Essays On Equilibrium

Essays on equilibrium labor market sorting

Tzuo Hann Law, University of Pennsylvania


The importance of time invariant, but unobserved characteristics of workers and their employers in the determination of wages is well known. This suggests that models of (un)employment featuring permanent worker and firm types are crucial for our understanding of labor markets. While such models are numerous, it was thought that even very simple ones were fundamentally not identifiable with wage data alone. Hence, the empirical content of these models were largely a mystery. With that, our understanding of permanent unobserved heterogeneity has been restricted to statistical models with limited economic interpretation. In the first chapter of my dissertation (joint with Marcus Hagedorn and Iourii Manovskii), I overcome this fundamental problem. I assess the empirical content of equilibrium models of labor market sorting based on unobserved (to economists) characteristics. Specifically, I develop quantitative tools to identify and estimate a wide class of models of labor market sorting. I not only find that many models are likely completely identifiable but that reliable estimates of key model primitives can be obtained using routinely available matched employer-employee datasets. In the second chapter of my dissertation (with Kory Kantenga), I apply the framework developed in the first chapter to study the role of worker and employer heterogeneity in driving German wage inequality between 1993 and 2007. The model I earlier developed fits overall wage variance, the wage function, search frictions, unemployment levels and the degree of sorting between workers and firms. The fit of the model is comparable to non-structural approaches which utilize many more degrees of freedom. In decomposing the rise in German wage inequality, I find that changes in the non-parametrically estimated production function and the sorting between worker and firm types that it induces accounts for most of the increase in German wage inequality. Finally, by testing whether log wage differences between employees who are coworkers at two distinct firms are constant, I show that the commonly assumed log additive separability approximation of log wages is rejected. Finally, the estimated model is capable of reproducing the degree of non additive separability in the data.^

Subject Area

Economics|Labor economics

Recommended Citation

Law, Tzuo Hann, "Essays on equilibrium labor market sorting" (2015). Dissertations available from ProQuest. AAI3706003.


Since July 24, 2015


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The film Equilibrium is set in the dystopian future (2072) in the fictional city-state of Libria, built by the survivors of the Third World War. The world-at-large is under the rule of a totalitarian regime that blames all societal conflict upon one thing: mankind’s capacity to feel emotion. In an attempt to prevent another catastrophic world war the government imposes the use of Prozium II, a psychotropic substance that suppresses emotions and promotes subservience, upon every man, woman, and child within its’ rule; and to further safeguard the tenuous peace, all potentially emotion-rousing materials, such as art, music, and literature are banned or destroyed altogether. Individuals who refuse to dose up on Prozium are labeled as “sense offenders” and are treated as subversives and are quickly put to death.

The city-state of Libria is ruled by the Tetragrammaton Council, which is in turn led by the enigmatic “Father,” a mysterious figure seen only via gigantic television screens that line the city. His propaganda messages are televised constantly throughout the day to condition the populace. Despite widespread use of prozium there is still a stubborn underground resistance, appropriately and unimaginatively named the “Underground,” that continues to defy the will of “Father” and plans to overthrow the current order of things. In order to quash this rebellion the Council has instituted the order of the Grammaton Clerics, an elite law enforcement unit trained in the lethal fictional martial art of the gun kata. The clerics make frequent forays into the outskirts of Libria to raid rebel strongholds hiding contraband materials as well as executing rebels when they find them.

The film revolves around Cleric John Preston’s journey from cold-blooded enforcer to freedom fighter. Despite being a high-ranking cleric with an amazing record of performance, John hides a troubled past. He executed a fellow cleric and trusted partner, Errol Partridge, when he discovered that he was secretly sympathizer of the rebellion and for refusing to consume his drug ration, effectively making him a sense offender as well as enemy of the state. The biggest scandal however is the death of his wife. His wife had secretly been skipping her daily ration of Prozium, out of a desire to feel emotions once more. John turns her over to the authorities and she is summarily executed as a sense offender.

While carrying out his mundane daily tasks John accidentally manages to break a vial of his day’s dose of Prozium. He is promptly reminded by his young son Robbie to report the loss and ask for a spare but due to the unpredictable nature of the raids he immediately goes out on his next mission completely missing a dose of the psychotropic. The missed dosage though is enough to shake him out of his usual cold-blooded efficiency. Suddenly he experiences brief but powerful surges of emotion, memories long suppressed by the medication come rushing back with a vengeance. He sensation is heady and decidedly addictive; and like a junkie looking for his next rush he deliberately misses the successive dosages of Prozium, hiding the unused doses behind his bathroom mirror where he thinks it won’t be discovered.

