Land II: Limited Liability, Risk Aversion, and Property Rights

This section continues developing the contract theory model under limited liability, which ties directly to Slides 11–12 in the lecture PDF. Let’s break it down clearly:

🔑 Recap of the Model So Far:

Goal: Design a contract to get the tenant to exert optimal effort (same effort as the landlord would exert on his own land).
The perfect incentive contract is a fixed rent contract:
- Tenant pays rent $R$ regardless of output.
- Tenant keeps all output — becomes a residual claimant.
- Gives first-best effort: $e^* = \frac{H}{c}$

❗ But here’s the problem: Limited Liability Constraint

"He’s typically a poor man... this may not be practical..."

🔻 The issue:

If output = 0 (e.g., crop fails), the tenant still owes rent $R$
This could mean a negative income: $\text{payment} = -R$
Poor tenants can’t afford to pay money they don’t have
Legal systems often don’t enforce negative payouts (you can’t force someone to pay what they don’t have)

🔐 This is the "Limited Liability" Constraint

"There’s a lower bound on how much you can end up with..."

In formal terms:

The contract must satisfy:
$l \geq 0$
(the tenant’s worst-case payout can’t be negative)
In other words: you can’t be forced to pay money you don’t have, just like declaring bankruptcy

🟨 Implication for Contracts:

The ideal contract (fixed rent with full residual claimancy) requires:
- $h = H - R$
- $l = -R$
But if $l < 0$ violates limited liability, then this contract becomes infeasible
- You can’t implement the perfect incentive contract

🟠 What Happens Next?

To respect the limited liability constraint, landlords must modify the contract — and this leads to:

Sharecropping as a compromise:
- Tenant receives a fraction of output
- Doesn't owe money in case of failure
- Provides some incentive, but less than first-best

This is exactly where the lecture goes next.

✅ Summary of Key Takeaways:

Concept	Explanation
Residual Claimant	Tenant keeps all marginal output; gives full incentive
Fixed Rent Contract	Provides ideal incentive, but requires tenant to pay even when output = 0
Limited Liability	Tenant can’t pay more than he has; $l \geq 0$ is required
Result	First-best contract may be infeasible for poor tenants → we need second-best solutions like sharecropping

This part of the lecture explains the “second-best” contract under limited liability, and it directly builds on the earlier discussion and connects to Slides 11–12 in the PDF.

Let’s walk through the key ideas and math clearly:

🧩 Context: Why Do We Need a Second-Best Solution?

In a first-best (ideal) contract (residual claimant), the tenant:
- Pays fixed rent $R$
- Keeps all output
- Exerts optimal effort $e^* = \frac{H}{c}$
BUT: This requires the tenant to pay even when output is zero, which violates the limited liability constraint:
$l \geq 0$

🟨 Second-Best Contract: Solve with Limited Liability (l ≥ 0)

🔧 Step 1: Assume l = 0

“Landlords don’t want to pay tenants when they fail – it's a cost and discourages effort.”

So optimal contract under limited liability sets:
- $l = 0$
- $h$ to be determined

🔧 Step 2: Solve Tenant’s Problem

Tenant chooses effort to maximize:
$e(h - l) - \frac{1}{2} c e^2 = e \cdot h - \frac{1}{2} c e^2$
First-order condition:
$h - c e = 0 \Rightarrow e = \frac{h}{c}$

🔧 Step 3: Solve Landlord’s Problem

Landlord earns:
$\text{Expected profit} = e(H - h) = \frac{h}{c}(H - h)$
Maximize:
$\max_h \frac{h}{c}(H - h) \Rightarrow \text{F.O.C: } H - 2h = 0 \Rightarrow h = \frac{H}{2}$

✅ Resulting Contract (Second Best):

$h = \frac{H}{2}$ , $l = 0$
Tenant effort:
$e = \frac{h}{c} = \frac{H}{2c}$
Landlord gets half of output in expectation

⚠️ Why Doesn't the Landlord Offer the First-Best Incentive?

“To get the tenant to exert effort $e = \frac{H}{c}$ , we need $h - l = H$ ”

If $l \geq 0$ , then:
$h \geq H$
So landlord has to pay $h = H$ when output is high, which leaves him zero profit.

➡️ Landlord prefers to sacrifice efficiency (get less effort/output) in exchange for higher own profits.

This is not a mistake, but a strategic choice:

“He knows he’s giving inefficient incentives — but that’s exactly what he wants to do to maximize his own income.”

