Chief Economist, South Asia Region. 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 authors may be
 contacted at ssharma1@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
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                                                        Produced by the Research Support Team
        Absentee Landlords and Land Tenancy
                                                                                        ∗
  Melanie Khamis, Annemie Maertens and Siddharth Sharma




   Keywords: migration, land tenancy, sharecropping, land rent,
India
   JEL Classification: O1, J61, Q13, Q15

   ∗
     Corresponding Author: Annemie Maertens (a.maertens@sussex.ac.uk) at Sussex Uni-
versity; Melanie Khamis (mkhamis@wesleyan.edu) at Wesleyan University and IZA; Sid-
dharth Sharma (ssharma1@worldbank.org) at the World Bank. We acknowledge excellent
research support from Deepika Pingali, Maika Schmidt, Sakshi Bhardwaj, Claudia Isabel
Medina Lopez, Aditi Guha and Morgan Usen, and support in obtaining the data from
Dipendra Das and Cyriac George, as well as Eswaran Jagadeesh and Anupama at ICRISAT.
Michael Norton at the World Bank generated the travel time data set using scanned maps
provided by Treb Allen. We are grateful to Sanjay Jain, AV Chari, Shingyi Wang, Laura
Schechter, Anukriti, Rachel Heath, Adriana Kugler, Ira Gang, Cory Smith, Amrit Ami-
rapu, Agyris Sakalis, Larry Blume and seminar participants at the 2019 AAEA, 2021 16th
Annual Conference on Economic Growth and Development (ISI), 2022 97th Annual Con-
ference WEAI, 2022 MLPortal 1st Workshop of Applied Microeconomics, 2022 100 Years
of Economic Development Conference Cornell University, 2023 Southern Economic Associ-
ation, Fordham University, CUNY Baruch and at Sussex University for excellent comments
and suggestions. The findings, interpretations, and conclusions expressed in this paper are
entirely those of the authors. They do not necessarily represent the view of the World Bank
or its Executive Directors.
1       Introduction
The distribution of land ownership and structure of landlord-tenant relation-
ships are central features of agricultural societies. In this paper, we theo-
rize and empirically document how internal migration impacts this structure,
thereby affecting the efficiency and equity of the rural sector.
    In traditional two-sector growth models, the rural economy serves as a
reservoir of labor. Rural-to-urban migration feeds a growing industrial sector,
eventually pushing rural wages upwards (Lewis, 1954; Ranis and Fei, 1961).
Later models explore other channels of interaction between migration and ru-
ral economies, such as rural asset markets (Taylor and Martin, 2001). Migra-
tion may affect access to insurance (Rosenzweig and Stark, 1989; Giles, 2006;
Munshi and Rosenzweig, 2016; Morten, 2019).1 Coupled with labor and land
market frictions in villages, migration may affect agriculture through labor loss
in migrant-sending households, causing changes in crop acreage, crop diversity
and capital intensity (Rozelle, Taylor and De Brauw, 1999; De Brauw, 2020;
Brewer, Larsen and Noack, 2024; Madhok et al., 2024). As such, migration
can spur mechanization (Hornbeck and Naidu, 2014) and result in spatial re-
organisation of agriculture (Madhok et al., 2024). It may further impact land
markets as emigrating landlords resort to selling or renting their land (Reddy,
1996).
    In this paper we contribute to this literature, and formalize and quantify
the latter channel. The linkage between emigration of landlords and land
rental markets has been somewhat overlooked by economists, but is of utmost
importance to understanding the increase in inequality in low and middle
income countries (Van Der Hoeven, 2019; The World Bank, 2021). Our study
is set in India, a middle income country with increasing internal migration,
an active land rental market and large agricultural labor force (Deininger,
Jin and Nagarajan, 2008; Kone et al., 2018). The availability of several data
sources makes India an ideal setting to study this linkage. We digitize, compile
    1
    In turn, credit constraints and uninsured risk may limit migration (Bryan, Chowdhury
and Mobarak, 2014; Angelucci, 2015; Gazeaud, Mvukiyehe and Sterck, 2023).



                                           2
and connect existing data, present a comprehensive picture of the land rental
market, and test the implications of a model connecting internal landlord
migration to the land market.
    We start with the observation that the Indian land rental market has
changed in the last few decades. Sharecropping, an arrangement in which the
tenant pays the landlord a share of the harvest, used to be the most common
arrangement. An estimated 50% of rented-out land was under sharecropping
in the late 1970s in India, as compared to about 16% in Latin America, 12% in
Europe and 31% in North America (Otsuka, Chuma and Hayami, 1992). This
share has declined in the last 30 years, with the most drastic decline occurring
after 2000. Sharecropping is being replaced by another arrangement: fixed
rent. In this case, the tenant pays the landlord a fixed amount, often a cash
amount at the start of the season or year.2
    These changes have a number of implications for economic efficiency as
well as income inequality and economic vulnerability. Economists have long
studied how the nature of the contractual arrangement determines efficiency.
Sharecropping, when effort cannot be observed nor contracted, taxes effort,
and may thereby reduce labor inputs, one of the most important inputs in
agricultural production. This may reduce labor productivity and generate
Marshallian inefficiency (Marshall, 1890).3
    This focus on the residual claimant and efficiency misses four advantages
of sharecropping which emerge in richer models of land markets. First, share-
   2
     While we did not collect India-wide data on the period preceding 1981, local accounts
note that fixed tenancy was also the norm prior to the 1950s. After independence, various
Indian states introduced acts on land tenancy and land reform, which might have resulted
in a shift away from both registered and fixed tenancy (Reddy, 1996).
   3
     Estimates of the degree of this inefficiency vary by context and method. In India,
Shaban (1987) shows that farmers generate 33% higher yields on own/fixed rent plots versus
sharecropping plots (controlling for land quality) in six villages. Deininger, Jin and Yadav
(2013), exploiting a land reform policy in West Bengal, note a reduction in longer term profits
of 20% (compared to owner-cultivators). Burchardi et al. (2019) report sizable effects using
a randomized controlled trial which varied the share of output among Ugandan farmers.
                            ´
See also Arcand, Ai and Ethier     (2007) and Jacoby and Mansuri (2009). Jaynes (1982),
Otsuka and Hayami (1988), Singh (1989 and 2004), Otsuka, Chuma and Hayami (1992),
Lastarria-Cornhiel, Melmed-Sanjak and Phillips (1999) provide an overview of the theory
and empirical work.



                                              3
cropping allows the landlord and the tenant to share the inherent risk in agri-
cultural production; in contrast, the tenant bears the entire risk under fixed
rent (Cheung, 1969; Stiglitz, 1974; Ghatak and Pandey, 2000). Second, share-
cropping can reduce the impacts of the tenant’s limited liability (Shetty, 1988;
Basu, 1992; Laffont and Matoussi, 1995; Sengupta, 1997; Ray and Singh, 2001).
Third, the control over the tenant in sharecropping might allow the landlord
to ensure a more sustainable use of the land (Reddy, 1996). Fourth, share-
cropping provides an incentive for the landlord to provide inputs, such as,
pesticides, fertilizers and managerial support, to the tenant (Newbery and
Stiglitz, 1979; Eswaran and Kotwal, 1985).
    Motivated by anecdotal evidence and this last argument, we develop a
theoretical framework which combines prior models (Eswaran and Kotwal,
1985) with the idea that when landlords migrate away from the village, the
opportunity cost of providing managerial inputs increases. This results (for
those who do not opt for land sales) in a preference for fixed over sharecropping
arrangements.
    To test this proposition we construct a district-level data set covering the
first decade of the 21st century. The choice of time period is dictated by both
data availability (we have detailed migration data only for the decades preced-
ing 2001 and 2011) and contextual considerations: liberalization in the 1990s
strengthened property rights, allowing for migration of the landed class (Giles
and Mu, 2018). This period also saw an acceleration in the trend towards fixed
rent arrangements: from 1992 to 2012, fixed rent agreements increased from
45% to 58% while sharecropping decreased from 45% to 31% (as a percentage
of total rented in acreage). The largest drop happened in the last decade under
consideration (Table 1).
    Establishing a causal link from migration to rental contracts is challenging
because of the presence of potential confounding factors. They include a ma-
jor rural bank branch expansion program (Burgess and Pande, 2005) which
could have simultaneously increased fixed rent arrangements (following Laffont
and Matoussi (1995) and evidenced by Das, de Janvry and Sadoulet (2019)
in Bangladesh) and migration (Shonchoy, Fujii and Raihan, 2018; Foltz, Guo


                                       4
and Yao, 2020; Gazeaud, Mvukiyehe and Sterck, 2023). Other potential con-
founding factors include trade liberalization, climate change and a rural roads
program.4
    To establish causality between migration and land rental contracts, we
employ an instrumental variable strategy relying on arguably exogenous mi-
gration “pull” factors. Our main explanatory variable is the share of the
high-skilled in total migrant outflows: lacking information on land ownership
of migrants, we use this measure to capture the out-migration of the landhold-
ing classes. We instrument for it by using a shift-share strategy (Card, 2001;
Anelli et al., 2023; Madhok et al., 2024). One unique feature of our paper is
that the data allows us exploit migration networks to instrument for internal
migration using this strategy.
    Our approach, which uses district-to-district migration flows from the 2001
and 2011 Population Censuses, can be explained as follows. For a given
migrant-sending (or, “source”) district, every other district in India is con-
sidered a potential “destination” district. We proxy for the attractiveness of
each destination district by considering the total immigration it from all other
districts (barring the source district). This is the shift component. The share
component is the historical share of each destination district in the total mi-
grants from the source district. The share-weighted shift yields a measure of
the migration pull factor for the source district. We construct two instruments,
one for high-skilled migrants and one for low-skilled migrants, and use these
to predict high-skilled out-migrants as a percentage of total out-migrants in
each district. This distinction by education level is unique and contributes to
   4
    Trade liberalization exposed farmers to increased volatility, affecting crop choices (Allen
and Atkin, 2022) and agricultural investments (Tian, Xia and Yang, 2021). Changes in
rainfall patterns (associated with climate change) may have impacted agricultural wages and
migration directly (Rosenzweig and Udry, 2014; Colmer, 2018; Brey and Hertweck, 2019;
Kaur, 2019), or indirectly through a declining groundwater tables (Blakeslee, Fishman and
Srinivasan, 2020). A rural roads construction program increased educational investment and
migration (Adukai, Asher and Nosovad, 2020), while affecting agricultural technology and
crop choice (Aggarwal, 2018; Shamdasani, 2021). Note, however, that trade liberalization
and climate change increase risk and should push land tenancy towards more sharecropping.
Hence they are not a competing explanation for the observed trends, although they can be
a threat to establishing causality.



                                              5
instrument exogeneity.
    Using this strategy, we find that a one point increase in high-skilled male
out-migrants (as a percentage of total male out-migrants) is associated with
a statistically significant increase of 2.6 percentage points in fixed rent ar-
rangements, and a reduction of 1.8 percentage points in sharecropping. This
represents an effect size of, respectively, 6% and 5%. This result is robust to
including controls for bank branches, roads, weather and other agro-climatic
factors.5
    A remaining concern arises from local inter-district connections in agricul-
tural markets coupled with the tendency of Indian migrants to move to nearby
districts (Kone et al., 2018). For example, the effects of a drought could reach
across neighboring districts, which would be a concern for our approach if
the historical migrant network too were strongly dominated by neighbouring
districts. While we include controls for weather conditions, we also present
a unique variation of instrumental variable strategy to address this concern.
We deduct the variation that can be explained by distance (specifically, travel
time) from the total variation in the historical migrant network, and utilize
this residual variation as the new share in our instrument. Using this tech-
nique results in very comparable numbers: an increase in high-skilled male
out-migrants by one percentage point increases fixed rent agreements by 2.7
percentage points and decreases sharecropping by 1.9 percentage points.
    We further show that this increase in fixed rent represents a broader trend
towards increased formalization in the land rental market (between 2002 and
2012), with an increase in written contracts and contracts of longer duration.
Migration appears to play some role in this increased formalization. Finally,
we note a mixed yield response to high-skilled male out-migrants, which may
reflect two countervailing forces: greater Marshallian efficiency of fixed rent
contracts versus the loss of the emigrant landlord’s labor and knowledge.
    Our contribution to the literature is threefold. First, we document the
   5
    Our results are also robust to controlling for the roll out of a rural employment guarantee
program which might have altered the relationship between tenants and landlords (Imbert
and Papp, 2015; Narayanan et al., 2017; Berg et al., 2018; Chari et al., 2019).



                                              6
importance of an (by economists) understudied link between labor and land
markets, thereby improving our understanding of the structural transformation
process in developing economies. Migration, by driving contractual change,
can alter the efficiency of the agricultural sector, and have implications for
equity and access. Second, we present three decades of national-level descrip-
tive statistics on the nature of the relationship between tenants and landlords
for India, one of the most populous country in the world which have a sig-
nificant share of the population in agriculture. Third, we introduce a novel
instrumental variable strategy for emigration: stripping the pull instrument
from distance-related components strengthens exogeneity and can be applied
in other contexts.
    The rest of the paper is structured as follows. In section 2, we provide
background on migration in India. Section 3 introduces the data. Section
4 presents descriptive statistics. Section 5 outlines a theoretical framework.
Section 6 presents the empirical identification strategy. Section 7 presents the
results. Section 8 concludes.


