Econ 551 Government Finance: Revenues Fall 2019 Given by Kevin - - PowerPoint PPT Presentation

ECON 551: Lecture 2b 1 of 34

Econ 551 Government Finance: Revenues Fall 2019

Given by Kevin Milligan Vancouver School of Economics University of British Columbia Lecture 2b: Positive Political Economy

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Agenda:

• 1. Models of Direct Democracy: Median Voter Theorem
• 2. Application: Voting over taxes
• 3. Models of Representative Democracy

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Models of Direct Democracy:

Direct democracy means citizens have a choice over the outcomes, not representatives.  Think of referenda. The notation and proof we go through come from Persson and Tabellini (2000). The examples of voting systems come from Levin and Nalebuff (1995).

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Black 1948:

Originated (or re-discovered) the idea to apply economic reasoning to politics  You can see how novel it is (or at least he thinks it is) in his tone. The theory, indeed, would appear to present the basis for the development of a pure science of politics. This would employ the same theory of relative valuation as economic science. It would employ a different definition of

• equilibrium. Equilibrium would now be defined in terms of voting, in place of

the type of definition employed in economic science. We could move from the

• ne science to the other with the alteration of a single definition. This, in the

view of the writer, would be the main function of the theory. Offered first proof of the median voter theorem—the workhorse of many modern models. Note that this pre-dated Arrow—which may account for the optimistic tone of his paper.

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The environment:

 Direct Democracy. Citizens vote for outcomes, rather than for candidates who will implement outcomes.  Sincere Voting. Citizens vote for their preferred outcome. Note that this is an assumption, not a result.  Open agenda. Decisions are made by placing policies against each other in sequential pairwise comparisons. It is ‘open’ because any policy can be put forward against any other; no agenda-setting.

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Notation:

 Set of social alternatives: X  Set of voters: Θ = {1,2, … , 𝑂}  For decisions 𝑦, 𝑧 ∈ 𝑌 𝑦𝑄𝜄𝑧 means that x is strictly preferred to y by guy θ. 𝑦𝑆𝜄𝑧 means that x is weakly preferred to y by guy θ. 𝜈(𝑦, 𝑧)is the fraction of voters for whom 𝑦𝑆𝜄𝑧 𝑦𝜄

∗is guy θ’s bliss policy; 𝑦∗𝑆𝜄𝑧, ∀𝑧 ∈ 𝑌

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Definition: A Condorcet winner

A policy 𝑦 ̃ ∈ 𝑌 is a Condorcet Winner if it beats all other policies 𝑧 ∈ 𝑌 in pairwise votes. 𝜈(𝑦 ̃, 𝑧) ≥ 𝜈(𝑧, 𝑦 ̃), ∀𝑧 ∈ 𝑌

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Definition: Single-Peakedness

Preferences are single-peaked if the distance from the bliss point dictates the preference

• rdering.

If 𝑦 ̂ ≤ 𝑦̅ ≤ 𝑦𝜄

∗ (or 𝑦

̂ ≥ 𝑦̅ ≥ 𝑦𝜄

∗) then 𝑦̅𝑆𝜄𝑦

̂ This just says the closer you are to the bliss-point, the better the option is (weakly).

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Illustration: Single-Peakedness

Quantity of x Zhu Singh Jones

Valuation of x

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Definition: Median voter

Order all voters 𝜄 ∈ Θ by their 𝑦𝜄

∗. The median voter is the θ with 𝑦𝜄 ∗ ranked

 (N+1)/2 if N is odd  (N/2) and (N/2) +1 if N is even.

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Proposition: The Median Voter Theorem

If all voters have single peaked preferences and the set of policies X is one dimensional, then:  ∃ a Condorcet winner, 𝑦 ̃.  The Condorcet winner is the bliss point of the median voter: 𝑦 ̃ = 𝑦𝑛

∗

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Proof: The Median Voter Theorem

The following is the proof of the case for which N is odd. (The even case can be proved, but is harder to do.) Take a policy 𝑦 < 𝑦𝑛

∗ , 𝑦 ∈ 𝑌

Single peakedness implies that all θ with 𝑦𝜄

∗ > 𝑦𝑛 ∗ will have 𝑦𝑛 ∗ 𝑆𝜄𝑦. This is (N-1)/2

voters. Median voter has 𝑦𝑛

∗ 𝑆𝜄𝑦 . This is one more voter.

So, we have (N-1)/2 + 1 = N/2 +1/2 > N/2 ∴ 𝜈(𝑦𝑛

∗ , 𝑦) > 0.5 and 𝑦𝑛 ∗ is a Condorcet winning policy.