✅ Summary:

Concept	First Best	Second Best (Limited Liability)
Tenant Payment (h, l)	$h = H - R, \; l = -R$	$h = \frac{H}{2}, \; l = 0$
Tenant Effort	$\frac{H}{c}$	$\frac{H}{2c}$
Output	Full	Half
Landlord’s Profit	Zero (if l ≥ 0)	Positive

🎯 Final Takeaway:

Under limited liability, the landlord deliberately offers weaker incentives to the tenant. The result is lower effort and output — but higher expected profit for the landlord, compared to offering full incentives and receiving no surplus.

This section of the lecture expands on the implications of limited liability for effort, output, and tenant utility, and connects directly to Slide 12 of the PDF.

Here’s a clear breakdown of the key points:

🔁 Recap: Limited Liability vs. No Constraint

🟢 Without Limited Liability (First Best):

Contract:
- $h = H - R$
- $l = -R$
Tenant becomes a residual claimant.
Effort:
$e^* = \frac{h - l}{c} = \frac{H}{c}$
Output is maximized (first-best level).

🔴 With Limited Liability (Second Best):

Contract:
- $h = \frac{H}{2}$
- $l = 0$
Effort:
$e_t = \frac{H}{2c}$
Output is lower (second-best outcome).

✅ Key message: The only reason we end up with lower output is because the tenant can't be forced to pay when output is low (limited liability). Without that, full incentives are possible.

🧮 Tenant's Utility in the Second-Best Contract

Expected utility of the tenant:

Expected payment:
$e \cdot h = \left( \frac{h}{c} \right) h = \frac{h^2}{c}$
Cost of effort:
$\frac{1}{2} c \left( \frac{h}{c} \right)^2 = \frac{h^2}{2c}$
Utility = Expected payment − cost:
$\frac{h^2}{c} - \frac{h^2}{2c} = \frac{h^2}{2c}$

Now plug in $h = \frac{H}{2}$ :

U = \frac{(H/2)^2}{2c} = \frac{H^2}{8c}

This is the tenant’s utility under the optimal limited liability contract.

🧠 Key Insight: Utility Exceeds the Outside Option

“This could be strictly bigger than $\bar{w}$ , the tenant’s outside wage...”

Even if the tenant would’ve worked for less (e.g., $\bar{w} = 2$ ), the landlord pays more (e.g., effective utility = 4).
This is not irrational — it’s strategic:
- Paying more incentivizes higher effort, which leads to higher output.
- Both the landlord and tenant benefit.

This is the central feature of incentive models:

The worker (tenant) must be given a "carrot" to perform — even if they would accept less in a no-effort world.

🚗 Analogy: Henry Ford’s $5/day wage

Ford famously increased wages not out of generosity, but because:

“Higher pay = better effort = higher profits”

That’s exactly the logic the professor applies here.

✅ Summary Takeaways:

Concept	Without Limited Liability	With Limited Liability
Tenant effort	$\frac{H}{c}$	$\frac{H}{2c}$
Output	Full (first best)	Half (second best)
Tenant utility	Depends on R	$\frac{H^2}{8c}$
Can exceed outside option?	Yes	✅ Yes

🟨 Incentives matter more than squeezing wages — paying more can be profit-maximizing.

This portion of the lecture builds on the second-best contract under limited liability, and draws out two major implications:

🧭 1. Incentives and the Role of Overpayment (above outside option)

“I pay you more than your outside option, so losing your job becomes costly...”

This leads to a powerful insight:

✅ When wages are above outside options:

The tenant values the job more than alternatives.
This allows the landlord to use the threat of dismissal as an additional incentive tool.

If the tenant is paid exactly what they could get elsewhere:

Being fired is not costly, so it’s not a credible threat.
Thus, overpaying enhances effort not only through rewards, but also by making dismissal more painful.

📌 Important implication:

For incentive-based contracts to work best, you often want:
- High-powered incentives (overpayment)
- Flexible dismissal rules

This will lead directly into an empirical policy example (he hints at it — we’ll see later that it involves India’s labor laws and firing protections).

🔁 2. Reconnecting to the Big Question: Why are large farms less productive?

“Why do people who don’t own land put in less effort?”

This loops back to the original motivation: understanding land markets and farm productivity.

From the model:

Tenants exert less effort than owners because:
- Landlords provide weaker incentives (to retain profit)
- Tenants are not residual claimants
In the second-best contract, tenants exert half the ideal effort, and output is lower

📉 Implication for Farm Size and Productivity

“If someone owns two plots and hires a tenant on one, it will be less productive than if both plots were owner-cultivated.”

