class: center, middle, inverse, title-slide # Aspirations in Economics ## An Introduction to Aspirations Theory ### Julius Ruschenpohler --- class: inverse, middle .pull-left[ .smaller[ ### THEORY I. Aspirations Failures (Dalton et al., 2016) II. Aspiration Frustration (Genicot, Ray, 2017) ] ] .pull-right[ .smaller[ ### DISCUSSION III. Discussion Points ] ] --- name: aspfail1a # I. Aspirations Failures ## General Set-up of Dalton et al. (2016) ### Production Fct An agent is endowed with initial capital `\(k\)`. To maximize utility, the agent decides whether or not to exert costly effort `\(e \in \{ 0,1 \}\)` to produce final wealth `\(y_{c}\)` according to the production fct: `$$y_{c} = f(e, k) = (1 + e) k$$` Hence, effort `\(e\)` and initial capital `\(k\)` are complementary. --- name: aspfail1b # I. Aspirations Failures ### Objective Fct The agent derives utility from two additively separable components: <br> <br> (i) final wealth `\(y_{c}\)` and <br> (ii) its relative level with respect to her aspirations `\(y_{c} - a_{c}\)`. Aspirations `\(a_{c}\)` can be thought of as a level of `\(y_{c}\)` that the agent desires to attain. The agent maximizes utility according to the objective fct: `$$U _ { c } \left( e , a _ { c } , y _ { c } \right) = b \left( y _ { c } \right) + v \left( \frac { y _ { c } - a _ { c } } { y _ { c } } \right) - c ( e )$$` --- name: aspfail2 # I. Aspirations Failures ## Types of Agents The model assumes two types of agents with two ways of endogenizing aspirations `\(a_{c}\)` in the production of final wealth `\(y_{c}\)`. ### 1. Rational Agent A rational agent, when choosing aspirations `\(a_{c}\)`, **internalizes the feedback from effort `\(e\)` onto aspirations `\(a_{c}\)`** (through realized outcomes). That is, `\(a_{c} = f(e, k)\)`. In effect, while maximizing utility, the rational agent consistently adjusts aspirations to exerted effort. ### 2. Behavioral Agent A behavioral agent, **takes aspirations `\(a_{c}\)` as exogenously given**! --- name: aspfail3a # I. Aspirations Failures ## Solutions ### 1. Rational Solution Given `\(k\)`, an effort-aspirations pair `\(\left(e^{*} , a_{c}^{*} \right)\)` is a rational solution if: `$$e ^ { * } \in \arg \max_{e\in \{0,1\} } U_{c} (e, f(e,k), f(e,k))$$` And if: `$$a_{c}^{*} = f\left( e^{*}, k\right)$$` Then there exists a level of initial capital `\(k^{*}\)` such that, whenever `\(k > k^{*}\)`, the **unique rational solution** is (high effort, high aspirations). (That is, `\(e^{*}=1\)` and `\(a^{*}=2k\)`.) --- name: aspfail3b # I. Aspirations Failures ### 2. Behavioral Solutions Given `\(k\)`, an effort-aspirations pair `\(\left(\tilde{e}, \tilde{a}_{ c } \right)\)` is a behavioral solution if: `$$\tilde { e } \in \arg \max _ { e \in \{ 0,1 \} } U _ { c } \left( e , \tilde { a } _ { c } , f ( e , k ) \right)$$` And if: `$$\tilde { a } _ { c } = f ( \tilde { e } , k )$$` Then there exist `\(k_{h}\)` and `\(k_{l}\)`, where `\(k_{h} > k > k_{l}\)` [1], such that: * if `\(k > k_{h}\)`, the unique behavioral solution is (high effort, high aspirations). * if `\(k < k_{l}\)`, the unique behavioral solution is (low effort, low aspirations). * if `\(k_{l} < k < k_{h}\)`, there is no unique behavioral solution (both high and low effort-aspirations pairs are behavioral solutions). [1] Omitting additional assumptions --- name: aspfail4a # I. Aspirations Failures ## Poverty Traps This gives us two types of poverty traps. ### 1. Classical Poverty Trap Arises when `\(k < k^{*}\)` (due to lack of resources). ### 2. Behavioral Poverty Trap Arises when `\(k^{*} < k < k_{h}\)`. A **sufficiently poor** agent with **sufficiently low aspirations** chooses suboptimally **low effort** (*because they started with low aspirations*!) --- name: aspfail4b # I. Aspirations Failures ### Intuition of Behavioral Poverty Trap A poor agent will exert less effort than a rich agent. Two reasons: 1. **Marginal return to effort lower for the poor** + Due to assumption of capital-effort complementarity (recall, `\(y_{c} = f(e, k) = (1 + e) k\)`) + Also in a rational equilibrium 1. **Feedback from effort onto aspirations** (through realized outcomes) + Lowers marginal return to effort further --- name: aspfrust1 # II. Aspiration Frustration ## General Set-up of Genicot and Ray (2017) ### Objective Fct An agent is endowed with initial capital `\(k\)`. The agent can choose to make investment `\(i\)` to achieve future income `\(z\)`. Again, aspirations `\(a_{z}\)` can be thought of as a level of `\(z\)` that the agent desires to attain. `\(e_{k} = max \{z - a_{z}, 0\}\)` is the excess of outcome `\(y\)` over aspiration threshold `\(a_{z}\)`. Crossing this threshold yields a separable payoff The agent maximizes utility according to the objective fct: `$$U _ { p } \left( i , a _ { z } , k, z \right) = u ( k, i ) + w _ { 0 } \left( z \right) + w _ { 1 } \left( \max \left\{ z - a _ { z } , 0 \right\} \right)$$` --- name: aspfrust2a # II. Aspiration Frustration ## Graphical Illustrations ### Components of the utility fct (additively seperable) <img src="aspTheory_files/figure-html/unnamed-chunk-1-1.svg" style="display: block; margin: auto;" /> --- name: aspfrust2b # II. Aspiration Frustration ## Graphical Illustrations ### Decision problem <img src="aspTheory_files/figure-html/unnamed-chunk-2-1.svg" style="display: block; margin: auto;" /> --- name: aspfrust2b # II. Aspiration Frustration ## Graphical Illustrations ### Shifting aspirations and resulting frustration <img src="aspTheory_files/figure-html/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" /> --- name: aspfrust2d # II. Aspiration Frustration ## Graphical Illustrations ### Multiple aspiration thresholds <img src="aspTheory_files/figure-html/unnamed-chunk-4-1.svg" style="display: block; margin: auto;" /> --- name: discuss1 # III. Discussion Points ### 1. How does psychology view aspirations Snyder's **hope** theory Bandura's **self-efficacy** Rotter's **locus of control** ### 2. What is the difference between hope and aspirations? ### 3. How does agency fit into aspirations theory? ### 4. What is the difference between expecations and aspirations? ### 5. How to measure aspirations? Expectations? Hope? ### 6. What are potentially fruitful areas of study?