2    Setting: Migration in India
India is often thought of as a country with low internal migration. Several
studies point to India’s low internal labor mobility and localised labor mar-
kets, which are associated with regional wage gaps, efficiency losses and high
local vulnerability (Jayachandran, 2006; Topalova, 2010; Chari et al., 2021).
In 2001, merely 2.8% of India’s population consisted of individuals who had
moved permanently to a different district in the last five years. In contrast,
9% of Brazil’s population had moved permanently to a different municipality
in the last five years, and 10% of China’s population had moved to a different
prefecture in the last five years (Kone et al., 2018). Research into the barriers
to migration and labor mobility pointed at the role of social networks (Mun-
shi and Rosenzweig, 2016), political and cultural inter-state differences (Kone
et al., 2018) and restrictive labor laws (Adhvaryu, Chari and Sharma, 2013).
    However, internal migration has been on the rise in India. According to

                                       7
the 2001 Population Census of India, 11% of India’s population consisted of
individuals who had moved permanently to their current district from a dif-
ferent district at some point in the past. In the 2011 Census, this share had
increased to 14 percent.6 Using railway data, the Government of India’s 2016-
17 Economic Survey Report estimates a doubling of internal migration rate
from 1991-2001 to 2001-2011 (Government of India, 2017).7
    India’s reputation as a low internal migration country is also being reconsid-
ered by economic historians (Cohen, 1995; Tumbe, 2018; Rajan and Sumeetha,
2019). Migration in the past two centuries consisted mostly of young men mi-
grating via caste networks to areas of economic opportunity, returning every
few years, and eventually settling back into their home villages. This type
of migration was common place: Tumbe (2018) estimates that 150 districts
experienced mass migration during the past 150 years (defined as more than
20% of households affected). Migration has increased in the last few decades
and is more permanent in nature. The high-skilled are increasingly dominant
in internal migration flows (Docquier and Rapoport, 2012). Yet, this recent
increase in migration builds on the migration networks established in the past
century and a half (Tumbe, 2018).
    The contribution of this study is to link migration to changes in land
tenancy. This link first became clear to us during a field visit in rural Utter
Pradesh, North India, in 2008, when we spoke with landlords about their
contract choice. We then confirmed these patterns with historical accounts
from other parts on India. Reddy (1996), for instance, collected land contracts
and interviewed farmers in Andhra Pradesh, South India, spanning the period
1850 to 1980. He repeatedly notes the unique role that absentee landlords
play in the rural economy. His analysis suggests that concerns about moral
hazard cause absentee landlord to prefer contracts involving simple, once-per-
   6
     The increase is larger when accounting for within-district migrants, who constitute an
estimated 60% of all internal migrants in 2001. The Census does not cover temporary mi-
gration, which is also on the increase due to factors such as changes in weather and National
Rural Employment Guarantee Act (Rosenzweig and Udry, 2014; Kaur, 2019; Morten, 2019).
   7
     See Hnatkovska and Lahiri (2015) for comparable statistics using National Sample Sur-
vey data.



                                             8
year cash payments.8 Other contemporaneous village level studies document
similar features in the economic arrangements between landlords and tenants
(Srinivas, 1976; Bliss and Stern, 1982; Walker and Ryan, 1990).


3       Data
We digitize, compile and connect existing data to construct a district-level
dataset. We draw measures of land tenancy from the National Sample Survey
(NSS) Land and Livestock Survey, a repeated cross section survey of about
35,000 agricultural landholdings across India. We build on custom-made tables
from the Population Census of India for measures of migration. We then add
information on banking, roads, distances between districts, weather and agro-
climate zones from other data sources. The details of these steps are included
in the online appendix. Here, we discuss the main sources, the NSS and the
Census, and highlight data challenges.


Tenancy: NSS Land and Livestock Survey
To obtain district-level data on land contracts we compiled data from the Na-
tional Sample Survey Land and Livestock Survey. The survey covers around
30,000 to 35,000 households from all of India (with exceptions in some rounds).9
    We make use of the rural sample of round 70 (conducted in 2013) and 59
(conducted in 2003). We utilize information from schedule 18.1 which lists all
    8
     On page 49, Reddy notes that, ‘The agreements entered into by absentee landlords were
more detailed than those of residents.’ On page 52, he notes that, ‘The rent in the case of
absentee lessors was generally paid once per year,’ and on page 76 that, ‘Absent landlords
preferred cash over grains except in times of sharp rising prices.’ This is followed up, on
page 69, with, ‘The shorter the distance, the greater was the preference for receipts in kind.’
Detailed contracts, specifying the crops and often inputs, were standard; and clauses such as:
‘You should cultivate this particular plot of land as well and carefully as the neighbouring
owner cultivators of similar field,’ commonplace.
   9
     The survey uses a stratified multi-stage design in which a number of census villages
are randomly drawn from each district (usually four in two independent samples). Within
each village, eight agricultural households are selected, stratified by landholding class. Each
sample household is visited twice, once at the end of the kharif season (rainy season) and
once at the end of the rabi season (dry season).


                                              9
cultivated, owned and otherwise possessed field (also called plots) of the house-
holds. It is these plots which are our unit of analysis from which we generate
(weighted) district-level statistics. The dependent variables are defined as a
percentage of the rented in acreage or rented in plots at a district level. For
each plot we have information on the location (within the village or not), soil
type (soil texture), land use, acreage, irrigation facilities/flood frequency, as
well as the ownership and rental agreement details.10 Our analysis builds on
plot-level data from the tenant side of the market, as all tenants, even landless
tenants, are considered in the sampling process.


Migration: Census of India
We use bilateral district-to-district migration data obtained from the 2001
and 2011 Population Censuses of India. The Census is the only data source
with information on both the source and origin district of migrants for all the
districts of India.
    The Census, which is conducted every decade, asks every individual if
the place in which they are enumerated during the census is different from
their “last usual place of residence”. As in Kone et al. (2018), we consider
a person a migrant if they reply in the affirmative.11 Additional follow up
questions allow us to capture bilateral migration flows. These include the
location (district) of the last place of residence, reason for migration (marriage,
education, employment etc.), and the duration of stay in the current residence
since migration. The census also includes information on the sex, education
and age of each individual (but notably not land ownership).
    Since the census does not provide unit-level data, under a special admin-
istrative agreement we requested them to provide us with aggregated data
on the volume of migration between every pair of districts. For a given pair
  10
     We omit plots which are categorized as non-agricultural, and might contain lakes, forest,
or other types of lands, in the analysis. We also drop plots which are located outside of the
district, when this information is available.
  11
     The previous residence does not necessarily imply the residence of the previous census,
but can be a residence of 3 years ago, 7 years ago, more than 10 years ago, or even during
childhood or shortly after birth - all will be considered migrants.


                                             10
of source district (the district of immediate last residence) and destination
district (the district of current residence and Census enumeration), this data
set contains the number of individuals who have moved from the former to
the latter, dis-aggregated by duration of stay in the destination district, sex,
age, education and the reason for migration (but not by urban/rural parts of
source/destination). We obtained these custom tables for the 2001 and 2011
Census. The dis-aggregation by the duration of stay in the destination dis-
trict distinguishes between individuals who migrated at most five years ago
and those who migrated six years ago or earlier. We supplemented these data
with census data on district population, also dis-aggregated by sex, age and
education.
    To construct the dependent variable, we obtain the number of out-migrants
for a given age/sex category for a given source district by summing up all
migrants within this category who moved in the past five years to all des-
tination districts. We distinguish between within-district and out-of-district
migrants.12


Data challenges and limitations
Harmonizing districts Our dataset is a district-level panel. Districts units
represent the third level of administrative units in India, and are commonly
used for data collection and dissemination purposes. Some district boundaries
and names altered over the period of our study. Defining 2001 as the base year,
we first checked for changes in names and renamed districts post 2001 using
the 2001 name. In the case of district splits, we mapped the post-2001 district
back to its parental district in 2001. This process automatically resulted in
a reduction of sample size as there were fewer districts in 2001 than in later
years (Kumar and Somanathan, 2015).
  12
    It is possible that a person moved twice or more in the past ten years prior to the
census. In this case, only his last residence would be mentioned, and we would rely on this
information to construct the measures.




                                            11
Using household survey data In most districts, the NSS collected data
from four villages. We use data from these four villages to generate district-
level aggregates. This process can result in sampling error. For example, the
sample could contain no households who rent in land, despite such households
being present in the district. This would result in missing data for this dis-
trict/year: 11% of districts do not have any tenant records for either year,
and 23% of districts have no tenant records for one out of two years. The
latter would imply that rental markets come and go, something which seems
unlikely.13

Rural to urban migration Our district-to-district migration data do not
map exactly to the rural/urban distinction implied by the theory. We do not
believe this to be a significant limitation. A significant share of migration is
not of the traditional rural to urban variant. Aggregate Census data of 2001
indicate that 55% of migration is between rural areas, 15% is between urban
areas, 21% is rural to urban migration, and 6% is urban to rural migration.
Part of the explanation for this is that areas which have seen a recent surge
in population are slow to be re-classified as urban areas. This results in errors
in any statistics which rely on this distinction. Ellis and Roberts (2016) note
that 30% of the increase in India’s urban population between 2001 and 2011
was due to a reclassification of census areas.


4      Descriptive statistics
Land tenancy
Table 1 presents statistics on the land rental market for the years 1992, 2002
and 2012. The top panel presents statistics converted to acreage terms while
  13
    We do not have any other reliable data which could serve as a comparison point. We
had coded up an alternative data source, the Agricultural Census. This Census is conducted
every five years by the Agricultural Census Division of the Ministry of Agriculture since 1970
and collects information on agricultural operational holdings in India. However, data quality
on land tenancy appeared to be poor, with often no land tenancy recorded in land-record
states (where formal registration records are in place).


                                             12
the bottom panel presents them in contract terms, that is, the number of
fields (plots) under a given contract. Both panels are in percentages of rented-
in land. The use of fixed rent has increased from 45% to 58% as a percentage of
the total acreage rented in, over the course of twenty years, while sharecropping
arrangements have decreased from 45% to 31%. The pattern is similar, albeit
less striking, in contract terms. Fixed rent arrangements have increased from
35% to 49% while sharecropping arrangements have decreased from 49% to
38%.14 We further split up fixed rent by fixed monetary rent (rent paid in
money), and fixed crop output (rent paid in produce), a distinction we explore
in the analysis.
    We focus our analysis on the acreage terms data. Using acreage terms
instead of contract terms gives us a more accurate representation as to the
amount of land, and by extension, the effect on input decision-making, and
regional yields.
    Due to the presence of other contract forms, the total percentages in Table
1 (that is, fixed rent plus sharecropping) do not add up to 100%. In Appendix
Figure A1 we display the percentage of contracts under various contract types,
including: ‘for fixed money’, ‘for fixed produce’, ‘for service contract’, ‘for
share of produce together with other terms’, ‘under usufructuary mortgage’,
‘from relatives under no specified terms’, and ‘under other terms’. Fixed and
sharecropping represent the majority of the rental contracts. Again, one notes
the increase in the various fixed terms (as opposed to sharing terms).
    Table 1 presents data from the kharif (rainy) season. The trends observed
are similar for the rabi (dry) season (see Appendix Table A1). Although
crop types and irrigation levels tend to differ across seasons, contractual forms
may be similar across them because multi-season and multi-year contracts
are increasingly common. In Appendix Figure A2 we indicate the duration
of the contract: 75% are of at least one agricultural year. As the kharif
season is the main season, we focus our analysis on this season. We consider
this and other aspects of formality in Table 1, that is, whether the field is
  14
    As a comparison point, in 1982, 45% of land rented in acreage was under sharecropping
and 17% was under a fixed rent arrangement.



                                           13
rented from relatives, the duration of the contract and whether a written
contract is present. Considering the 2002-2012 period, we note an increase in
formalization, with longer, written contracts.
    In Figure 1 we display maps of selected areas, East, North and West, and
South, in India, with district boundaries following the 2001 Census. Panel A
displays the maps representing the situation in 2002. Panel B maps represent
the situation in 2012. The blue colour represents high levels of fixed rent,
while the yellow represents low levels (with the red an in between stage). Note
that most of the populous states in the south of India, such as Tamil Nadu,
Andhra Pradesh, Telangana and Kerala, have witnessed a substantial increase
in fixed rent arrangements.