Why?

Owner-farmers exert first-best effort (they are their own boss)
Tenants exert second-best effort (constrained by landlord incentives)
Larger farms = more plots managed through tenants ⇒ lower average productivity

🔁 Redistribution Implication:

“If I take land from a large landowner and give it to a landless tenant, total output goes up.”

This is a rare case in economics where efficiency and equity move in the same direction:

Action	Result
Land redistribution	Poor tenant becomes owner
Tenant becomes own boss	Exerts optimal effort
Output	Increases (more productive use of land)

🔮 Preview of What’s Coming:

“If I change the assumptions slightly, I’ll get very different answers.”

This hints that the model depends heavily on assumptions, and in later sections we’ll see that different labor market features or credit constraints can reverse these conclusions.
For now, under current assumptions (limited liability + no other frictions), the conclusion is:

Redistribution = more output, because owners work harder than tenants.

✅ Summary of Key Takeaways:

Concept	Insight
Overpayment	Strengthens incentives via effort and dismissal threat
Limited liability	Forces landlord to give weaker incentives, reducing effort
Tenants vs. Owners	Tenants exert less effort due to imperfect incentives
Farm Size	Larger farms with tenants = less productive
Redistribution	Turning tenants into owners = more output + more equity

This passage introduces a real-world policy intervention—tenancy reform in West Bengal, India (late 1970s)—and shows how it maps directly onto the incentive theory model just developed in class.

Let’s break down the key economic ideas clearly:

🧭 Context: The West Bengal Tenancy Reform

Implemented by a newly elected communist government, the reform involved two major policy changes:

🔶 1. Minimum Share Requirement (Increased h):

“You have to give the tenant at least 75% of output.”

In model terms:
$h = \frac{3H}{4} \quad \text{(instead of } \frac{H}{2} \text{)}$
Effect: This increases the incentive spread ( $h - l$ ), encouraging the tenant to exert more effort.
Result:
✅ Output goes up

This is referred to as the:

✅ Bargaining Power Effect

The tenant can demand more output.
They may or may not get all of it in cash, but their bargaining position improves, pushing incentives and effort upward.
Good for productivity.

🔷 2. Security of Tenure (Dismissal Ban):

“If the tenant pays 75%, the landlord can’t evict them.”

In the model:
- This removes the threat of dismissal.
- If the tenant no longer fears being fired, they lose a key incentive to perform.
Effect:
🔻 Effort and output fall

This is referred to as the:

⚠️ Security of Tenure Effect

The tenant is less responsive to performance pressure.
Because being fired is no longer a risk, motivation weakens.
Bad for productivity.

🔁 Two Opposing Effects in One Policy

Reform Component	Economic Effect	Impact on Output
Raise tenant's share (h ↑)	Stronger incentives	🔺 Output ↑
Make tenant undismissable	Weaker threat = weaker effort	🔻 Output ↓

🧪 Empirical Question Introduced:

“So what we are going to do is look at that question.”

The lecture now sets up an empirical test:

What was the net effect of these two opposing forces?
Did output rise overall?
Did the policy help or hurt?

This sets the stage for the next section of the lecture, where real data from West Bengal will be used to test the predictions of the model.

✅ Summary of Takeaways:

Concept	Description
Bargaining Power Effect	Tenant demands more output share → higher effort → higher productivity
Security of Tenure Effect	Tenant can’t be fired → less pressure to perform → lower productivity
Policy Outcome	Depends on which effect dominates — to be determined empirically

This section of the lecture explains how the West Bengal land reform was empirically evaluated, using quasi-experimental strategies to estimate the impact of the policy on agricultural output. It connects to the theoretical insights covered earlier, including the bargaining power and security of tenure effects.

🔍 How Was the Reform Implemented?

Problem: Once landlords learned tenants might be legally entitled to a larger share (75%), many pretended they never had tenants, or tried to evict them before the reform took hold.
Solution: The government sent bureaucrats to register tenants, village by village.
- Registered tenants were officially granted rights and protected from eviction.
- This staggered rollout provided variation across time and place, which could be exploited for causal analysis.

🧪 Two Empirical Strategies Used:

1. Difference-in-Differences (DiD) Within West Bengal

Approach: Compare:
- Villages where registration happened early
- Villages where registration happened later
Logic: If the reform is what caused output to rise, then output should increase earlier in places where registration happened earlier.
This captures within-state, over-time variation, controlling for common shocks.