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Comments on the Median Voter Theorem:

 The social ordering works. How does this square with Arrow IT? MVT requires restriction on preferences to be single peaked. This violates the (U) axiom.  We have social transitivity. This is great. Without transitivity, the order in which pairwise comparisons are made determines the outcome; agenda-setting matters. This conveys a lot of power on the agenda setter.  We restricted attention to the case of a single policy dimension. What if policies are multi-dimensional? Stronger restrictions on preferences are required.

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Example 1:

Θ = {𝑇𝑏𝑚𝑚𝑧, 𝐶𝑝𝑐𝑐𝑧, 𝐿𝑓𝑜𝑜𝑧} 𝑌 = {𝐵, 𝐶, 𝐷} with 𝐵 < 𝐶 < 𝐷 Rank preferences look like this: A B C Sally 1 2 3 Bobby 2 1 3 Kenny 3 2 1

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Example 1:

 Are all three single peaked?  Who is the median voter?  What is the median voter’s preferred policy.  Can other policies beat that one? Try it.  Transitive?  Agenda-independent?

A C B Kenny Sally Bobby

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Example 2:

Θ = {𝑇𝑏𝑚𝑚𝑧, 𝐶𝑝𝑐𝑐𝑧, 𝐿𝑓𝑜𝑜𝑧} 𝑌 = {𝐵, 𝐶, 𝐷} with 𝐵 < 𝐶 < 𝐷 Rank preferences look like this: A B C Sally 1 3 2 Bobby 2 1 3 Kenny 3 2 1

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Example 2:

 Are all three single peaked?  Who is the median voter?  What is the median voter’s preferred policy.  Can other policies beat that one? Try it.  Transitive?  Agenda-independent?

A C B Sally

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Example 3: Ends against the middle

Epple and Romano (1996) Imagine the following:  Paying for a local public good (e.g. schooling) out of local tax.  Choice is X = {𝑚𝑝𝑥, 𝑛𝑓𝑒𝑗𝑣𝑛, ℎ𝑗𝑕ℎ}, where low means you get low taxes and low quality; high is opposite.  Population is Θ = {𝑞𝑝𝑝𝑠, 𝑛𝑗𝑒𝑒𝑚𝑓, 𝑠𝑗𝑑ℎ}.  Say each group has the ‘obvious’ bliss point. (poor likes low, middle likes medium, rich likes high.)  Rich has outside option—private school—which they will take if X<high.  But Rich has to pay taxes, no matter what X is chosen. Q: Who is median voter? Is median voter decisive? Q: What is Rich’s preference ranking? Q: Are there any signs of trouble here? Q: What problems could arise?

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Agenda:

• 1. Models of Direct Democracy: Median Voter Theorem
• 2. Application: Voting over taxes
• 3. Models of Representative Democracy

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Application: Voting on Taxes

This application draws on what’s known as the Meltzer-Richards (1981) model. Consider:  A society with N individuals indexed by i, ∈ {1, … , 𝑂}.  Each has an identical utility function which takes only consumption as an argument: 𝑉𝑗 = 𝑉(𝑑𝑗).  Each individual has exogenous income yi.  Income is taxed at a flat rate of t. Taxed income is returned to individuals through a uniform lump sum transfer d. The budget is balanced, so that 𝑂𝑒 = ∑ 𝑢𝑧𝑗

𝑗

 Define 𝑧 =

∑ 𝑧𝑗

𝑗

𝑂 , so that 𝑒 = 𝑢 × 𝑧.

 Define utility level when t=0 to be U0.

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Application: Voting on Taxes

Decision faced by electorate is whether to institute the tax/transfer plan.  Each voter evaluates whether 𝑉𝑗 ≤≥ 𝑉0

𝑗.

Write down the budget constraint: 𝑑𝑗 = 𝑧𝑗(1 − 𝑢) + 𝑒 From the government budget constraint we can substitute in for d: 𝑑𝑗 = 𝑧𝑗(1 − 𝑢) + 𝑢𝑧 and simplify to 𝑑𝑗 = 𝑧𝑗 + 𝑢(𝑧 − 𝑧𝑗) Note: 𝑑0

𝑗 = 𝑧𝑗, if there is no transfer.

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Application: Voting on Taxes

If the distribution of yi is single-peaked, then the median voter will be decisive. Call the median voter i=m. Then redistribution will pass the referendum iff 𝑧 > 𝑧𝑛 (by the median voter theorem). The predictions from this model therefore are: 1) if the mean income is higher than the median, then government will be larger. 2) If the mean income is higher than the median, there will be more redistribution.

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Comments on the model:

1) It explains too much. Why don’t the ‘poor’ completely expropriate the rich? 2) This model might help explain why the right to vote was extended from the landed to the working classes only slowly – in the model why would you ever extend the franchise? 3) The model has often performed quite poorly in empirical tests. (e.g. Frank Rich: “What’s the matter with Kansas” ie why do poor rural states vote for right wing parties?) 4) Note: Pickering and Rajput (2018) provide recent cross-country evidence that supports key predictions of the model: higher inequality leads to higher reliance on redistributive income taxes; bigger effect in stronger democracies. 5) If redistributional motives don’t explain the size/growth of government, then what does? Maybe interest groups / pork barreling. Maybe bureaucrats. Maybe insurance motives. Maybe voter turnout. Maybe….