Errol is replaced with an up-and-coming cleric, Brandt. Brandt is an ambitious young cleric who looks up to John for his dedication, skill in unearthing rebels, and deadly efficiency, openly praising him. Together on their first mission they apprehend a citizen for being a sense offender, Mary O’Brien. The punishment for a sense offender is immediate execution without trial, so Brandt is puzzled by John’s announcement to apprehend Mary rather than kill her outright. His doubts grow over time as John continues to display contrary behavior: refusing to kill sense offenders or destroy banned materials. Having skipped his daily medication John is now completely free from the influence of Prozium and now feels guilt for having executed Errol and to make matters worse he is now developing feelings for Mary. Eventually, John Preston meets up with the leader of the resistance, Jurgen, who manages to win him over to their cause. John agrees to help them eliminate Father and halt the production and distribution of Prozium long enough to free people from it’s numbing influence and stir them into a revolution.

John collaboration with the resistance has been kept pretty well hidden thus far and for his faithful service he is granted an audience with Vice-Counsel DuPont to be honored. Upon meeting John the Vice-Counsel divulges that he is aware that there is a traitor in their midst and John is tasked with revealing and neutralizing the defector. He is relieved that he hasn’t been discovered but he must now double his efforts to find the rebels and eradicate them if only to maintain the pretense... John also finds out that Mary is arranged to be executed but Jurgen warns him not to intervene, as it would compromise their plans to initiate a mass revolt.

Jurgen commands the leadership of the Underground to be taken by Preston to earn the Council’s trust and gain access to Father and assassinate him. He manages to pull off looking like he had finally quashed the rebellion but he finds that Mary is about to be executed and without the aid of Prozium John is unable to contain himself and he barges in an attempt to prevent her death but is his efforts are in vain and she is killed anyway. John Preston then breaks down in grand fashion in clear sight of the citizens of Libria--and Cleric Brandt--who promptly arrests him and takes him directly the Vice-Counsel to be tried for being a sense offender and a traitor to the state.

Despite his arrest, John still manages to manipulate Vice-Counsel DuPont into judging that the actual conspirator is the upstart cleric, Brandt. Brandt's is quickly taken into custody of the authorities for questioning. Meanwhile John is told that his residence will be investigated, but merely as a formality rather than an actual inquest. News of this house examination alarms him and he hurries home to destroy the incriminating evidence: the ampoules of unused Prozium he keeps hidden in his medicine cabinet. He returns home and to his great surprise finds that his young son Robbie, has already disposed of the vials. The boy then discloses that he had actually stopped taking the drug after his mother was arrested and executed. His reasons for ditching the Prozium are never fully discussed in the film.

Carrying out the last stages of their grand plan, John hand over Jurgen and other top members of the resistance to the Council. Having done this his reputation and loyalty are now indisputable and he is granted an private audience with the inscrutable Father as a reward for having single-handedly crushed a possible uprising. The tables quickly turn however as the supposed appointment with Father turns out to be a counterplot devised to reveal John’s true loyalties. He comes face to face with Cleric Brandt who had been conspiring with the Vice-Counsel DuPont who divulges that he has been impersonating Father, covertly substituting himself upon the actual Father’s death.

Upon facing the Vice-Counsel it becomes evident that he too is free from the control of Prozium and can feel a broad range of emotions. He uses this to his advantage, provoking John into a rage by asking him how he felt when he deceived his comrades. This taunting is effective, angering the cleric into attacking, but it is clear that rather than make him a sloppy fighter it turns him into a passionate one. Strengthened by his righteous anger he blazes through cadre after cadre of DuPont’s guards, finally facing off with Cleric Brandt in an old-fashioned sword fight. John wins the duel then faces off with DuPont who, surprisingly, is also adept at gun kata, able to hold his own with him for a couple of minutes. Preston’s superior skills and conditioning prevail and he defeats the Vice-Counsel. The outdone DuPont unpredictably begins to appeal to John, asking to be spared. The former cleric is unmoved; he executes the Vice-Counsel then proceeds to demolish the headquarters, cutting off the propaganda transmissions. Without the leadership of “Father” the Underground is able to carry out the rest of its plans, destroying Prozium factories and distribution centers and freeing sense offenders. John, breaking into a broad grin of what looks to be satisfaction, observes the uprising unfold from the former Vice-Counsel’s office.

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