2. Cross-Border Comparison: West Bengal vs. Bangladesh

Rationale: Bangladesh and West Bengal are culturally, linguistically, and geographically similar.
West Bengal = treatment group, Bangladesh = control group
Pre-reform trends in output are parallel, lending credibility to the comparison.

📉📈 What Did They Find?

❌ Short-run effect:

Output in West Bengal dropped briefly right after the reform.
→ Likely due to political unrest, landlord pushback, and implementation chaos.

✅ Long-run effect:

After stabilization, output in West Bengal increased by ~20% relative to Bangladesh.
DiD estimates show:
- Initial dip of ~8%
- Eventual increase of ~18%

🎯 Interpretation:

The bargaining power effect (higher tenant share) likely boosted effort and output.
The security of tenure effect (weakened dismissal threat) may have partially offset this, but not entirely.
Net result: positive long-term impact on output, consistent with the theoretical prediction that better incentives (via higher share) can dominate.

🧠 Additional Insight:

Threats of firing were common, but actual firings were rare
This aligns with the idea that in equilibrium, threats alone are enough to induce effort — actual dismissals need not be observed.

✅ Summary of Key Takeaways:

Component	Description
Reform	Guaranteed tenants 75% of output + eviction protection
Identification Strategy 1	Difference-in-differences using early vs. late registration
Identification Strategy 2	West Bengal vs. Bangladesh comparison
Short-run effect	Temporary decline due to unrest
Long-run effect	~20% increase in output
Interpretation	Incentive improvements outweighed reduction in firing threats

This part of the lecture goes deeper into the empirical strategy used to assess the impact of land reforms in West Bengal—specifically using a difference-in-differences (DiD) framework that exploits variation in the timing of tenant registration across districts.

Let’s summarize the key ideas:

📊 What is being analyzed?

The government reform registered tenants in villages at different times across West Bengal during the 1980s. So:

Every district eventually got tenant registration.
But some districts were registered earlier, others later.
Each year, each district has an observed output level (agricultural output).

🔍 What is the core question?

Does output in a district rise around the time that tenant registration increases in that district?

This tests whether the policy implementation (registration) actually caused productivity gains, as predicted by the incentive model.

🛠️ Empirical Strategy:

✅ Difference-in-Differences (DiD) with Fixed Effects

Unit of observation: District-year
Fixed effects used:
- District fixed effects ( $\eta_d$ ) → control for time-invariant differences in productivity across districts.
- Time fixed effects ( $\lambda_t$ ) → control for state-wide shocks (e.g., monsoons, policy changes affecting all districts).
Key regressor: Registration rate (percentage of land/tenants registered) in district $d$ at time $t$

🔁 What's measured:

Is there a correlation between increases in registration and increases in output within the same district over time?

This isolates within-district changes, net of permanent differences and common shocks.

🔁 Illustrated Example:

Two districts:

Both eventually reach 100% tenant registration.
One reaches it early (e.g., 1982), the other late (e.g., 1989).
Researchers ask: Did output rise earlier in the early-registering district?

➡️ This matches timing of reform implementation to timing of productivity changes, the hallmark of a DiD design.

🚫 What isn’t being asked:

“Are districts with higher registration levels more productive?”
No — that would be a cross-sectional (level-on-level) analysis and would suffer from endogeneity.

Instead, the analysis focuses on:

✅ Changes-on-changes
→ Do increases in registration coincide with increases in output, within a district, over time?

✅ Summary of Key Concepts:

Concept	Description
Unit of analysis	District-year
Treatment	Timing of tenant registration
Design	Difference-in-differences
Controls	District fixed effects + Time fixed effects
Key idea	Match output trends to registration timing
Main question	Did output rise when registration increased within a district?

This is a clean and credible way to isolate the causal effect of reform despite the lack of a randomized experiment.

This portion of the lecture provides a detailed interpretation of the regression results from the empirical analysis of the West Bengal land reform and reinforces the key theoretical insight: rights empower tenants not just through enforcement, but by giving them bargaining power through credible threat.

📊 Interpreting the Regression Table (Table 5)

Each model (1)–(6) represents a different version of the same core regression, estimating the effect of sharecropper registration (lagged one year) on log rice yield, while progressively adding more control variables.

🧩 Why include more controls?

“Is it the effect of the policy, or of something else that changed at the same time?”

