Consider an urn holding 101 balls, each marked with a number from 1 through 4. You don't know the... more Consider an urn holding 101 balls, each marked with a number from 1 through 4. You don't know the number of balls of each type, but you do know that exactly 50 are marked with either a 1 or a 2, and 51 are marked with either a 3 or a 4. This is a variation on the classic urns of Daniel Ellsberg (1961). Given its information structure, you don't know the probability of any given number being drawn, but you do know there's an exact 50/101 chance of it being either a 1 or a 2, and a 51/101 chance of it being either a 3 or a 4. Say you were offered the following pair of bets on this urn. Which one would you choose? (Of course, you could be indifferent between the two bets.) Say you were instead offered the following bets. In this case, which would you choose? Call this urn and the bets above the 50:51 example.
Almost all fishery models assume time-invariant parameter values of the underlying biological gro... more Almost all fishery models assume time-invariant parameter values of the underlying biological growth function except for an i.i.d. error term. We examine the economic implications of cyclical growth parameters in both single and multi-species models, which are frequently observed in many real-world fisheries. Neither optimal harvest rates nor optimal escapement (remaining fish stock after fishing) remain constant as current models would predict. The amplitude of the optimal escapement is increasing in the amplitude of the biological growth function. Moreover, the optimal harvest rate lags the cycle of the biological growth function, i.e., the highest harvest rate is observed after biological conditions have started to decline and the optimal escapement level has already decreased. This is in sharp contrast to current policies which are in phase with biological conditions and hence imply an increase/decrease in harvest quotas when the biological system is improving/deteriorating. In our model, harvest closures are only optimal during time periods when growth parameters are improving most rapidly. We show that once the periodicity of the biological growth function is incorporated, many of the traditional policy prescriptions reverse.
Ambiguous choice problems which involve three or more outcome values can reveal aspects of ambigu... more Ambiguous choice problems which involve three or more outcome values can reveal aspects of ambiguity and ambiguity aversion which cannot be displayed in the classic two-outcome Ellsberg urn problems, and hence are not always captured by models designed to accommodate them. These aspects include Allais-type preferences over purely subjective acts, attitudes toward different sources involving different amounts of ambiguity, and attitudes toward ambiguity at different outcome levels. This paper presents a few such examples, and examines the standard models' predictions and performance in such cases. (JEL D81)
Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected u... more Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected utility”) preferences over subjective gambles might be subject to the same difficulties that Ellsberg's earlier examples posed for subjective expected utility. These difficulties stem from event-separability properties that rank-dependent preferences partially retain from expected utility, and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes. (JEL D81)
that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms w... more that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., "temporal") risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of "generalized expected utility analysis" (M. J. Machina, Econometrica 50 (1982), 277-323) and the theory of support functions (R. T. Rockafellar, "Convex Analysis," Princeton Univ. Press, 1970) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.
Researchers have shown that many, though not all, of the basic results of expected utility analys... more Researchers have shown that many, though not all, of the basic results of expected utility analysis can be more or less directly generalized to non-expected utility preferences. This paper describes the essential difference between results which can be extended in this manner and those which cannot and shows that an important family of comparative statics theorems falls into the former class. Journal of Economic Literature Classification Number: 026.
In discussing Catherine II's proficiency in the Russian language, the historian Kliuchevaskii... more In discussing Catherine II's proficiency in the Russian language, the historian Kliuchevaskii remarked that “she could make four mistakes in spelling a Russian word consisting of three letters.” According to Peter Toumanoff, we have performed a similar feat by making no fewer than five major mistakes in a single paper.
The paper examines the thesis, popular among Russian Marxists, that Russian serfdom had become un... more The paper examines the thesis, popular among Russian Marxists, that Russian serfdom had become unprofitable for the serfowners before the emancipation of the serfs in 1861. Four theoretical models are constructed in order to determine the effects on serfdom of population growth, rise in grain prices, certain restrictions on the serfs' labor obligations, and the replacement of labor services with money payments. Prices of serfs for the several regions and provinces are estimated by regression.With the exception of Lithuania, neither the theoretical nor the empirical results confirm the Marxist hypothesis.