Migration
We do not have any direct measure of landlord migrants, as there is no in-
formation on land ownership in the Census. We proxy for landlord migrants
using high-skilled migrants, a group defined by a cut-off of at least 10 years
of education.15 This assumption is supported, at least to some degree, by
the data. Using the NSS Land and Livestock Survey round 70 (conducted in
2013), we note a significant, positive correlation between acreage of land owned
and the education (in years of education) of the household head (a correlation
coefficient of 10%). In Appendix Figure A3 we present the histogram of the
education level of the head of the household, by type of landholding. On the
left-hand side are the landless, defined as possessing less than 2 hectares, and
on the right-hand side, the landed, defined as owning more than 2 hectares.
While there is an overlap between the educational distributions of the landless
and the landed, we note that very few of the landless have more than ten years
of education. We notice a similar pattern using the national ARIS-REDS panel
survey of rural households from 2005. Using the sample of all individuals who
engaged in migration that year (that is, temporary migrants), we find that
  15
    This cut-off follows the structure of education in India: At the end of lower secondary
education, in year 10, an exam has to be taken and passed in order to progress, and further
education often requires travelling further afield.


                                            14
households of high-skilled migrants have twice as much owned land compared
to households of low-skilled migrants (1.8 acres as opposed to 0.86 acre).
    In Table 2 we present the average number of out-migrants across districts,
by year and by category (with standard deviations in parentheses). We only
include male migrants between the ages of 20 and 64 who migrated in the past
five years. These represent working age men.16 We distinguish between low-
skilled (less than 10 years of education) and high-skilled (more than 10 years
of education) in the top and bottom panels, respectively. We also distinguish
between within- and out-of-district migrants.
    The number of low-skilled out-of-district migrants has hardly changed be-
tween 2001 and 2011, but the number of low-skilled within-district migrants
has increased by 18%. The number of high-skilled out-of-district migrants has
increased by 33% while the number of high-skilled within-district migrants has
increased by 60%. Within-district migration is becoming more important over
time, especially among the high-skilled. The increase in migration, in absolute
numbers, is mostly noted among the high-skilled. A significant component of
this might be that the number of high-skilled individuals themselves are in-
creasing, as more individuals, as a percentage of the population in their age
group, are now high-skilled.
    Our analysis uses the number of high-skilled out-of-district migrants ex-
pressed as a percentage of the total number of out-of-district migrants as the
key explanatory variable. We control for the total populations in both skill
categories, as we want to capture the differential opportunities for high and
low skilled, and not simply their supply.17
  16
     Women in India tend to migrate largely for marital reasons (Rosenzweig and Stark,
1989).
  17
     Appendix Table A2 presents the absolute numbers of high-skilled and low-skilled males
residing in the districts between the ages of 20 and 64 in both 2001 and 2011. We note
that both numbers increased, reflecting population growth, but that, relatively speaking,
the number of high-skilled individuals increased more.




                                           15
5      Theoretical framework
Our theoretical base is a principal-agent model in which the principal, the
landlord, devises a contract to serve his interests and presents a take it or
leave it offer to the agent, the tenant, assumed to be a landless laborer. The
latter decides whether to accept the contract, comparing the contract with
his outside opportunities (reservation utility) and conditional on accepting,
decides on the amount of effort to put in.18
    To integrate the role of the absentee landlord, we modify this base as a
double incentive problem, as first introduced by Eswaran and Kotwal (1985),
in which the landlord too puts labor effort into the production of crops and
needs to decide on his degree of engagement. We build on the interpretation
of Singh (1989 and 2004).19
    We consider this to be a realistic model in the Indian context. Reddy
(1996) notes that the type of tenancy, the quantity and quality of produce or
amount in cash, the details of transport and delivery methods are commonly
determined by the landlord. 20 Other village level studies, such as Bliss and
Stern (1982) and Walker and Ryan (1990), concur.
  18
     Perhaps this choice of model needs some justification. Why, for instance, do we not start
with a general equilibrium setting instead? As first noted by Newbery (1974), the share in
a sharecropping contract cannot be viewed as a price in the standard Walrasian equilibrium
sense, as, if it were a price, the tenant taking the share as given will demand more land, up
to the point where the marginal product of land is zero. An equilibrium share would then
be determined as equating this demand to the village supply. Unless land is abundant, this
equilibrium will not exist.
  19
     We do not consider screening effects as in Hallagan (1978) and Newbery and Stiglitz
(1979): while it is the case that in-migration might increase the percentage of unknown
tenants, hence tempting landlords to use a menu of agreements to screen the tenants; the
dominance of one agreement over another in most villages seems to conflict with this screen-
ing explanation.
  20
     Reddy (1996) distinguishes between three contract components, the main lease (kaul),
the mutchalika and the rent receipts. It is only the mutchalika which is joint written by the
tenant.




                                             16
Setup
We start with one landlord and one tenant. We suppress the quantity of land
(assuming a fixed plot size), and abstract away from other inputs, such as,
animal power, fertilizers, seeds, machinery and irrigation, and by consequence,
ignore other forms of input sharing. The agricultural production function takes
the following form:

                            ˜ (L, θ) = θ ∗ Q(M, E )
                            Q                                               (1)

    where θ is a random variable with mean 1, capturing the role of, among
others, weather and pests in agricultural production. M denotes managerial
input and E effective labor input. The production function is concave and
increasing in all its arguments, and its value is 0 when θ is less than or equal
to zero or when both forms of labor are zero. The effective labor input, E , is
defined as:

                                E = E (S, L; t)                             (2)

   where S denotes supervisory input, L labor inputs and t (between 0 and 1)
represents the supervision technology, capturing the importance of supervision
in making the labor inputs effective (with if t=0, E=L, i.e., no supervision is
needed). Substituting in for E in Expression (1), we obtain:

                          ˜ (L, θ) = θ ∗ Q(M, S, L; t)
                          Q                                                 (3)

    We can now introduce moral hazard. We assume that while L is observable,
M and S are not. We differentiate between the landlord and the tenant. The
landlord is assumed to be high-skilled, while the tenant is low-skilled. This
translates into the landlord being better at management, M , with the tenant
having an advantage in supervision, S . We follow the notation of Singh (1989
and 2004) and denote the advantage of the landlord as γ (1 hour of the tenant’s
time on management is equivalent to γ < 1 hours of the landlord’s time on
this task) and the advantage of the tenant as δ (1 hour of the landlord’s time


                                      17
on supervision is equivalent to δ < 1 hours of the tenant’s time on this task).
Both landlord and tenant are constrained in their total number of labor units
available, normalized to 1 unit.


Opportunity costs and migration
We integrate migration into this model by considering the opportunity costs
faced by both landlords and tenants.
    In the rural areas, the only jobs available are agricultural labor jobs, which
are low-skilled jobs, valued at w. In urban areas, there is a range of jobs, in
construction, the personal service sector, but also in IT, banking, engineering
etc. The high-skilled jobs are only accessible to high-skilled individuals (i.e.
the landlords) and are valued at m. The low-skilled jobs in the urban areas are
accessible to all, including the tenants, and are valued at s. We assume that
w ≤ s < m, reflecting these differential opportunities. Hence, the opportunity
cost of the landlord is m and the opportunity cost of the tenant is s. As noted,
we use w for the rural (casual) wage rate.


Contract choices
We allow for three distinct contractual options. The first option is for the
landlord to cultivate the land on his own. The second option is for the land-
lord to provide the land to the tenant for a fixed rent. The third option is
sharecropping.

Self cultivation

Assuming the landlord is risk-neutral, he maximizes the expected profit from
self-cultivation. The profits consist of the revenues of the crop minus the costs
of the labor inputs and whatever is earned in the urban sector.

                 max Q(M, δS, L; t) − wL + (1 − M − S ) ∗ m                   (4)
                 M,S,L




                                       18
    where the landlord provides both M and S but hires in L. The value of
the landlord’s time is evaluated at m, its highest value, the opportunity cost
in urban areas. The price of output is normalized at 1. Denote the maximand
of this problem as:

                             πself = π (w, m, δ ; t)                        (5)

Fixed rent

Under the fixed-rent contract, the landlord charges rental rate R and his profit
is:

                             πF,landlord = R + m                            (6)

   where the landlord spends all his time on the alternative occupation valued
at m. The rental rate, R, is set as to meet the participation constraint of the
tenant. The tenant’s expected (gross) profit from crop cultivation under such
an arrangement is:

                   Q(γM, S, L; t) − wL + (1 − M − S ) ∗ s                   (7)

   Assuming risk-neutrality, the tenant maximizes expression (7) with respect
to M, S and L. Denote this maximand as:

                            πF,tenant = π (w, s, γ ; t)                     (8)

   The landlord chooses R∗ as to set this expected profit net of the rent paid
equal to the tenant’s best outside opportunities, s, or:

                              s = πF,tenant − R∗                            (9)

   The resulting outcome for the landlord is then:

                             πF,landlord = R∗ + m                         (10)



                                        19
Sharecropping

In a sharecropping contract, both parties contribute to the production process.
The landlord contributes managerial input, while the tenant contributes su-
pervisory input. Both decide on their respective labor contributions, given the
contract terms (which are decided beforehand by the landlord as to maximize
his profits). The landlord’s profit may be derived using backward induction.
We start by defining a restricted profit function, the expected output net of
the hired labor cost:

                   π (M, S ; t, w) = max Q(M, S, L; t) − wL               (11)
                                        L

   The optimal choice of labor L, is conditional on the parameters of the
problem, w and t, and the labor inputs of tenant and landlord:

                                 L = L(M, S ; t, w)                       (12)

   where we added the parameter w to emphasize that this is conditional on
the wage rate.
   The sharing rule takes the following shape:

                           Share = β + α ∗ π (M, S ; t, w)                (13)

   The share contract assigns α of the net profits to the tenant, and the re-
mainder (1 - α) to the landlord. β is a fixed sum which goes to the tenant.
Given a set contract, both tenant and landlord choose their labor allocation,
non-cooperatively (taking into account the optimal hire of labor L as in ex-
pression 12).
   For the landlord:

                 max(1 − α)π (M, S ; t, w) + (1 − M ) ∗ m − β             (14)
                  M

   and for the tenant:

                      max απ (M, S ; t, w) + (1 − S ) ∗ s + β             (15)
                       S


                                            20
    Note that the transfer of β does not enter either maximization exercise.
Recall also that we assumed full specialization: the tenant contributes super-
vision while the landlord contributes managerial input. The best response
functions of the landlord and tenant are, respectively:

                                 M = M (S, α; t, w, m)                               (16)


                                  S = S (M, α; t, w, s)                              (17)

    Denote the resulting Nash equilibrium as (M ∗ (α), S ∗ (α)). The landlord,
anticipating these responses, now chooses the share parameter α to solve the
following equation:21

                   max(1 − α)π (M ∗ (α), S ∗ (α)) + (1 − M ∗ (α)) ∗ m                (18)
                     α

    Once the parameter α is set, the landlord determines the second parameter
of the share contract β as to set the tenant’s profits equal to his outside option,
or:

                             β = S ∗ ∗ s − α ∗ π (M ∗ , S ∗ ; t)                     (19)

      Denote the maximand of this exercise (for the landlord) as:

                                πS,landlord = π (w, s, m; t)                         (20)


Solution
The landlord compares the profits between these three arrangements, that is,
the profits from expressions (5), (10) and (20) and chooses the contract that
yields the highest expected profit.
    Instead of deriving an analytical solution, we present the result of a series
of simulations, where we vary the opportunity cost of time for landlords m.
 21
      We omit β and any reference to the various wages to keep the notation simple



                                             21
Keeping s constant, we map the landlord’s profits as a function of the ratio
m/s (which, according to the assumptions above, is always a number above
one) for the three scenarios, and observe when the landlord’s preferred contract
shifts.
    The parameters and specifications of this simulation are included in the
online Appendix. We opt for a Cobb-Douglas specification, and following
Eswaran and Kotwal (1985), ignore the uncertainty element and set θ equal
to its expected value of 1.
    In Appendix Figure A4 we map the landlord’s profit as a function of the
wage ratio m/s in the case of self-cultivation (labelled ‘fixed wage’ in the
figure as the landlord employs wage workers in that scenario). In this case, the
landlord works on his own farm, but as the opportunity cost increases, replaces
his own labor with wage labor. However, due to the nature of the production
process, some own labor will always be required. Even when m/s = 20, the
optimal values are M = 0.16; S = 0.06 and L = 6.4.
    In Appendix Figure A5 we map the landlord’s profit as a function of the
wage ratio m/s in the case of fixed rent. In this scenario, all of the landlord’s
time is spent on the alternative occupation valued at m. The rental rate, R, is
set as to meet the participation constraint of the tenant. As m increases, the
profit obtained from farming does not increase (as the tenant simply remains
against their participation constraint), but what the landlord can earn in urban
areas increase linearly. This time, for m/s = 20, the optimal values are M =
0.71; S = 0.28 and L = 21.79. Note that the sum of M and S is 1, as expected,
as the landlord pushes the tenant against their participation constraint and
demands full-time work of the tenant.
    In Appendix Figure A6 we map the landlord’s profit as a function of the
wage ratio m/s in the case of sharecropping. In this scenario, both the landlord
and tenant specialize fully. We again compute the resulting labour choice for
m/s = 20, and obtain the values of M = 0.1; S = 1 and L = 10.02. Note
that S is now 1, as expected, as the landlord works outside the farm while the
tenant hits their participation constraint. As m increase, profits increase but
not by much, as the landlord must balance obtaining this outside wage with


                                      22
continued farm work.
    We bring the three functions together in Figure 2, capping the range of the
wage ratio at 20. We are now in a position to trace the preferred contract.
The sharecropping yields a higher profit when the wage ratio is low, reflecting
the fact that twice as much labour is available for farming. However, as m
increases, the landlord starts taking up opportunities in urban areas, reducing
their input into farming. At the ratio m/s = 16, their preferred contract shifts
from sharecropping to fixed rent recognizing that it has become too expense
for them to contribute to farming directly.