To rule out confounding, the models control for:

Rainfall — affects productivity
Irrigation & roads — may have improved alongside registration
HYV share (high-yielding rice) — could drive yield increases
Sharecropping × year — to capture whether areas with more tenants were improving due to some unrelated trend

✅ Key findings:

Across all models, the coefficient on sharecropper registration remains positive, statistically significant, and quite large.
In the most complete model (6), the effect is still about 35%:

A move from 0% to 100% registration is associated with a 35% increase in rice yields

📈 Why is the $R^2$ so high?

“Fixed effects regressions typically have very high R²”

Because the model includes district fixed effects:

It allows each district to have its own baseline level of productivity
That absorbs a lot of variation, leaving only changes over time within each district to explain

🧠 Deeper Conceptual Insight: Rights as Credible Threats

“There isn’t a big difference in productivity between those who were registered and those who were not.”

Rather than contradicting the theory, this supports it:

Even unregistered tenants benefit from the reform because they can credibly threaten to register
That threat shifts bargaining power, leading landlords to voluntarily improve terms
Thus, actual registration is not always necessary for the reform to raise productivity

This reinforces the broader principle:

✅ Rights don’t need to be exercised to have power.
Their mere existence, if credible, empowers the rights-holder.

✅ Final Summary of Key Points:

Topic	Insight
Regression controls	Added to rule out alternative explanations for yield gains
35% result	Consistent and robust across specifications
High R²	Due to district fixed effects absorbing level differences
Registration vs. actual productivity	Productivity gains stem from threats, not just formal registration
Core idea	Credible legal rights shift bargaining power, even if not enforced

📊 Interpreting the Regression Table (Table 5)

🧩 Why include more controls?

“Is it the effect of the policy, or of something else that changed at the same time?”

To rule out confounding, the models control for:

Rainfall — affects productivity
Irrigation & roads — may have improved alongside registration
HYV share (high-yielding rice) — could drive yield increases
Sharecropping × year — to capture whether areas with more tenants were improving due to some unrelated trend

✅ Key findings:

Across all models, the coefficient on sharecropper registration remains positive, statistically significant, and quite large.
In the most complete model (6), the effect is still about 35%:

A move from 0% to 100% registration is associated with a 35% increase in rice yields

📈 Why is the $R^2$ so high?

“Fixed effects regressions typically have very high R²”

Because the model includes district fixed effects:

It allows each district to have its own baseline level of productivity
That absorbs a lot of variation, leaving only changes over time within each district to explain

🧠 Deeper Conceptual Insight: Rights as Credible Threats

“There isn’t a big difference in productivity between those who were registered and those who were not.”

Rather than contradicting the theory, this supports it:

Even unregistered tenants benefit from the reform because they can credibly threaten to register
That threat shifts bargaining power, leading landlords to voluntarily improve terms
Thus, actual registration is not always necessary for the reform to raise productivity

This reinforces the broader principle:

✅ Rights don’t need to be exercised to have power.
Their mere existence, if credible, empowers the rights-holder.

✅ Final Summary of Key Points:

Topic	Insight
Regression controls	Added to rule out alternative explanations for yield gains
35% result	Consistent and robust across specifications
High R²	Due to district fixed effects absorbing level differences
Registration vs. actual productivity	Productivity gains stem from threats, not just formal registration
Core idea	Credible legal rights shift bargaining power, even if not enforced

TABLE 5

Effect of Registration on the Log of Rice Yield in West Bengal, 1979–93 (N = 210)

Variable	Model 1 (1)	Model 2 (2)	Model 3 (3)	Model 4 (4)	Model 5 (5)	Model 6 (6)
Sharecropper registration (1-year lagged)	0.43*** (3.46)	0.42*** (3.44)	0.43*** (3.55)	0.35*** (2.69)	0.36*** (2.64)	0.36*** (2.63)
Log(rainfall)	—	-0.07* (-1.67)	-0.08* (-1.82)	-0.07 (-1.59)	-0.08* (-1.74)	-0.08* (-1.77)
Log(public irrigation)	—	0.02 (1.01)	0.01 (0.70)	0.01 (0.60)	0.02 (0.83)	0.02 (0.79)
Log(roads)	—	0.28*** (2.75)	0.25*** (2.46)	0.21** (1.99)	0.19 (1.55)	0.22 (1.54)
HYV share of rice area	—	—	0.57*** (2.85)	0.45*** (2.10)	0.47*** (2.16)	0.47*** (2.16)
F-statistic
south × yearᵃ	—	—	—	4.73***	4.36***	4.38***
LeftFront × yearᵇ	—	—	—	—	2.64**	2.65**
Sharecropping × yearᶜ	—	—	—	—	2.64**	0.12
District fixed effects	72.23***	15.10***	8.99***	9.01***	8.47***	7.68***
Year fixed effects	28.31***	27.67***	21.60***	17.63***	17.83***	12.17***
$R^2$	0.91	0.92	0.92	0.92	0.92	0.92

