### The Case for Subsidizing Harm:

Second-best Pigouvian Taxation with Multiple Externalities

##### Jaqua, Daniel and Schaffa, Daniel

Most energy production activities are subsidized despite generating negative externalities. We explain this phenomenon by developing a model that generalizes previous work on second-best Pigouvian taxation. In this model the policymaker will optimally subsidize a harmful production activity if a constraint or cost prevents the first-best correction of an even more harmful alternative. We highlight three examples. First, it may be optimal to subsidize a harmful activity if a constraint prevents the taxation of an even more harmful substitute. Second, it may be optimal to subsidize a harmful activity if there is a large administrative cost associated with taxing an even more harmful substitute. Third, it may be optimal to subsidize a harmful production process if the activity mix at lower levels of output uses more harmful activities than the activity mix at higher levels of output.

### How to Select the Correct Discount Rates for Public Policy

##### Jaqua, Daniel

The current approach to valuing public policy incorrectly identifies cost effective interventions as too costly and vice versa. The current approach also incorrectly ranks the cost effectiveness of policies. For example, the EPA uses the same discount rate for any intervention. Many countries set one discount rate which is used to value any public health intervention. The proper discount rate for valuation depends on the opportunity cost, which is related to the risks of the intervention and varies over time. This paper explains the correct approach, which applies portfolio theory to the decisions of a benevolent social planner. This paper also describes several alternative approaches which may be useful in special circumstances. The current approach limits manipulation by interested parties but creates inaccurate valuations. One possible compromise is to require set standards for how the discount rate is determined. Another compromise would be to report valuations using more than one discount rate.

### Apples to Apples; Data on Variety Competition and New Product Entry in the US Apple Market

##### Butler, John and Jaqua, Daniel

This paper estimates the supply and demand for different apple varieties in the United States. Previous work treats apples as homogeneous goods. We show large and persistent differences in the price of different apple varieties. This paper treats apple varieties as differentiated products.

### The Principal Agent Problem in Corporate Tax Preparation

##### Jaqua, Daniel

Corporations hiring employees or firms to prepare tax returns face a principal agent problem. In addition to inefficient risk sharing and effort provision in tax preparation, auditors are strategic agents. This paper models the multilayered principal agent problem the corporation faces.The paper then describes additional legal and imperfect contracting problems faced by the principal and modifies the models to predict the impact the principal agent problem will have on corporate tax returns.

### How to Catch Capone: The Optimal Punishment of Interrelated Crimes

##### Jaqua, Daniel and Schaffa, Daniel

This paper characterizes optimal criminal punishments when there are multiple interrelated crimes. Optimal punishments are functions of the extent to which related crimes are complements or substitutes weighted by their relative harms to society. This insight applies more generally to Pigouvian taxation with costly administration: in a second-best setting, the optimal Pigouvian tax is partly a function of spillovers to other externality-generating activities. The available evidence suggests that the actual harm reduction of a marginal increase in arrests for an index crime is about 1.5-3 times greater than the harm reduction calculated without these effects.

### Deterrence and Incapacitation

##### Jaqua, Daniel and Schaffa, Daniel

When criminals allocate time to different activities, including crimes, deterrence and incapacitation are the substitution and wealth effects of a change in punishment. The incapacitation effect is related to the social burden of increasing punishment. For many formulations of the optimal criminal justice policy, the total response of the crime rate to the enforcement policies is sufficient to determine the optimal policy. That is, if the total response to a policy is known, then the optimal policy does not depend on what fraction of the response could be attributed to deterrence, and what fraction to incapacitation.

### Should the Audit Rule be Public?

##### Jaqua, Daniel

This paper characterizes the optimal amount of uncertainty in the auditing rate. Most tax authorities do not publish the auditing rate.Most analyses of optimal taxation assume that taxpayers know the auditing rate with certainty. This paper shows that it is not always optimal to obfuscate the auditing rate. In fact there is an optimal amount of ambiguity which is determined by the risk aversion and the ambiguity aversion of the taxpayer.