6    Empirical strategy
The theoretical model highlights the role of opportunity cost of labor for tenant
and landlord as a driving force of contract choice. While the model represents
this as wages, there are other factors which might impact the landlord’s choice.
For example, absentee landlords cannot easily confirm yields and the cost of
migration might be more easily born by wealthier landlords. Hence, changes
in the wage ratios are only part of the driving force towards fixed rent. In
the empirical analysis, we will use the migration flows themselves and not the
wages. This also allows us to take advantage of our data on bilateral migration
flows between districts.
    We start with the following specification, where subscript i denotes the
district and subscript t denotes the time period:

                       Yit = β0 + β1 Mit + γXit + δt +   it                 (21)

    The dependent variable Y is a measure of land tenure arrangements in
district i and year t, including: acreage under sharecropping, acreage under
fixed rent (paid by money) and acreage under fixed rent (paid by produce),
duration of the contract (above 2 years of duration) and degree of formality
(whether the contract is written, and whether the land is leased from relatives),
all as a percentage of the acreage leased in.


                                       23
    The migration variable M in equation (21) is the number of high-skilled
male individuals, 20-64 years of age, who have moved residence in the past five
years, expressed as a percentage of the total number of male migrants (of 20-64
years of age who have moved residence in the past five years). As discussed
earlier, we define high-skilled as having completed 10 years of education. To set
the stage for the instrumental variable specification, which builds on between-
district migration flows due to exogeneity concerns, we include only individuals
who have left the district and omit within-district migrants.
    The coefficient of interest is β1 , which measures the relationship between
migration (M ) and land tenure arrangements (Y ). Our hypothesis is that β1
is positive for fixed rent prevalence and measures of contract formalization,
and negative for sharecropping and renting from relatives.
    To take into account changes in the underlying population, the control
vector Xit includes the total population (in 1000s), the sex ratio (number of
females for 100 males), the population density (in 1000s per square km) and
the share of high-skilled males (as a percentage of the male individuals of 20-64
years of age).
    The remainder of the time-variant control variables aim to capture the
alternative mechanisms. We include the number of bank branches within each
district (Reserve Bank of India), road length in each district (in km, ICRISAT),
and a measure of rain and temperature events (University of Delaware). These
measures are detailed in the Appendix. The inclusion of year fixed effects (δt )
allow us to further control for time variant country-wide factors, such as, trade
rules and regulations relating to agricultural output prices.
    To capture district-specific factors, we follow Derenoncourt (2022) and add
a vector of time-invariant district-level controls which account for differences in
agro-ecological zones: soils (NSS, using categories of soil texture), length of the
growing season (in days, ICRISAT), and measures of water stress (ICRISAT).
These measures are detailed in the Appendix.
    We omit district-fixed effects as for a significant number of districts we have
only one data point (see Figure 1), and the panel covers only two time periods
(unlike, for example, Liu, Shamdasani and Taraz (2023)). In addition, the


                                        24
majority of the variation is between district, not within districts (unlike, for
example, Breza and Kinnan (2021)). This method has also been applied in the
Indian context by Mukherjee (2020) who uses REDS district-level data to look
at the link between credit markets and technology adoption, and includes a
host of demographic, economic and soil controls, and Viswanathan and Kumar
(2015) who connects weather with migration using district-level data, and
includes controls for the agro-ecological zones.
    The descriptive statistics of all variables are presented in Appendix Table
A3.


IV specification
While the number of control variables is extensive, we might have missed some
remaining time-variant connections between land and labor markets. Unob-
served shocks to local agro-industries, for example, labor strikes, accidents,
and road construction, can both affect emigration (through wages and lack
of jobs which might push migrants out) and land tenure (through changes in
input markets and available agricultural technologies).
    To make further headway in the identification strategy, we distinguish be-
tween migrant push factors versus migrant pull factors. Push factors relate
to the conditions in the source district and “push” migrants out. Pull factors
relate to conditions in the destination district and “pull” migrants in. Most
concerns regarding identification of the effects of out-migration relate to push
factors. Hence, we instrument for emigration with measures of pull factors
that influence emigration but are plausibly exogenous to local land and labor
market conditions.
    This requires a measure of a pull force which varies across districts and
time. We arrive at this measure using a shift-share approach which exploits
differences in migrant networks across districts as measured in our bilateral
migration data. This is an adaptation of an approach used in studies of the
impact of international immigration on local labor markets (Card, 2001; Peri,
Shih and Sparber, 2015). Our instrument for migration is composed of two


                                      25
parts: (1) The shift component: a measure of the pull of potential destination
districts, and (2) A share component: a measure of the strength of the connec-
tion between the source and the potential destination districts. We detail each
in turn below and note that both shift and share component are skill-specific,
as in Peri, Shih and Sparber (2015).
    Our shift component - the proxy for the pull of each (destination) district -
is the total immigration into that district in the past five years from all districts
(barring the one source district under consideration, that is, a “leave-one-out”
measure). It is based on the idea that when a location has many economic
opportunities, it will attract migrants from a variety of locations.22
    Our share component - the measure of the migration connections between
the source district and potential destinations - consists of the historical shares
of various destination districts in the total out-migrants from the source dis-
trict. Specifically, the connection between a destination district j and source
district i in year t is the share of district j in the total number of individuals
who migrated out of district i five years or more before year t.23
    This approach of using the historical migrant network as a measure of con-
nection follows Card (2009). It is based on the insight that social networks
have a strong influence on the location decisions of migrants, with migrants
more likely to go to places to which more individuals from their network have
previously migrated (Munshi, 2003; Munshi and Rosenzweig, 2016; Munshi,
2020). Within the Indian context, the role of networks in migrants’ destina-
tions has also been highlighted by Gore (1970) who notes that ‘the nearest
town is not always the best option’, referring to the importance of the famil-
iarity of fellow villagers in a new location.24
  22
     This approach of using total migration flows as the shift component follows studies such
as Card (2001), Card (2009) and Goldsmith-Pinkham, Sorkin and Swift (2020) in spirit.
The details differ because these studies are interested in arriving at exogenous measures of
immigration rather than emigration. In this sense, our approach might be more similar to
Anelli et al. (2023) and Madhok et al. (2024) who use destination country/district economic
shocks as the shift for out-migration.
  23
     In calculating this stock, we consider only male individuals of 20-64 years.
  24
     For more recent examples, see among others, Munshi and Rosenzweig (2006); Tumbe
(2018).



                                            26
    Putting these two components together, the instrument for the level of
emigration of individuals of skill group s (where s ∈ {low, high}) from source
district i at time t is:

                                s           s       s
                             IVi,t =       Mj,−i,t Nj,i,t−5                     (22)
                                       j
               s
     where Mj,   −i,t are the total number of migrants of skill level s who moved
to district j between t and t − 5 years from all districts other than i (this is
                                                         s
the the shift component). The share component Nj,i,t       −5 is the historical (5
years ago and earlier) share of destination district j in the total migrants of
skill level s who left district i (capturing the exposure of district i to a shift in
j ). The instrumental variable regression uses both high-skilled and low-skilled
instruments.
     Madhok et al. (2024) and Anelli et al. (2023) are two recent studies which
also employ shift-share instruments for out-migration. Like our study, Madhok
et al. (2024) is in the context of internal migration in India. However, unlike
Madhok et al. (2024) where the share component is based on distance, we
exploit bilateral migration data in constructing the share component.


Residual network IV specification
We present a unique variation on the share component which takes into account
the fact that migrants tend to move to nearby districts (Kone et al., 2018).
   One concern in this case is that nearby districts can be affected by the same
agronomic shocks driving both land and labour market. Given that migrant
networks are biased towards nearby districts, this could make our instrumental
variable strategy invalid. While controls for local weather conditions might
mitigate some of these concerns, we present a more demanding first-stage
specification in which we use the variation in the historical migrant network
that remains after the distance between them has been taken into account. In
other words, we exploit that part of the historical migrant network that is not
explained by distance (specifically, travel time, as detailed in the Appendix).


                                           27
  Denote by T imej,i,t−5 the travel time between districts j and i at time t − 5.
We estimate the following regression on the bilateral district migration data:

                         s
                        Nj,i,t−5 = θT imej,i,t−5 +     j,i,t−5              (23)
                                                  s
  We then use the residual from this regression, Rj,i,t−5 , as the share variable
when constructing the migration instrument for skill level s:

                              s             s       s
                          IV Ri,t =        Mj,−i,t Rj,i,t−5                 (24)
                                      j


Instrument validity
Instrument relevance

Table A4 presents the first stage results. Columns (1) through (3) refer to
the standard instrumental variable, while Columns (4) through (6) refer to
the residual network approach. Columns (2) and (5) add the main set of con-
trol variables: population, weather (temperature and rainfall adverse events),
number of bank branches and road length. Columns (3) and (6) add con-
trols for the agro-climate zone, including soils, length of the growing season
(in days) and reference ETo (a measure of water stress). We note that the
instrument is strong across the board, with an F-statistic ranging from 13 to
39.

Instrument exogeneity

Identification with shift-share instruments is based on an assumption of exoge-
nous shifts (Borusyak, Hull and Jaravel (2022)) or exogenous shares (Goldsmith-
Pinkham, Sorkin and Swift (2020)). Translated to our setting, the assumption
of exogenous shifts means that total immigration into a district from all dis-
tricts other than a given source district is uncorrelated with current land out-
comes in that source district (conditional on controls). The exogenous shares
assumption translates into assuming that patterns of out-migration in the past
are unrelated with current land outcomes (again, conditional on controls).

                                          28
    This latter assumption may be more challenging to meet in our setting.
The concern is that districts which are close in the sense of historical migrant
networks are also spatially close, and could therefore be close in other ways
which matter to the land market. For example, they could have close product
market linkages which results in a regional response to drought. Our empirical
strategy is set up to minimize this concern.
    First, as explained earlier, the residual network specification removes the
spatial proximity from the share component, relying exclusively on the varia-
tion in historical networks. We find that the results are comparable across this
specification, and the standard specification, indicating that in this context,
concerns related to linked output markets are limited.
    Second, we exploit the difference in the network of high-skilled and low-
skilled emigrants. In effect, controlling for the low-skilled migrant network-
weighted shock, we rely on the high-skilled migrant network-weighted shock
as the instrument. Hence, a key identifying assumption of our instrumental
variable specification is that these high-skilled and low-skilled networks do
not entirely overlap, and that their difference is exogenous to the phenomena
under study.
    Another way of making the point that high-skilled and low-skilled networks
do not entirely overlap, and that their ratio is quasi-random, is to show that
districts with high ratio are not fundamentally different from districts with a
low ratio. We regress the ratio of the two instruments on our most extensive set
of control variables, those in Column (3) in Table A4, and derive the residual of
this regression. In Table A5, we present a t-test for differences between districts
which have a higher than median residual (of this regression) compared to a
lower than median residual. We select a set of variables which are not used
within our set of control variables, but are informative: market access and
output prices of the main crops. We find that the two sets of districts are
comparable across these indicators.
    To further illustrate how this strategy helps address concerns regarding
spatial correlation, we follow Khanna et al. (2022), and create a heat map of
the predicted migration variable. This is a geographical map of the number of


                                       29
high-skilled as a percentage of the total number of male individuals of 20-64
years of age who have moved residence in the past five years predicted by the
two instruments - as in Columns (1) and (4) of Table A4 but excluding the
year fixed effect. Figure A7 presents the results, using 2001 census district
boundaries. The top panel refers to the 2001 year, while the bottom panel
refers to the 2011 year. The maps on the first row of each panel refer to the
standard instrument, while the maps on the second row of each panel refer to
the residual network instrument.
    We draw two conclusions. First, we note little difference between the rows
of each panel, reinforcing the claim that the residual instrument method yields
similar results as the standard instrument. Second, we note that for most
regions, there is little geographical clustering, alleviating concerns regarding
any remaining, unobservable, regionally correlated effects.