Notes:

***p<0.01, **p<0.05, *p<0.1
ᵃᵇᶜ Interaction terms or policy environment fixed effects (details in original paper)

🔁 What fixed effects are doing in this regression

In Table 5, you see two types of fixed effects in all models (1) through (6):

Fixed Effect Type	What It Controls For
District fixed effects	Any time-invariant differences between districts (e.g., soil, geography, historical productivity)
Year fixed effects	Any state-wide shocks or trends common to all districts in a given year (e.g., monsoons, inflation, national policies)

✅ So what remains?

After including these fixed effects, the only variation left for identifying the effect of the land reform comes from:

Differences in registration timing within a district over time
(i.e., when and how much a district increased its registration rate)

This is why the regression can isolate the impact of registration from other influences:

Any constant district-level factor (like being near a river or consistently better land) is absorbed by the district fixed effect
Any state-wide trend in any year is absorbed by the year fixed effect
What’s left is variation like:

“District A increased registration in 1983, District B in 1988 — did output rise in A earlier?”

🧪 Why add more controls across models (2)–(6)?

You're right to notice that models 2–6 add more variables (rainfall, roads, irrigation, HYV use, etc.). These are not fixed effects but time-varying covariates.

These control for:	Example purpose
Rainfall	Maybe yields rose due to good rain, not reform
Irrigation	If areas with earlier registration also got more irrigation
Roads	Infrastructure may correlate with reform timing
HYV share	Technological adoption that also affects yields

These don’t absorb variation like fixed effects — they explain it, helping ensure the reform effect isn’t spuriously attributed.

📌 Key Insight:

Fixed effects clean out the noise from permanent differences.
Controls clean out the noise from shifting, correlated variables.

Together, they let us credibly isolate the effect of the reform (tenant registration) on rice yields.

✅ Summary:

Component	Purpose
District fixed effects	Control for unchanging district differences (like land quality)
Year fixed effects	Control for events that affect all districts in a given year
Time-varying controls	Rule out other changing factors (rainfall, roads, etc.) as explanations
Registration variation	The main source of identification: timing of reform by district

This part of the lecture introduces a second fundamental reason (beyond limited liability) for why real-world incentive contracts often fall short of the ideal “first-best” solution:

🔍 New Explanation: Risk Aversion and Incentive Contracts

Previously, we saw that limited liability (you can't force tenants to pay in bad times) prevents implementing the optimal contract (e.g., fixed rent).

Now, Professor Banerjee discusses how even without limited liability, another problem arises:

🎯 People don’t like risk.
This is called risk aversion.

⚖️ Trade-Off Between Incentives and Insurance

🧪 Ideal Incentive Contract (Recap):

Tenant pays a fixed rent $R$
Keeps all the output
If harvest is bad, the tenant still owes money → huge downside risk

➡️ This creates strong incentives, but it also exposes the tenant to a lot of risk (income volatility).

😟 But tenants are risk-averse:

A contract with large variation in income (depending on harvest) makes them worse off
If forced into risky contracts, tenants will:
- Demand higher compensation
- Or refuse to work under those terms

🤝 Result: Landlord must share risk

To get tenants to accept the contract, landlords offer:

Weaker incentives (e.g., sharecropping instead of fixed rent)
In exchange for less risk exposure

💡 Core Insight:

Incentives increase risk. Insurance reduces incentives.
The optimal contract strikes a balance between motivating effort and protecting against risk.

This explains why real-world contracts are often imperfect:
They intentionally sacrifice productivity (lower effort) to keep tenants insured and engaged.

🔁 Comparison with Limited Liability

Constraint	Effect on Contract
Limited liability	Tenant can't be forced to pay in bad times
Risk aversion	Tenant doesn’t want unpredictable income
Result in both	Landlord offers weaker incentives to make contract feasible

✅ Summary of Key Points:

Strong incentives often come with more risk
Tenants may reject or demand compensation for risky contracts
Risk-averse tenants prefer less variable income, even if it means less total output
So landlords offer contracts with weaker incentives (e.g., sharecropping)
This helps explain why real contracts don’t always push tenants to the productivity max

This lecture segment presents a more nuanced model that explores how risk preferences influence land productivity and the potential unintended consequences of land reform. While it builds on earlier incentive models, it introduces a new behavioral layer: individual heterogeneity in risk aversion.