Consider an urn holding 101 balls, each marked with a number from 1 through 4. You don't know the... more Consider an urn holding 101 balls, each marked with a number from 1 through 4. You don't know the number of balls of each type, but you do know that exactly 50 are marked with either a 1 or a 2, and 51 are marked with either a 3 or a 4. This is a variation on the classic urns of Daniel Ellsberg (1961). Given its information structure, you don't know the probability of any given number being drawn, but you do know there's an exact 50/101 chance of it being either a 1 or a 2, and a 51/101 chance of it being either a 3 or a 4. Say you were offered the following pair of bets on this urn. Which one would you choose? (Of course, you could be indifferent between the two bets.) Say you were instead offered the following bets. In this case, which would you choose? Call this urn and the bets above the 50:51 example.
Almost all fishery models assume time-invariant parameter values of the underlying biological gro... more Almost all fishery models assume time-invariant parameter values of the underlying biological growth function except for an i.i.d. error term. We examine the economic implications of cyclical growth parameters in both single and multi-species models, which are frequently observed in many real-world fisheries. Neither optimal harvest rates nor optimal escapement (remaining fish stock after fishing) remain constant as current models would predict. The amplitude of the optimal escapement is increasing in the amplitude of the biological growth function. Moreover, the optimal harvest rate lags the cycle of the biological growth function, i.e., the highest harvest rate is observed after biological conditions have started to decline and the optimal escapement level has already decreased. This is in sharp contrast to current policies which are in phase with biological conditions and hence imply an increase/decrease in harvest quotas when the biological system is improving/deteriorating. In our model, harvest closures are only optimal during time periods when growth parameters are improving most rapidly. We show that once the periodicity of the biological growth function is incorporated, many of the traditional policy prescriptions reverse.
Ambiguous choice problems which involve three or more outcome values can reveal aspects of ambigu... more Ambiguous choice problems which involve three or more outcome values can reveal aspects of ambiguity and ambiguity aversion which cannot be displayed in the classic two-outcome Ellsberg urn problems, and hence are not always captured by models designed to accommodate them. These aspects include Allais-type preferences over purely subjective acts, attitudes toward different sources involving different amounts of ambiguity, and attitudes toward ambiguity at different outcome levels. This paper presents a few such examples, and examines the standard models' predictions and performance in such cases. (JEL D81)
Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected u... more Choice problems in the spirit of Ellsberg (1961) suggest that rank-dependent (“Choquet expected utility”) preferences over subjective gambles might be subject to the same difficulties that Ellsberg's earlier examples posed for subjective expected utility. These difficulties stem from event-separability properties that rank-dependent preferences partially retain from expected utility, and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes. (JEL D81)
that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms w... more that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., "temporal") risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of "generalized expected utility analysis" (M. J. Machina, Econometrica 50 (1982), 277-323) and the theory of support functions (R. T. Rockafellar, "Convex Analysis," Princeton Univ. Press, 1970) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.
Researchers have shown that many, though not all, of the basic results of expected utility analys... more Researchers have shown that many, though not all, of the basic results of expected utility analysis can be more or less directly generalized to non-expected utility preferences. This paper describes the essential difference between results which can be extended in this manner and those which cannot and shows that an important family of comparative statics theorems falls into the former class. Journal of Economic Literature Classification Number: 026.
In discussing Catherine II's proficiency in the Russian language, the historian Kliuchevaskii... more In discussing Catherine II's proficiency in the Russian language, the historian Kliuchevaskii remarked that “she could make four mistakes in spelling a Russian word consisting of three letters.” According to Peter Toumanoff, we have performed a similar feat by making no fewer than five major mistakes in a single paper.
The paper examines the thesis, popular among Russian Marxists, that Russian serfdom had become un... more The paper examines the thesis, popular among Russian Marxists, that Russian serfdom had become unprofitable for the serfowners before the emancipation of the serfs in 1861. Four theoretical models are constructed in order to determine the effects on serfdom of population growth, rise in grain prices, certain restrictions on the serfs' labor obligations, and the replacement of labor services with money payments. Prices of serfs for the several regions and provinces are estimated by regression.With the exception of Lithuania, neither the theoretical nor the empirical results confirm the Marxist hypothesis.
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Papers by Mark Machina