7    Results
Table 3 presents the correlation between migration and land tenure arrange-
ments, exploiting variation between districts in 2002 and 2012. The dependent
variable is the percentage acreage rented in under specific terms. Column (1)
refers to fixed rent, column (2) to the sub-category of fixed rent under mon-
etary terms, column (3) to the sub-category of fixed rent under crop terms,
column (4) to sharecropping, column (5) to renting from relatives, column (5)
to two-year or longer contracts and column (6) to written contracts. All the
dependent variables are included in percentage terms, that is, as a percentage
of the rented-in acreage.
    We find that as hypothesized, the out-migration of high-skilled males has
a statistically significant positive correlation with the prevalence of fixed rent
contracts under money terms, and a negative correlation with the prevalence of
sharecropping. The raw association between high-skilled male out-migration
and the prevalence of fixed rent contracts paid in produce is negative; as
discussed further below, such contracts are in between sharecropping and fixed
rent contracts in money terms and their expected correlation with migration

                                      30
is ambiguous.
    Counter to our hypothesis, there is a positive correlation between the out-
migration of high-skilled males and renting from relatives.
    These correlations are sensitive to the specification, and in particular, the
control variables included. Table 4 adds our main set of control variables to
the OLS following specification 21: the vector of population controls, bank
branches, road length, and measures of adverse weather events. The corre-
lations between the out-migration of high-skilled men and the prevalence of
fixed rent in money terms or sharecropping are no longer statistically signifi-
cant. Expanding the list of control variables to measures of the agro-climatic
zone (soils, length of growing season and water stress levels through evapo-
transpiration) yields similar patterns (Table A6). The latter specification has
a smaller sample due the missing data in the ICRISAT dataset. Table 4 is our
preferred specification as it controls for weather effects.


Main results: Standard IV specification
Table 5 presents the results using our standard instrumental variable specifi-
cation. The set of dependent variables is the same as in Table 4. The results
indicate that migration has been a driving force in the shift from sharecrop-
ping to fixed rent: the coefficient on high-skilled male out-migrants is positive
and significant for Column (1) and Column (2), both for fixed rent and fixed
rent in monetary terms. The negative relationship with sharecropping is also
statistically significant at the 5% level. A one percentage point increase in
high-skilled (male) out-migrants increases fixed rent arrangements with 2.7
percentage points and reduces sharecropping with 1.9 percentage points in
sharecropping arrangements. This corresponds to an effect size of, respec-
tively, 6% and 5%. The sign on relatives has changed direction and is now
the expected negative sign, but we note no statistically significant relationship
with either contract length or written contracts in Columns (6) and (7).
    The results with a more extensive set of controls in Appendix Table A8 are
very similar, while the results without the control variables (Appendix table


                                      31
A7) appear muted. Notably, in both cases the effect on written contracts is
statistically significant and sizable. Note again the drop in sample size in the
former specification.
    This suggests that migration plays a role in the formalization of the land
rental market. Recall that the probability of a written and longer contract
increased between 2002 and 2012 (see Table 1). Migration increases the prob-
ability of a written contract (in most specifications), but does not affect con-
tract length. Migration also (in most specifications) decreases the probability
of renting from relatives.
    We also note a differential impact between the two types of fixed rent
contracts in Table 5. Most fixed rent contracts are in money terms (Appendix
Figure A1), and it is on these types of contracts that we see a consistent
impact. The lack of effect on the second type of contract could be due to
statistical reasons, or because it represents an in-between contract. On the
one hand, payment in produce might entail a significant transaction cost. On
the other hand, moral hazard on the part of the tenant can largely be avoided
as the amount of produce is fixed.25


Residual network IV specification
Table 6 presents the results using our alternative instrumental variable specifi-
cation, where the instrument is stripped from the component which relates to
distances between districts. The set of dependent variables is again the same
as in Table 4.
    The results remain similar in terms of sign, size and significance compared
to the standard instrumental variable, with the only difference that in this more
demanding specification the effects on contracts with relatives lacks precision.
In the Appendix, we again present the results without controls (Appendix
Table A9), and a more extensive set of controls (Appendix Table A10). Again,
the effects in the former case are more muted, while the robust errors on the
contract with relatives varies as per specification.
 25
      Although a fluctuating output price might complicate matters further.



                                            32
Additional robustness checks
The National Rural Employment Act (NREGA), a large-scale public employ-
ment scheme rolled out in rural India in 2005, has affected rural labor markets
during our study period, including by increasing wages (Imbert and Papp,
2015; Berg et al., 2018). While NREGA does not necessarily interfere with
our identification strategy, we check the robustness of our findings with respect
to this scheme. In Appendix Table A11 we present a split-sample analysis
of Table 5. The first two columns are the districts where NREGA started in
2006 (Phase 1). The third and fourth columns are the districts where NREGA
started in 2007 (Phase 2). The fifth and sixth columns are the districts where
NREGA started in 2008 (Phase 3). We note similar effects in the first and
last set of districts, but appear to lack power for the middle set. Chari et al.
(2019) notes that while the exact criteria are not known, the assignment of
districts into phases was intended to prioritize the most ‘backward’ districts.
This might have resulted in the stronger result in the first set, which might be
more rural as well.
    Another concern relates to demand-side channels. Structural transforma-
tion is associated with demand shifting away from staple food crops (Her-
rendorf, Rogerson and Akos´    Valentinyi, 2014). This change in demand may
impact the land market and also correlate with migration flows. To check this
possibility, we use the standard IV specification and the acreage of cash crops
(as a percentage of the cultivated acreage) as the dependent variable in Ta-
ble A12.26 There is no statistically significant relationship between migration
and cash crop prevalence, suggesting that these types of correlated effects are
unlikely to be a threat to the main results.


Absentee landlords and farm yields
Finally, we examine the relationship between high-skilled migration and crop
yields. The direction of this relationship is theoretically ambiguous. The Mar-
  26
    This is the percentage acreage of crops which are not rice, wheat, maize or sorghum
using ICRISAT data.



                                          33
shallian argument suggests that the shift towards fixed rent contracts should
increase yields. Remittances (which we cannot observe in our data) may fur-
ther increase yields by facilitating large-scale investments, such as in tractors
and irrigation systems. However, high-skilled migration may reduce yields
through a loss of labor (as in Rozelle, Taylor and De Brauw (1999)); specif-
ically, a loss of the landlord’s labor inputs and know-how which may not be
easily replaceable.
    In Appendix Table A13 we present the result of the standard IV specifica-
tion, with the yield of all major crops (in kg/ha in natural log) as a dependent
variables. Due to the large number of connected variables, we apply a stan-
dard multiple hypothesis correction following Anderson (2008). Note that the
sample size varies as not all crops are cultivated in all districts.
    We note imprecisely estimated null effects for the majority of crops. Fo-
cusing on the main grains, the food crops, we note a positive impact on rice
and maize (estimated at 5% and 4%. respectively), and a negative impact on
wheat (estimated at 5%). The former is consistent with Marshallian theory,
with the labor incentive (and possibly remittance) effect dominating. The lat-
ter implies the dominance of other channels related to the loss of crop-specific
knowledge and labor.


8    Conclusion
This paper contributes to a longstanding question in the study of economic
development: the causes and consequences of the reallocation of labor from
rural to urban areas. Employing an empirical strategy that exploits district-
level bilateral migration network data, we find that in early 21st century India,
out-migration of high-skilled males contributed to the shift from sharecropping
to fixed rental arrangements. This is a to-date undocumented consequence of
rural-urban migration in developing countries, with important implications for
efficiency and welfare.
    High-skilled out-migration, through an institutional response of changed
rental contracts, appears to increase yields for some key crops, countering the

                                       34
effects of a loss of labour and knowledge. High-skilled out-migration also ap-
pears to contribute to formalization of land markets, increasing the length
of land rental contracts and reducing renting to relatives. The productivity
implications of this formalization would be interesting to study in future re-
search. Longer contracts may improve incentives for cultivators, while decrease
in within-family tenancy may improve allocation of talent on farms.
    The results also advance our understanding of the changing incidence of
risk in the rural sector of low- and middle-income economies in the 1990s and
2000s, an era in which trade liberalization and accelerating climate change
increased farm income volatility. Our analysis suggests that higher skilled
agricultural land-owning households are better placed to mitigate this risk by
shifting its incidence to poorer tenant households through fixed rent contracts
and migrating out of rural areas. This adds to a more standard view that
farming (land-owning) households mitigate their risk from trade and climate
shocks through changes in crop portfolio and planting decisions (for example,
Allen and Atkin (2022); Taraz (2017); Cui and Xie (2022)).
    Our paper contributes to a more comprehensive understanding of land
rental markets. A large share of farmland in developing countries is under a
rental arrangement: Otsuka (2007) estimated rates in the early 1990s at 10% in
Latin America, to 12% in Asia and 18% in Africa. Recent studies suggest there
could be sizable productivity gains from removing restrictions on agricultural
land rental markets (Otsuka, 2007; Christiaensen and Demery, 2018; Chen,
Restuccia and Santaeul`  alia-Llopis, 2022). The results in this paper imply that
the effects on efficiency will be contingent on the nature of the land rental
contracts which emerge after the liberalization of these markets.




                                       35
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Figures and Tables

          Figure 1: Percent acreage under fixed term arrangements


                               Panel A: 2002




                                Panel B: 2012




Note: Kharif season. NSS Land and Livestock Survey. Panel A presents the
percentage acreage under fixed terms in 2002. Panel B presents the percentage
acreage under fixed terms in 2012. Districts for which no data is available in a
given year are left light grey. The maps use district boundaries of 2001. The
left-most maps display East India, the middle maps North and West India,
and the right-most South India.




                                      46
         Figure 2: Profit as a function of w/s in the three scenarios




Note: This figure plots the relationship between the landlord’s profit and m/s
in the three scenarios. w = 0.01 ; s = 0.05 ; t = 0.5; time equivalent ratios are
γ =0.8 and δ = 0.8; production parameters are a = 0.4 and b = 0.5. Range
capped at 20.




                                       47
            Table 1: Types of contracts, in percentage, by year

                                                 In acreage terms
    year                                 1992          2002         2012
    sharecropping                         45            43           31
    fixed terms                            45            50           58
          fixed amount of money            25            30           41
          fixed amount of crop output      20            20           17
    from relatives                         6             4            8
    duration more than two years          42            41           65
    written contract                      18            10           15
                                                In contract terms
    year                                 1992          2002         2012
    sharecropping                         49            51           38
    fixed terms                            35            41           49
          fixed amount of money            15            22           30
          fixed amount of crop output      19            20           20
    from relatives                        10             3            9
    duration more than two years          50            40           66
    written contract                      18            10           11

Note: Kharif (rainy) season. India NSS Land and Livestock Survey Rounds
48, 59 and 70. The top panel presents the percentages in acreage terms (as
a percentage of the total acreage rented in). The bottom panel presents the
percentages in contract terms (as a percentage of the total number of rented
in fields (plots)). Statistics are generated using NSS population weights to
generate nationally representative statistics.




                                    48
           Table 2: Migration flows, in absolute numbers, by year

                                       Low-skilled
        year                              2001           2011
        male migrants within-district 3,728 (3,952) 4,419 (5,375)
        male migrants out-of-district 4,834 (4,935) 5,022 (4,684)
                                      High-skilled
        year                              2001           2011
        male migrants within-district 4,712 (5,557) 7,586 (11,158)
        male migrants out-of-district 7,712 (6,762) 10,289 (9,341)

Note: In this table we present the trends in district-level migration flows,
in absolute numbers, from 2001 to 2011. The numbers presented are the
average (and standard deviation in brackets) number of out-migrants across
all districts. We only include male migrants between the ages of 20 and 64
who migrated in the past five years, but distinguish between low-skilled (less
than 10 years of education) and high-skilled (more than 10 years of education)
at the top and bottom panel, respectively.