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Agenda:

• 1. Models of Direct Democracy: Median Voter Theorem
• 2. Application: Voting over taxes
• 3. Models of Representative Democracy

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Models of Representative Democracy:

 Models of direct democracy (such as the MVM) are useful for analyzing the work of small committees, or of the general population in referenda.  However, many of our social decisions are not made directly, but instead by representatives.  For this reason, we turn to the study of representative democracy to further our understanding of decision processes.  Theory in this area has advanced a lot over the last 20 years, trying to understand how legislators vote on policy.  But we’ll just introduce the basic workhorse model here today: Downs (1957)

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The Downsian model:

 The workhorse model of representative democracy is Anthony Downs (1957), “An Economic Theory of Democracy”.  In the book, Downs attempted to show that political competition would lead to efficient outcomes.  Note that this was after Arrow, so he was hoping to find ways to overcome the AIT.

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The Downsian framework:

 Voters are rational, self-interested, and completely informed.  Parties / candidates seek to optimize their own objective functions.  Their objective function is to win power. “… parties formulate policies in order to win elections, rather than win elections in order to formulate policies.”  This means they are non-ideological. They are in politics for power, not to satisfy their own policy preferences.  Policy promises are completely credible. After winning, the promised policy is implemented.  The number of candidates is exogenously set to 2.

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Model timing:

• 1. Two candidates simultaneously and non-cooperatively announce platforms.
• 2. Elections are held, with voters choosing their preferred candidates.
• 3. Elected candidate implements her platform.

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Candidate positioning:

Suppose that the policy space is uni-dimensional. For example, low tax/spend or high tax/spend. Let’s refer to it simply as Left-Right. Suppose further that voters are continuously distributed along the Left-Right spectrum, with a unimodal distribution.

Policy position L R Density

• f

voters

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Voting and equilibrium:

A voter is assumed to vote for the candidate that chooses a position closest to the voter’s preferred policy. Note that this is essentially an extension of the Hotelling model in I/O to the political

• sphere. Also, it is very similar to the MVM.

Parties in period 1 choose a position on the platform. Let’s look at this heuristically.  Pick an arbitrary place on the spectrum.  If the other candidate is to your right, then you get all votes to your left.  You also get all of the votes up to the halfway point between your position and your

• pponent’s.

 To maximize your vote share, you will want to be exactly at the middle, so that you will either get all of the voters to the left or to the right – at least half.  Furthermore, your opponent will do exactly the same.

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Predictions of the Downsian model:

 Policy convergence. Both parties offer the same policy in equilibrium.  Moderate policies. The policy offered will be one favoured by voters in the middle.  Lots of turnover. Since policies are identical, election outcomes should be more or less random.

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How well do Downsian predictions hold up?

 Ralph Nader in 2000 kept on talking about the ‘two corporate parties’ and referred to Bush and Gore as Tweedle-dee and Tweedle-dum.  In Canada, the NDP used to say ‘Liberal, Tory, same old story.”  We also see parties trying to ‘take the issue off the table’ by matching another party on a key issue.

• Health by Harper/CPC in 2004/2006.
• Gun registry by Trudeau/LPC in 2015.

 However, at the same time we see very divergent policy proposals to the voters.

• Micro-targeted policies are aimed at specific groups of voters, not broad-based pitches.
• Turnout-focused strategies aim to raise turnout of the voters likely to vote for you.

 So, strategic rather than complete differentiation.  Also, in the US, we see a huge advantage for incumbents. We don’t see the kind of turnover we might expect from the Downsian model.

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Summary of Collective Decision Making:

 We started off pondering the question of how to choose from among the allocations

• n the Pareto frontier.

 In the 1930s and 1940s, economists were really excited about coming up with a SWF that would give us a ‘scientific’ way of making these kinds of social choices. If only the ‘right’ SWF can be found, we would have a great tool to combat the world’s problems!  Unfortunately, Arrow showed that SWFs would either have to be dictatorial or not produce coherent results.  This generated lots of research in the 1960s and 1970s about how to relax Arrow’s axioms to allow a social ordering.  Modern work has pretty much stopped the search for ‘the’ ideal SWF. We seem to be more cynical now. Instead, most modern work seeks just to explain and characterize the way the world does work. This is much less ambitious, but at least it isn’t impossible.

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Next Class:

We will start on taxes! Looking at excess burden. Reading for next class: Hines, James R. Jr. (1999), “Three Sides of Harberger Triangles,” Journal of Economic Perspectives, Vol. 13, No. 2, pp. 167-188.