🧠 Key Concepts Introduced:

1. Heterogeneity in Risk Aversion

People differ in how much risk they are willing to bear.
Those who are highly risk-averse prefer stable, insured incomes — even if that means earning less and working under weaker incentives.
Those who are risk-tolerant prefer to farm their own land and reap high rewards — with stronger incentives but more risk.

2. Three Roles in the Land Market Emerge

Depending on risk tolerance, people sort themselves into roles:

Role	Traits	Outcome
Yeoman farmers	Risk-tolerant; farm their own land	High effort, high productivity
Tenants	Risk-averse; lease land	Lower effort, lower productivity
Landlords	Wealthy; provide land & insurance	Absorb risk, earn rents

So small farms (owned and cultivated) are more productive not because of size per se, but because of who chooses to farm them.

3. Why Redistribution Might Fail in This Model

"What if we take land from a landlord and give it to a tenant?"

At first glance, you might expect productivity to rise, since ownership aligns incentives.

But in this model:

The tenant is risk-averse.
Once made a landowner, he now bears risk he does not want.
So he “sells” the land back to the landlord (or reverts to tenancy), undoing the redistribution.

➡️ No change in output — redistribution is neutralized by behavior.

4. Possible Caveat: Wealth Effects

There’s one exception:

When you give someone land, you also make them wealthier, and wealth can reduce risk aversion.

So, if risk aversion declines with wealth, the tenant might choose to farm the land after all, and output might rise.

⚖️ Why This Model Matters:

It teaches a critical lesson for policy:

Observing lower productivity on large farms does not automatically justify redistribution.
The mechanism behind the productivity gap matters.

You need to ask:

Is it about incentives?
Is it about selection and risk aversion?
How will people respond after the policy is implemented?

✅ Summary:

Insight	Implication
People self-select into farming or tenancy based on risk tolerance	Small farms are more productive because of who farms them, not just farm size
Redistributing land may backfire	Risk-averse new owners may return land to landlords to avoid risk
Wealth may reduce risk aversion	Redistribution could raise output if new owners become more risk-tolerant
Careful modeling of behavior matters	Surface-level observations can mislead policy without understanding underlying incentives

🧠 Key Concepts Introduced:

1. Heterogeneity in Risk Aversion

People differ in how much risk they are willing to bear.
Those who are highly risk-averse prefer stable, insured incomes — even if that means earning less and working under weaker incentives.
Those who are risk-tolerant prefer to farm their own land and reap high rewards — with stronger incentives but more risk.

2. Three Roles in the Land Market Emerge

Depending on risk tolerance, people sort themselves into roles:

Role	Traits	Outcome
Yeoman farmers	Risk-tolerant; farm their own land	High effort, high productivity
Tenants	Risk-averse; lease land	Lower effort, lower productivity
Landlords	Wealthy; provide land & insurance	Absorb risk, earn rents

So small farms (owned and cultivated) are more productive not because of size per se, but because of who chooses to farm them.

3. Why Redistribution Might Fail in This Model

"What if we take land from a landlord and give it to a tenant?"

At first glance, you might expect productivity to rise, since ownership aligns incentives.

But in this model:

The tenant is risk-averse.
Once made a landowner, he now bears risk he does not want.
So he “sells” the land back to the landlord (or reverts to tenancy), undoing the redistribution.

➡️ No change in output — redistribution is neutralized by behavior.

4. Possible Caveat: Wealth Effects

There’s one exception:

When you give someone land, you also make them wealthier, and wealth can reduce risk aversion.

So, if risk aversion declines with wealth, the tenant might choose to farm the land after all, and output might rise.

⚖️ Why This Model Matters:

It teaches a critical lesson for policy:

Observing lower productivity on large farms does not automatically justify redistribution.
The mechanism behind the productivity gap matters.

You need to ask:

Is it about incentives?
Is it about selection and risk aversion?
How will people respond after the policy is implemented?