                                     49
                        Table 3: Correlation between migration and land tenure arrangements (OLS)
                            (1)           (2)            (3)            (4)          (5)            (6)                (7)
                        fixed rent   fixed (money)   fixed (crop)   sharecropping    relatives   contract length   written contract
         migration       0.182*       0.431***      -0.249***      -0.540***      0.291***       0.290***            -0.0232
                         (0.103)      (0.0879)       (0.0779)        (0.102)      (0.0673)       (0.0978)           (0.0740)
         2012 year        -3.247        -0.307         -2.940         -3.947     7.420***        20.78***            3.541**
                         (2.618)       (2.427)        (1.807)        (2.578)       (1.518)        (2.468)            (1.702)
         Constant       33.96***        0.905        33.05***       76.86***     -13.25***       18.82***           12.70***
                         (6.622)       (5.469)        (5.071)        (6.603)       (4.111)        (6.238)            (4.796)
         Observations       927           927            927           927           927            927                927
         R-squared         0.004         0.022          0.019         0.036         0.056          0.090              0.005

     Note: This table uses an OLS regression to present the correlation between the percentage of rented-in acreage
     under various terms and the number of high-skilled male out-migrants between the ages of 20-64 years (as a
     percentage of the total male out-migrants between the ages of 20-64 years). The dependent variable is as a
50




     percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
             Table 4: Correlation between migration and land tenure arrangements (OLS with main controls)

                                    (1)           (2)           (3)             (4)           (5)             (6)                (7)
                               fixed rent    fixed (money)   fixed (crop)   sharecropping     relatives   contract length   written contract
      migration                   -0.165       0.0194        -0.184*          -0.210      0.263***           0.196             -0.0558
                                 (0.157)       (0.143)       (0.110)         (0.160)       (0.0935)         (0.145)            (0.108)
      bank branches (number)      0.0236       0.0354*       -0.0118         -0.0279        0.0118        -0.000616          0.0323**
                                (0.0221)      (0.0195)      (0.0103)        (0.0227)       (0.0107)        (0.0152)           (0.0146)
      road length (km)          6.74e-06      -6.72e-05     7.39e-05        0.000191      -0.000207      0.00165***          -0.000420
                               (0.000457)    (0.000440)    (0.000283)      (0.000476)    (0.000269)      (0.000428)         (0.000322)
      2012 year                  -5.238*        -2.888        -2.350          -4.203      7.715***        22.50***            3.854**
                                 (2.880)       (2.638)       (1.933)         (2.860)        (1.812)         (2.700)            (1.864)
      observations                  878           878          878             878            878             878                878
      R-squared                    0.027         0.075        0.035           0.055          0.079           0.129              0.034
      mean dep. var.              45.34          27.83        17.51           34.13          4.92            36.90              11.25
51




     Note: This table uses an OLS regression to present the correlation between the percentage of rented-in acreage
     under various terms and the number of high-skilled male out-migrants between the ages of 20-64 years (as a
     percentage of the total male out-migrants between the ages of 20-64 years). The population controls include
     total population, sex ratio, population density and share of high-skilled males. Remaining controls include the
     percentage of adverse rain events and the percentage of adverse temperature events. The dependent variable is
     as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
                         Table 5: IV regression: The effect of migration on land tenure arrangements

                                    (1)            (2)          (3)              (4)          (5)            (6)                (7)
                               fixed rent    fixed (money)   fixed (crop)   sharecropping    relatives   contract length   written contract
      migration                 2.607***      2.199***        0.409          -1.787**      -1.041*          0.209              0.459
                                  (0.832)       (0.652)      (0.502)          (0.865)      (0.577)         (0.728)            (0.425)
      bank branches (number)      -0.0252      -0.00298     -0.0222*        -0.000115     0.0347**       -0.000842            0.0233
                                 (0.0242)      (0.0204)     (0.0131)         (0.0255)     (0.0174)        (0.0198)           (0.0151)
      road length (km)          -0.000722     -0.000640     -8.20e-05       0.000606      0.000136      0.00164***          -0.000556
                               (0.000631)    (0.000556)    (0.000316)      (0.000553)    (0.000360)     (0.000473)         (0.000348)
      2012 year                   -5.709*        -3.258       -2.451           -3.936     7.936***       22.50***            3.767**
                                  (3.400)       (3.003)      (1.956)          (3.028)      (2.013)         (2.685)            (1.884)
      observations                  878            878         878              878          878             878                878
      mean dep. var.               45.34          27.83       17.51            34.13         4.92           36.90              11.25

     Note: This table uses the shift-share instrumental variable regression to present the relation between the percent-
52




     age of rented-in acreage under various terms and the number of high-skilled male out-migrants between the ages
     of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The population
     controls include total population, sex ratio, population density and share of high-skilled males. Remaining controls
     include the percentage of adverse rain events and the percentage of adverse temperature events. The dependent
     variable is as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
        Table 6: IV regression: The effect of migration on land tenure arrangements, using the residual approach

                                    (1)            (2)           (3)            (4)           (5)           (6)                 (7)
                               fixed rent    fixed (money)   fixed (crop)   sharecropping    relatives   contract length   written contract
      migration                 2.682***      2.182***         0.500        -1.882**        -0.916         0.150               0.462
                                  (0.855)       (0.663)       (0.517)        (0.886)       (0.587)        (0.745)             (0.427)
      bank branches (number)      -0.0265      -0.00269      -0.0239*        0.00156       0.0325*       0.000205             0.0232
                                 (0.0245)      (0.0207)      (0.0131)       (0.0257)      (0.0174)       (0.0200)            (0.0153)
      road length (km)          -0.000742     -0.000636     -0.000106       0.000631      0.000103      0.00166***          -0.000557
                               (0.000641)    (0.000558)    (0.000322)      (0.000560)    (0.000351)     (0.000476)         (0.000348)
      2012 year                   -5.722*        -3.255        -2.466         -3.920      7.915***       22.51***            3.766**
                                  (3.428)       (2.998)       (1.972)        (3.048)       (1.977)        (2.685)             (1.882)
      observations                  878            878          878            878           878            878                 878
      mean dep. var.               45.34          27.83        17.51          34.13          4.92          36.90               11.25

     Note: This table uses the residual shift-share instrumental variable regression to present the relation between the
53




     percentage of rented-in acreage under various terms and the number of high-skilled male out-migrants between the
     ages of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The population
     controls include total population, sex ratio, population density and share of high-skilled males. Remaining controls
     include the percentage of adverse rain events and the percentage of adverse temperature events. The dependent
     variable is as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
For online publication: Appendix
Data
This section provides details on other data sources employed.

Credit: Reserve Bank of India

We obtained data on bank branches from the Reserve Bank of India.27 We
obtained the number of commercial (which include both private and public
sector banks) by district for the years 2002 and 2012 for both rural and urban
areas.28 . This measure provides a proxy for banking activity in the district.

Weather: University of Delaware

We also aim to include control variables for adverse weather conditions in the
years preceding the year under consideration. We utilized two databases of the
University of Delaware’s Global Climate Database: Earth Precipitation: 1900-
2017 Monthly Time Series in Grid, and Earth’s Air Temperature: 1900-2017
Time Series in monthly grid.29 These databases contain monthly precipitation
and air temperature for the 1900-2017 period, based on weather station data,
but interpolated to a 0.5-degree by 0.5-degree latitude/longitude grid (with
the grid nodes centered on the 0.25 degree).
    Using the 2001 district census boundaries, we average the precipitation/air
temperature data of all data points within each district boundary to create
district-level averages for all the years between 1970 and 2012.
    Using these district-level time series, we classify years (in each district) as
to whether or not adverse weather conditions prevail, and then aggregate this
information (at the district level) over five years.
    We define an rain adverse event as a year in which the annual rainfall
is below the 20th percentile or over the 80th percentile of the long term (30
  27
     see: https://www.rbi.org.in/ under the annual publications tab.
  28
     The data from 2012 used the 2008 district boundaries; we mapped up the data points
using our district harmonization method
  29
     See: http://climate.geog.udel.edu.


                                          54
year) series. An adverse temperature event is similarly defined. The long series
covers the available years 1971-2001 for the 2002 year and the years 1981-2011
for the 2012 year.
    Next, we define a measure of weather adversity. Let ai,τ takes the value
of 1 if an adverse event happened at time τ in district location i. Ni,t counts
the total number of events within district boundary i during the five years
under consideration (this is usually 5, unless there are missing data). Then,
the percentage of adverse events (for either temperature or rainfall) is defined
as:

                                         t
                              Ai,t =           ai,τ /Ni,t ∗ 100                      (25)
                                       τ =−5


Agro-climatic zones, roads and yields: ICRISAT

We obtained information on the agro-climatic zone from the ICRISAT meso-
level database.30 We use a standardized measure of crop water requirements,
the yearly evapotranspiration (measured in mm), and the length of the growing
period (defined as the period when normal precipitation exceeds 0.5 ETo).31
These time-invariant data are presented using the 2011 district census bound-
aries. We imputed missing values in these ICRISAT data using information
on the nearest neighbour using 2011 district census boundaries.32
    In addition, we obtained the 2001 and 2011 ICRISAT time-variant data on
the total road length and the number of markets in the district (in km). For
both years, we also obtained measures of crop (output) price (Rs/100 kg), crop
  30
     See: http://data.icrisat.org/dld/
  31
     ICRISAT records what it terms the normal monthly and annual potential evapotran-
spiration. Most documents refer to this concept as the ”reference crop evapotransporation”
denoted ETo. This refers to a hypothetical crop and relies on climatic inputs only, not
taking into account the specific crop or soil conditions. See Allen et al. 1998. We use the
monthly values and compute an annual value from this.
  32
     There are 421 districts in the ICRISAT file, compared to a total of 640 in India 2011
NSS. So about 35% are missing. However, our final dataset has about 575 districts (because
we don’t use all the states), so according to this 27% districts are missing in ICRISAT.To
deal with the missing, we assigned the value of the nearest non-missing neighbor out of 4
closest neighbors.



                                               55
area (in ‘000 hectares) and crop productions (in ’000 tons) and crop yields (in
kg/ha), for the main crops in the country. This includes maize and rice. These
allow us to create a measure of crop yields and shares.

Soils: NSS Land and Livestock Survey

Recall that the NSS land and livestock survey collected information on the soil
texture. These data are only available in Round 59 (which covers year 2002),
but as texture tends to be stable over time, this suffices for our purpose of
generating a district level control variable on soil conditions. Soils, at the field
level, are classified into the following texture categories: sand - 1, loam - 2, silt
- 3, light clay - 4, heavy clay - 5, others - 9. We use a district-level (weighted)
vector which indicates the percentage of soils into each soil category.

Distance: Digitization of road maps and computation of the mini-
mum travel time between districts

We obtained scanned paper maps of India from 1996 and 2011 via the work of
Allen and Atkin (2022). These maps included different types of roads which
are distinguished by color. For instance, a highway has a different color than
a local road. Different road types imply different travel times: for example,
it would typically take less time to travel 1 km on a highway than on a local
road.
    Using GIS software, we superimposed the road maps onto district shape
files of 2001 and 2011 (geo-coding, in GIS parlance). We then converted the
road map into color-coded pixel data (raster data, in GIS parlance). Using
information on the location of each district, and the roads connecting them,
we computed a measure of the minimum travel time between districts.33
    This calculation attributed a “cost of distance” to each road type: the
highways were attributed a cost of one, medium roads a cost of two, and small
roads a cost of three per cell. That is, higher costs reflect slower average
speeds. To compute the travel time along a given path, the distances/cells
  33
       We are grateful to Michael Norton (World Bank) for generating these calculations.


                                              56
traveled along these various types of roads on that path were weighted with
the associated costs.34 Next, the fastest of all possible paths between two
districts (the “accumulated least cost distance”) was computed using Dijkstra’s
algorithm (Dijkstra (2022)). For this calculation, the centroid of the sub-
district with the highest population density within a district was chosen as
the starting/ending point of that district.35 Note that the resulting unit of
this minimum travel time is not in hour, or minutes, but a km based measure.
    We validated this method using Bing Maps travel time, comparing our 2011
estimate of the minimum travel time with the current travel time according to
Bing Maps. Our method accounts for 95.7% of the variation in travel times of
Bing maps using a random sample of 100 district pairs. Note that this method
is similar to what Allen and Atkin (2022) use to link to location of highways
to trade costs. It is likely to be an improvement over the more commonly used
as-the-crow-flies distance (for example, in Madhok et al. (2024)) as it accounts
for the variation in road connectivity within India.
    We use the matrix of minimum travel time (in our weighted km unit)
between districts in the construction of the instrumental variable.




  34
      While the use of raster data allows us to do these tasks in a time-efficient manner; the
method can result in district combinations which are not connected, that is, which have
gaps in the roads. When computing the travel time we allowed for “jumps” assuming that
our digitization/ process is imperfect.
   35
      Using the centroid of the district was less satisfactory as it would often be separated
from the road network by some distance.


                                             57
Simulations
This section provides the technical details of the simulation exercise.
   We opt for a standard Cobb-Douglas production function with decreasing
returns to scale:

                              ˜ = θ ∗ (S t ∗ Lt−1 )a ∗ M b
                              Q                                                       (26)

    Across the three scenarios, we fix the following parameters: t, recall the
supervision technology, is set at 0.5. The remaining production parameter, a
is set at 0.4 and b is set at 0.5. Then, γ and δ , the time management equivalent
ratios, are both set at 0.8. These ratios are critical in determining how the
three solutions match up; for further analysis of their role, refer to Eswaran
and Kotwal (1985).36
    In the first scenario the landlord’s payoff can be written as:

            πself = [(γS )0.5 ∗ L0.5 ]0.5 ∗ M 0.4 − wL + (1 − M − S ) ∗ m             (27)

    We vary m from 0.05 to 1 (and set s at 0.05 and w at 0.01) - which implies
that m/s ranges from 1 to 20 - and maximise the landlord’s payoff for each
value of m by choosing the values of M , S and L subject to constraints (recall,
the sum of M and S is capped at one). Recall also that γ is set at 0.8.
    The result of this exercise is presented in Appendix Figure A4. We compute
that at m/s = 20 we have M = 0.16; S = 0.06 and L = 6.4, hence the landlord
in this scenario works both on the land as well as make use of outside options.
    In the second scenario, the landlord spends all her time on the alternative
occupation valued at m. The rental rate, R, is set as to meet the participation
constraint of the tenant. We keep t, the supervision technology, set at 0.5. The
remaining production parameters a and b are set at 0.4 and 0.5, respectively,
as before. δ , the time management equivalent ratio is set at 0.8. We follow
  36
    They show that if γ and δ are low (meaning both landlord and tenant are ill suited
at doing each-other’s tasks of management and supervision, respectively), sharecropping is
preferred. However, when γ is high, meaning the tenant is quite skilled at management
tasks, a fixed rent contract dominates, and if δ is high, meaning the landlord is capable to
engage in supervision, owner cultivation is preferred.