### The Case for Subsidizing Harm:

Second-best Pigouvian Taxation with Multiple Externalities

### A previous draft was circulated under the title: “Pigouvian Taxation with Multiple Externalities and Costly Administration”

##### Jaqua, Daniel and Schaffa, Daniel

Most energy production activities are subsidized despite generatingnegative externalities. We explain this phenomenon by developing a model thatgeneralizes previous work on second-best Pigouvian taxation. In this model thepolicymaker will optimally subsidize a harmful production activity if aconstraint or cost prevents the first-best correction of an even more harmfulalternative. We highlight three examples. First, it may be optimal to subsidizea harmful activity if a constraint prevents the taxation of an even moreharmful substitute. Second, it may be optimal to subsidize a harmful activityif there is a large administrative cost associated with taxing an even moreharmful substitute. Third, it may be optimal to subsidize a harmful productionprocess if the activity mix at lower levels of output uses more harmfulactivities than the activity mix at higher levels of output.

### How to Select the Correct Discount Rates for Public Policy

##### Jaqua, Daniel

The current approach to valuing public policy incorrectly identifies cost effective interventions as too costly and vice versa. The current approach also incorrectly ranks the cost effectiveness of policies. For example, the EPA uses the same discount rate for any intervention. Many countries set one discount rate which is used to value any public health intervention. The proper discount rate for valuation depends on the opportunity cost, which is related to the risks of the intervention and varies over time. This paper explains the correct approach, which applies portfolio theory to the decisions of a benevolent social planner. This paper also describes several alternative approaches which may be useful in special circumstances. The current approach limits manipulation by interested parties but creates inaccurate valuations. One possible compromise is to require set standards for how the discount rate is determined. Another compromise would be to report valuations using more than one discount rate.

### Apples to Apples; Data on Variety Competition and New Product Entry in the US Apple Market

##### Butler, John and Jaqua, Daniel

This paper estimates the supply and demand for different apple varieties in the United States. Previous work treats apples as homogeneous goods. We show large and persistent differences in the price of different apple varieties. This paper treats apple varieties as differentiated products.

### The Principal Agent Problem in Corporate Tax Preparation

##### Jaqua, Daniel

Corporations hiring employees or firms to prepare tax returns face a principal agent problem. In addition to inefficient risk sharing and effort provision in tax preparation, auditors are strategic agents. This paper models the multilayered principal agent problem the corporation faces.The paper then describes additional legal and imperfect contracting problems faced by the principal and modifies the models to predict the impact the principal agent problem will have on corporate tax returns.

### How to Catch Capone: The Optimal Punishment of Interrelated Crimes

##### Jaqua, Daniel and Schaffa, Daniel

This paper characterizes optimal criminal punishments when there are multiple interrelated crimes. Optimal punishments are functions of the extent to which related crimes are complements or substitutes weighted by their relative harms to society. This insight applies more generally to Pigouvian taxation with costly administration: in a second-best setting, the optimal Pigouvian tax is partly a function of spillovers to other externality-generating activities. The available evidence suggests that the actual harm reduction of a marginal increase in arrests for an index crime is about 1.5-3 times greater than the harm reduction calculated without these effects.

### Deterrence and Incapacitation

##### Jaqua, Daniel and Schaffa, Daniel

When criminals allocate time to different activities, including crimes, deterrence and incapacitation are the substitution and wealth effects of a change in punishment. The incapacitation effect is related to the social burden of increasing punishment. For many formulations of the optimal criminal justice policy, the total response of the crime rate to the enforcement policies is sufficient to determine the optimal policy. That is, if the total response to a policy is known, then the optimal policy does not depend on what fraction of the response could be attributed to deterrence, and what fraction to incapacitation.

### Should the Audit Rule be Public?

##### Jaqua, Daniel

This paper characterizes the optimal amount of uncertainty in the auditing rate. Most tax authorities do not publish the auditing rate.Most analyses of optimal taxation assume that taxpayers know the auditing rate with certainty. This paper shows that it is not always optimal to obfuscate the auditing rate. In fact there is an optimal amount of ambiguity which is determined by the risk aversion and the ambiguity aversion of the taxpayer.