✅ Summary:

Insight	Implication
People self-select into farming or tenancy based on risk tolerance	Small farms are more productive because of who farms them, not just farm size
Redistributing land may backfire	Risk-averse new owners may return land to landlords to avoid risk
Wealth may reduce risk aversion	Redistribution could raise output if new owners become more risk-tolerant
Careful modeling of behavior matters	Surface-level observations can mislead policy without understanding underlying incentives

This lecture segment shifts from land redistribution to a related but distinct topic: property rights, specifically focusing on how the security of property rights affects investment and productivity.

🔑 Key Takeaways:

1. Property Rights and Investment: Theory vs. Evidence

Economic theory says secure property rights are essential for encouraging investment:
- If people fear their land can be taken, they will not invest (e.g. planting trees, building irrigation).
But when we ask: What does the empirical evidence say? — the answer is surprisingly weak or mixed.

2. Example 1: Tree Planting in Ghana

Compared plots with secure private rights vs. communal tenure (common in much of Africa).
Theory: Farmers with secure ownership should invest more (e.g., plant trees).
Finding:
- With OLS regression, plots with private rights show slightly more tree planting (~3% increase).
- But with household fixed effects (i.e., comparing plots owned by the same person), the effect disappears.
👉 Suggests: Weak and non-robust evidence that secure property rights boost investment.

3. Example 2: Barbed Wire & Property Rights in the U.S. Plains

📍 Historical natural experiment: The invention and spread of barbed wire fencing in the 1880s.

Problem: Before barbed wire, fencing was expensive (wood was scarce), so property boundaries were weak → cattle wandered and damaged crops.
Barbed wire revolutionized property protection, especially where wood was limited.
Study compared productivity and land improvement across counties with low vs. high wood availability.

✅ Findings:

In counties with low wood, productivity & land improvement surged after barbed wire was introduced.
The difference in land improvement vanished within 10 years between low- and high-wood counties.

🧠 Conclusion: This is strong evidence that technology enabling secure property rights (barbed wire) led to increased investment and output.

⚖️ Summary:

Concept	Key Insight
Property rights theory	Secure rights → more investment → higher productivity
Ghana tree-planting evidence	Weak, inconclusive; secure rights didn't strongly increase investment
Barbed wire study (Hornbeck)	Strong evidence: better property protection → more land improvement & output
Overall message	Economists believe property rights matter, but robust empirical evidence is scarce

💬 Final Reflection:

"This is an area where ideology is ahead of science."
— Professor Banerjee, emphasizing that while economic models assume secure property rights are crucial, real-world evidence is more nuanced, and empirical rigor is essential before making policy claims.

🔑 Key Takeaways:

1. Property Rights and Investment: Theory vs. Evidence

Economic theory says secure property rights are essential for encouraging investment:
- If people fear their land can be taken, they will not invest (e.g. planting trees, building irrigation).
But when we ask: What does the empirical evidence say? — the answer is surprisingly weak or mixed.

2. Example 1: Tree Planting in Ghana

Compared plots with secure private rights vs. communal tenure (common in much of Africa).
Theory: Farmers with secure ownership should invest more (e.g., plant trees).
Finding:
- With OLS regression, plots with private rights show slightly more tree planting (~3% increase).
- But with household fixed effects (i.e., comparing plots owned by the same person), the effect disappears.
👉 Suggests: Weak and non-robust evidence that secure property rights boost investment.

3. Example 2: Barbed Wire & Property Rights in the U.S. Plains

📍 Historical natural experiment: The invention and spread of barbed wire fencing in the 1880s.

Problem: Before barbed wire, fencing was expensive (wood was scarce), so property boundaries were weak → cattle wandered and damaged crops.
Barbed wire revolutionized property protection, especially where wood was limited.
Study compared productivity and land improvement across counties with low vs. high wood availability.

✅ Findings:

In counties with low wood, productivity & land improvement surged after barbed wire was introduced.
The difference in land improvement vanished within 10 years between low- and high-wood counties.

🧠 Conclusion: This is strong evidence that technology enabling secure property rights (barbed wire) led to increased investment and output.

⚖️ Summary:

Concept	Key Insight
Property rights theory	Secure rights → more investment → higher productivity
Ghana tree-planting evidence	Weak, inconclusive; secure rights didn't strongly increase investment
Barbed wire study (Hornbeck)	Strong evidence: better property protection → more land improvement & output
Overall message	Economists believe property rights matter, but robust empirical evidence is scarce

💬 Final Reflection:

"This is an area where ideology is ahead of science."
— Professor Banerjee, emphasizing that while economic models assume secure property rights are crucial, real-world evidence is more nuanced, and empirical rigor is essential before making policy claims.

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