                                            58
a sequence of steps to compute the landlord’s payoff. We again vary the
parametric values of m ranging from 0.05 to 1 (while fixing w at 0.01 and
s at 0.05). We then compute the optimal values of M , S and L subject
to constraints (with the sum of M and S capped at one), and use these to
compute the landlord’s payoff.
    The result of this exercise is presented in Appendix Figure A5. We note
that for m/s = 20, we obtain optimal values of M = 0.71; S = 0.28 and
L = 21.79. Note that the sum of M and S is 1, as expected, as the landlord
pushes the tenant against their participation constraint and hence will demand
full-time work of the tenant.
    In the third scenario, we assume full specialization. We first derive the
conditional profit function by finding the optimal L as a function of M and S .
Again, we fix t at 0.5 and the production parameters a and b at 0.4 and 0.5,
respectively. We fix w at 0.01 and s at 0.05. The optimal L as a function of
S and M is:

                       L = ((0.2/w) ∗ M 0.5 ∗ S 0.2 )1/0.8               (28)

   When taking this conditional profit function to the next step, a standard
Nash game, it should be noted that the responses of both parties depend on
the exact value of α. So we fix α as a number between 0 and 1, and then plug
the conditional profit function into the Nash Equilibrium optimisation exercise
using the NIRA Nash Algorithm (Nikaido-Isoda Relaxation Algorithm) and
compute the Nash S and M responses for this fixed value of α. We plug the
choices of M and S back into the optimal response for L and use the updated
unconditional profit to obtain a measure for the payoff of the landlord and
tenant.
   We repeat this exercises for selected values of α within the 0-1 range,
and compute the landlord’s payoff. The result of this scenario is presented
in Appendix Figure A6. We again compute the resulting labor choice for
m/s = 20, and obtain the values of M = 0.1; S = 1 and L = 10.02. Note
that S is now 1, as expected, as the landlord pushes the tenant against his
participation constraint but himself works outside the farm.

                                       59
For online publication: Appendix Figures and
Tables




                     60
                                          Figure A1: Contract terms (by year)
61




     Note: This figure presents the percentage of contracts leased-in under various arrangements. Kharif season. NSS
     Land and Livestock Survey. The top panel is 1992, the middle 2002 and the bottom panel 2012.
                                        Figure A2: Duration contract (by year)
62




     Note: This figure presents the percentage of contracts leased-in under various duration. Kharif season. NSS Land
     and Livestock Survey. The top panel is 1992, the middle 2002 and the bottom panel 2012.
                Figure A3: Education and Land Ownership




Note: 01 ”not literate” 02 ”literate without formal schooling: EGS/ NFEC/
AEC” 03 ”literate without formal schooling: TLC” 04 ”literate without formal
schooling: others” 05 ”literate: below primary” 06 ”primary” 07 ”middle” 08
”secondary” 10 ”higher secondary” 11 ”diploma/certificate course” 12 ”grad-
uate” 13 ”postgraduate and above”. The landless are defined as possessing
less than 2 hectare. The landed are defined as owning more than 2 hectare.
NSS Land and Livestock Survey round 70 (2013).




                                    63
      Figure A4: Profit as a function of w/s in self-cultivation scenario




Note: This figure plots the relationship between the landlord’s profit and m/s
in the self-cultivation scenario. w = 0.01 ; s = 0.05 ; t = 0.5 ; time equivalent
ratios are γ =0.8 and δ = 0.8; production parameters are a = 0.4 and b = 0.5.
Range capped at 20.




                                       64
         Figure A5: Profit as a function of w/s in fixed rent scenario




Note: This figure plots the relationship between the landlord’s profit and m/s
in the fixed rent scenario. w = 0.01 ; s = 0.05 ; t = 0.5; time equivalent ratios
are γ =0.8 and δ = 0.8; production parameters are a = 0.4 and b = 0.5. Range
capped at 20.




                                      65
    Figure A6: Profit as a function of w/s in the sharecropping scenario




Note: This figure plots the relationship between the landlord’s profit and m/s
in the fixed rent scenario. w = 0.01 ; s = 0.05; t = 0.5; time equivalent ratios
are γ =0.8 and δ = 0.8; the production parameters are a = 0.4 and b = 0.5.
Range capped at 20.




                                      66
Figure A7: Predicted value of migration using instruments for 2001 and 2011


                               Panel A: 2001




                                Panel B: 2011




Note: This figure maps the number of high-skilled as a percentage of the total
number of male individuals of 20-64 years of age who have moved residence
in the past five years predicted by the two instruments (as in Columns (1)
and (4) of Table A4 but excluding the year fixed effect)). We use 2001 census
boundaries to present the results. The top panel refers to the 2001 year, while
the bottom panel refers to the 2011 year. The maps on the first of row of each
                                      67 while the maps on the second row of
panel refer to the standard instrument,
each panel refer to the residual network instrument. The left-hand side maps
display East India, the middle maps North and West India, and the right-hand
side South India.
            Table A1: Types of contracts, in percentage, by year

                                                 In acreage terms
    year                                 1992          2002         2012
    sharecropping                         51            42           31
    fixed terms                            36            51           57
          fixed amount of money            17            31           42
          fixed amount of crop out         19            19           15
    from relatives                         9             3            6
    duration more than two years          48            43           59
    written contract                      14             9           12
                                                In contract terms
    year                                 1992          2002         2012
    sharecropping                         53            49           38
    fixed terms                            32            42           49
          fixed amount of money            13            23           32
          fixed amount of crop output      19            20           17
    from relatives                        11             3            7
    duration more than two years          48            38           62
    written contract                      17             9           10

Note: Rabi (dry) season. India NSS Land and Livestock Survey Rounds 48,
59 and 70. The top panel presents the percentages in acreage terms (as a
percentage of the total acreage rented in). The bottom panel presents the
percentages in contract terms (as a percentage of the total number of rented
in fields (plots)). Statistics are generated using NSS population weights to
generate nationally representative statistics.




                                    68
       Table A2: Numbers of high and low-skilled individuals, by year

       year                             2001              2011
       low-skilled individuals    628,889 (503,887) 772,797 (646,578)
       high-skilled individuals   139,840 (138,648) 203,442 (211,104)

Note: In this table we present the trends in district-level high and low-skilled
individuals from 2001 to 2011 in absolute numbers. The standard deviations
are included in parenthesis next to the averages. We only include male indi-
viduals between the ages of 20 and 64 who migrated in the past five years.
Low-skilled are defined as less than 10 years of education and high-skilled as
more than 10 years of education.




                                      69
                                        Table A3: Descriptive statistics, by year

                                                                     2002               2012
                                                             mean      sd        n     mean      sd    n
            area under fixed rent (%)                         45.34   38.66      452    42.88   39.72 475
            (monetary rent) (%)                              27.83   35.64      452     29.39  37.43 475
            (crop rents) (%)                                 17.51   26.88      452    13.49   26.72 475
            area under sharecropping (%)                     43.13   38.71      452    36.85   39.57 475
            area with contract to relatives (%)               4.92   16.46      452    13.60   28.66 475
            area with contract longer than 2 years (%)       36.90   35.36      452    58.93   38.66 475
            area with written contract (%)                   11.25   22.60      452    14.69   27.99 475
            migration ratio (%)                              62.69   13.59      560    67.21   12.25 575
            percentage of adverse rain events (%)            31.64   20.69      560    42.40   20.53 575
            percentage of temperature adverse events (%)     46.39   21.23      560    47.37   16.57 575
70




            bank branches (number)                          107.83   89.82      560   162.69 163.29 575
            road length (km)                                2934.80 3096.62     489   2324.33 3289.62 575
            total population (in 1000s)                     1747.68 1304.18     560   2028.08 1574.15 575
            population density (in 1000s per square km)       0.46    0.51      543     0.53    0.49  562
            sex ratio (in %)                                 93.74    6.03      560     94.74   5.98  575
            high-skilled males (as % of total)               17.29    5.05      559    19.85    5.57  573
            sandy soils (%)                                  11.70   19.43      560     11.73  19.43 560
            loam soils (%)                                   26.77   27.13      560    26.74   27.12 560
            silt soils (%)                                    7.55   11.73      560      7.55  11.73 560
            clay soil (%)                                    39.71   27.42      560     39.81  27.54 560
            heavy clay soil (%)                              10.39   16.03      560     10.28  15.89 560
            other soil (%)                                    3.89   11.50      560     3.89   11.50 560
            growing period (days)                           191.58   48.87      436    191.58  48.87 436
            annual ET0 (mm)                                 1480.62 201.89      526   1477.57 210.18 537

     Note: This table presents the mean and standard deviation of the variables associated with the analysis tables,
     by year. The area variables are as a percentage of acreage of rented in land.
                  Table A4: First Stage Regressions: The relationship between the instruments and migration
                                                            (1)           (2)            (3)          (4)           (5)            (6)
                                                        Migration     Migration      Migration     Migration     Migration      Migration
                        IV high                          136.4***      56.80***       48.33***
                                                          (16.69)       (13.53)        (13.13)
                        IV low                          -151.9***     -85.19***      -72.45***
                                                          (17.20)       (14.31)        (14.55)
                        IVR high                                                                    0.132***      0.0581***      0.0473***
                                                                                                    (0.0164)       (0.0137)       (0.0130)
                        IVR low                                                                    -0.149***     -0.0854***     -0.0741***
                                                                                                    (0.0173)       (0.0146)       (0.0147)
                        perc. of adverse rain events                     0.0208          0.0157                      0.0212         0.0154
                                                                        (0.0137)       (0.0149)                    (0.0137)       (0.0148)
                        perc. of adverse temp events                     -0.0169        -0.0283                     -0.0193        -0.0284
                                                                        (0.0168)       (0.0178)                    (0.0167)       (0.0178)
                        bank branches                                 0.0132***      0.00720**                    0.0132***       0.00696*
                                                                       (0.00384)      (0.00359)                   (0.00385)      (0.00364)
                        road length (km)                             0.000278**     0.000389***                  0.000251**    0.000402***
                                                                      (0.000119)     (0.000127)                  (0.000119)     (0.000126)
71




                        population                                   -0.00230***    -0.00167***                 -0.00234***    -0.00165***
                                                                      (0.000442)     (0.000417)                  (0.000444)     (0.000419)
                        population density                                -1.061        -1.462*                      -0.951         -1.296
                                                                         (0.878)        (0.868)                     (0.878)        (0.868)
                        sex ratio                                      0.263***        0.151**                    0.276***        0.169**
                                                                        (0.0557)       (0.0677)                    (0.0562)       (0.0683)
                        ratio high-skilled males                       1.601***       1.676***                    1.596***       1.676***
                                                                        (0.0687)       (0.0738)                    (0.0687)       (0.0736)
                        2012 year                        3.034***        -0.0101         0.576     3.391***           0.177         0.692
                                                          (0.759)        (0.613)        (0.620)     (0.755)         (0.609)        (0.614)
                        Constant                         63.25***       13.27**       26.14***     62.76***        11.71**       24.23***
                                                          (0.685)        (5.572)        (7.329)     (0.636)         (5.632)        (7.402)
                        agro-ecological zone                No              No            Yes         No               No            Yes
                        observations                       1,135           1,048          843        1,135           1,048           843
                        R-squared                          0.094           0.554         0.576       0.089           0.553          0.576
                        IV F-stat                          39.41          19.18          12.78       37.90           17.92          13.16

     Note: This table presents the first-stage regressions. The outcome variable is the number of high-skilled male out-migrants between the ages of 20-64 years
     (as a percentage of the total male out-migrants between the ages of 20-64 years). The first three columns present the standard shift-share instrument, the
     second three columns present the residual shift-share instrument. The agro-ecological controls include soils, length of the growing season (in days) and
     reference ETo (a measure of water stress). Robust standard errors included. *** p<0.01, ** p<0.05, * p<0.1
Table A5: The relationship between the instrument residual and economic
conditions

                         residual below median        residual above median    p-value
 number of markets             8.24 (0.98)                  7.30 (0.65)         0.43
 wheat price (Rs/100 kg)       676 (7.60)                   660 (8.05)          0.15
 paddy price (Rs/100 kg)       517 (0.40)                   515 (8.20)          0.87

Note: This table presents the results of a t-test with unequal variances between
two groups of districts in 2002. The districts are grouped based on their value
of the residual of a regression which maps the ratio of the high-skilled over
the low-skilled instrument on the control variables. Column (1) presents the
mean and standard error of the residuals of the districts which have a residual
below the median. Column (2) presents the mean and standard error of the
residuals of the districts which have a residual above the median. Column (3)
presents the p-value of the t-test comparing these means.




                                      72
          Table A6: Correlation between migration and land tenure arrangements: Acreage, Extended Controls

                                     (1)           (2)          (3)            (4)            (5)            (6)                 (7)
                               fixed rent    fixed (money)   fixed (crop)   sharecropping     relatives   contract length   written contract
      migration                    -0.279       -0.0768       -0.202         0.0685          0.118          0.194             -0.0675
                                  (0.176)       (0.157)      (0.127)         (0.182)       (0.0945)        (0.166)            (0.125)
      bank branches (number)      0.0239         0.0209      0.00304         -0.0254       0.00423         0.0129              0.0201
                                 (0.0247)      (0.0205)     (0.0124)        (0.0233)       (0.0122)       (0.0153)           (0.0123)
      road length (km)          -0.000366     -0.000518     0.000152        0.000279      -0.000118      0.00156***        -0.000629*
                               (0.000498)    (0.000484)    (0.000299)      (0.000514)    (0.000291)      (0.000480)         (0.000371)
      2012 year                    -4.445        -1.020       -3.425         -5.512*      7.714***        21.96***           5.725***
                                  (3.150)       (2.858)      (2.113)         (3.174)        (1.925)        (3.034)            (2.093)
      Observations                   722           722         722             722            722            722                 722
      R-squared                     0.090         0.181       0.059           0.095          0.053          0.141               0.057

     Note: This table uses an OLS regression to present the correlation between the percentage of rented-in acreage
73




     under various terms and the number of high-skilled male out-migrants between the ages of 20-64 years (as a
     percentage of the total male out-migrants between the ages of 20-64 years). The population controls include
     total population, sex ratio, population density and share of high-skilled males. Remaining controls include the
     percentage of adverse rain events and the percentage of adverse temperature events. The agro-ecological controls
     include soils, length of the growing season (in days) and reference ETo (a measure of water stress). The dependent
     variable is as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
          Table A7: IV regression: The effect of migration on land tenure arrangements: Acreage, No Controls
                           (1)           (2)           (3)            (4)           (5)            (6)                (7)
                        fixed rent   fixed (money)   fixed (crop)   sharecropping   relatives   contract length   written contract

         migration        0.769*      0.778**       -0.00873        -0.735*       -0.0306         0.501            0.476*
                         (0.411)      (0.347)        (0.284)        (0.433)       (0.238)        (0.402)           (0.270)
         2012 year       -5.788*       -1.807        -3.980*         -3.106      8.813***       19.86***            1.377
                         (3.187)      (2.863)        (2.238)        (3.155)       (1.860)        (2.979)           (2.089)
         Constant         -2.660       -20.72         18.05        88.99***        6.824          5.606             -18.49
                         (25.68)      (21.60)        (17.64)        (27.08)       (14.90)        (25.12)           (16.84)
         Observations      927          927            927            927           927            927               927

     Note: This table uses the shift-share instrumental variable regression to present the relation between the percent-
     age of rented-in acreage under various terms and the number of high-skilled male out-migrants between the ages
     of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The dependent
74




     variable is as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
       Table A8: IV regression: The effect of migration on land tenure arrangements: Acreage, Extended Controls

                                  (1)            (2)           (3)            (4)            (5)            (6)                (7)
                               fixed rent    fixed (money)   fixed (crop)   sharecropping    relatives   contract length   written contract

      migration                 3.371***      2.917***        0.454         -1.759*       -1.700**         -0.229            0.912*
                                 (1.087)       (0.865)       (0.585)        (1.000)        (0.742)        (0.885)            (0.538)
      bank branches (number)     -0.0188       -0.0142      -0.00465       -0.00403        0.0255         0.0179            0.00865
                                (0.0246)      (0.0211)      (0.0130)       (0.0233)       (0.0183)       (0.0185)           (0.0121)
      road length (km)         -0.00170**    -0.00162**     -8.84e-05      0.000949       0.000549      0.00171***        -0.000988**
                               (0.000813)    (0.000707)    (0.000359)     (0.000649)     (0.000470)     (0.000598)         (0.000434)
      2012 year                  -6.661*        -2.837       -3.824*         -4.403       8.818***       22.22***            5.130**
                                 (3.995)       (3.521)       (2.144)        (3.429)        (2.292)        (3.043)            (2.201)
      Observations                 722           722           722            722            722            722                722

     Note: This table uses the shift-share instrumental variable regression to present the relation between the per-
75




     centage of rented-in acreage under various terms and the number of high-skilled male out-migrants between the
     ages of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The popu-
     lation controls include total population, sex ratio, population density and share of high-skilled males. Remaining
     controls include the percentage of adverse rain events and the percentage of adverse temperature events. The
     agro-ecological controls include soils, length of the growing season (in days) and reference ETo (a measure of
     water stress). The dependent variable is as percentage of acreage of rented in land. The dependent variable is as
     a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
     Table A9: IV regression: The effect of migration on land tenure arrangements, using the residual approach:
     Acreage, No controls
                           (1)           (2)           (3)            (4)           (5)            (6)                (7)
                        fixed rent   fixed (money)   fixed (crop)   sharecropping   relatives   contract length   written contract

         migration       0.959**      0.982***       -0.0228        -0.823*       -0.0471         0.457            0.445*
                         (0.417)       (0.350)       (0.287)        (0.438)       (0.316)        (0.404)           (0.266)
         2012 year      -6.611**        -2.691       -3.919*         -2.721      8.885***       20.05***            1.511
                         (3.228)       (2.901)       (2.253)        (3.169)       (2.110)        (2.980)           (2.051)
         Constant         -14.52        -33.45        18.93        94.52***        7.859          8.357             -16.55
                         (26.01)       (21.77)       (17.81)        (27.39)       (19.71)        (25.25)           (16.62)
         Observations      927           927           927            927           927            927               927

     Note: This table uses the residual shift-share instrumental variable regression to present the relation between the
     percentage of rented-in acreage under various terms and the number of high-skilled male out-migrants between
76




     the ages of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The
     dependent variable is as a percentage of acreage of rented in land. Robust standard errors. *** p<0.01, **
     p<0.05, * p<0.1.
     Table A10: IV regression: The effect of migration on land tenure arrangements, using the residual approach:
     Acreage, Extended Controls

                                    (1)           (2)           (3)             (4)         (5)             (6)               (7)
                                fixed rent   fixed (money)   fixed (crop)   sharecropping   relatives   contract length   written contract
      migration                 3.144***      2.646***         0.498         -1.769*     -1.483**         -0.231             0.788
                                  (1.036)      (0.802)        (0.574)        (0.974)      (0.715)        (0.863)            (0.505)
      bank branches (number)      -0.0162      -0.0110       -0.00516       -0.00393      0.0230         0.0179             0.0101
                                 (0.0242)     (0.0207)       (0.0129)       (0.0231)     (0.0176)       (0.0183)           (0.0120)
      road length (km)         -0.00162**    -0.00152**     -0.000104      0.000953      0.000469      0.00171***        -0.000942**
      2012 year                   -6.523*       -2.673        -3.850*         -4.397     8.686***       22.22***           5.205**
                                  (3.905)      (3.418)        (2.157)        (3.428)      (2.206)        (3.039)            (2.172)
      Observations                  722          722            722            722          722            722                722

     Note: This table uses the residual shift-share instrumental variable regression to present the relation between the
     percentage of rented-in acreage under various terms and the number of high-skilled male out-migrants between the
77




     ages of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). The population
     controls include total population, sex ratio, population density and share of high-skilled males. Remaining controls
     include the percentage of adverse rain events and the percentage of adverse temperature events. The agro-
     ecological controls include soils, length of the growing season (in days) and reference ETo (a measure of water
     stress). The dependent variable is as percentage of acreage of rented in land. The dependent variable is as a
     percentage of acreage of rented in land. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.
          Table A11: IV regression: The effect of migration on land tenure arrangements by NREGA start date
                                        (1)            (2)           (3)           (4)           (5)           (6)
                                   fixed rent    sharecropping   fixed rent   sharecropping   fixed rent   sharecropping
                migration             1.469*         -1.138        1.508         0.450         5.466         -4.604
                                     (0.801)        (1.091)       (1.201)       (1.109)       (3.526)       (3.162)
                banks                -0.0514        0.0880       0.0821*      -0.114***       -0.0327       0.0154
                                    (0.0484)       (0.0556)      (0.0445)      (0.0351)      (0.0441)      (0.0422)
                road length (km)    -0.00106       0.000105      0.00151      -0.000294     -0.000671      0.00123
                                   (0.000786)     (0.000764)    (0.00136)     (0.00108)     (0.00137)     (0.00113)
                year 2012             0.0527         -7.608        -10.39        -5.021        -4.005        -4.432
                                     (5.612)        (5.877)       (6.636)       (5.950)       (7.808)       (6.834)
                observations            296           296           202           202           375           375

     Note: This table uses the shift-share instrumental variable regression to present the relation between the percent-
     age of rented-in acreage under various terms and the number of high-skilled male out-migrants between the ages
78




     of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). Columns (1)
     and (2) are districts with NREGA start = 1, Columns (3) and (4) are districts with NREGA start = 2, Columns
     (5) and (6) are districts with NREGA start = 3. The population controls include total population, sex ratio,
     population density and share of high-skilled males. Remaining controls include the percentage of adverse rain
     events and the percentage of adverse temperature events. Robust standard errors. *** p<0.01, ** p<0.05, *
     p<0.1.
 Table A12: IV regression: The effect of migration on cash crops prevalence

                                      cash crops (%)
                       migration           -0.257
                                          (0.438)
                       observations         980
                       mean dep. var.        40

Note: This table uses the shift-share instrumental variable regression to
present the relation between acreage of cash crops as a percentage of the total
cultivated acreage (where cash crop is defined as not being wheat, rice, maize
and sorghum), and the number of high-skilled male out-migrants between the
ages of 20-64 years (as a percentage of the total male out-migrants between
the ages of 20-64 years). The population controls include total population, sex
ratio, population density and share of high-skilled males. Remaining controls
include the percentage of adverse rain events and the percentage of adverse
temperature events. Robust standard errors. *** p<0.01, ** p<0.05, * p<0.1.




                                      79
                                    Table A13: IV regression: The effect of migration on yields
                                        (1)         (2)          (3)         (4)        (5)          (6)        (7)         (8)         (9)
                                     Wheat         Rice      Sorghum     P millet      Maize     F millet    Barley    Chickpea    Pigeonpea
                   migration       -0.0461***   0.0454***     0.00150    0.00361    0.0392***     -0.0148    0.00201    -0.00680     -0.0132
                                    (0.0113)    (0.00993)    (0.00903)   (0.0154)    (0.0109)    (0.0114)   (0.0115)   (0.00704)   (0.00992)
                   FDR q-values      [0.001]      [0.001]      [0.510]    [0.510]     [0.001]     [0.267]    [0.510]     [0.402]     [0.267]
                   observations        838          919          412        365         533         195        286         509         510
                   mean dep var.       7.45        7.26         6.41        6.43       7.20         6.68       7.38        6.53        6.35
                                       (10)        (11)         (12)        (13)       (14)         (15)       (16)        (17)        (18)
                                   Groundnut      Sesame        R/M       Castor     Linseed        Sun       Soya        Sugar      Cotton
                   migration         0.0186     0.0371**    -0.0767***    -0.0426     0.0101     0.0183*    -0.00656     -0.0165     -0.0200
                                    (0.0168)     (0.0167)     (0.0229)   (0.0318)   (0.00915)   (0.00993)   (0.0123)    (0.0106)    (0.0140)
                   FDR q-values      [0.332]      [0.079]      [0.004]    [0.267]     [0.332]     [0.167]    [0.462]     [0.262]     [0.267]
                   observations        467          511          462        231         259         259        227         490         286
                   mean dep var.       6.68        5.48         6.34        6.10       5.97         6.67       6.55        8.34        5.20



     Note: This table uses the shift-share instrumental variable regression to present the relation between the yields
     of all major crops (in natural log in kg/ha) and the number of high-skilled male out-migrants between the ages
     of 20-64 years (as a percentage of the total male out-migrants between the ages of 20-64 years). P millet refers to
     pearl millet. F millet refers to finger millet and R/M refers to rapeseed and mustard seed. The population controls
80




     include total population, sex ratio, population density and share of high-skilled males. Remaining controls include
     the percentage of adverse rain events and the percentage of adverse temperature events. Robust standard errors
     are reported in simple parenthesis. FDR-adjusted standard errors following Benjamini, Krieger and Yekutieli
     (2006) and using the code of Anderson (2008) are reported in block parenthesis. *** p<0.01, ** p<0.05, * p<0.1.