Spending Tradeoffs slide 1

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A Hitchhikers Guide to Guns vs Butter

• A multimedia presentation

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Guns vs. Butter

• There is a classic characterization in the
  literature that there is a tradeoff between
  Guns and Butter.
• In other words, between security and prosperity
  or economic benefit.
• This is generally regarded as the tradeoff
  between military and social welfare spending.

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Tradeoffs

• In simple terms, it would seem that if you spend
  a dollar more on defense, you have a dollar less
  to spend on social welfare (or any other sector
  of the budget)
• In a similar fashion, if one sectors share of
  the budget increases, it would seem to come at
  some other sectors share (as measured in
  percentage terms.)

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Tradeoffs the Classic Model

• Thus, in order to detect or measure tradeoffs, we
  regress the percentage change in military
  spending on the percentage change in some other
  sector.
• We must also control for growth in the overall
  pie the percentage change in total spending

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The confirmation of tradeoffs

• In the classic model represented by Equation (1)
  the existence of tradeoffs is confirmed by a
  significant negative coefficient for B2
• Researchers have attempted to repair this model
  by examining different spending categories and
  adding other factors to control for specification
  error.

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The Record of the Classic Model

• It simply doesnt pan out
• The literature (Russett, Domke, Eichenburg,
  Kelleher, and Mintz, among others) simply does
  not support the systematic tradeoff between
  defense and social welfare or education or
  health, etc.

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The Puzzle

• Why should what seems so intuitively obvious be
  unsupported by the literature?

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Approaches to solving the tradeoff puzzle

• The literature has tried several strategies to
  detect these tradeoffs
• Looking for tradeoffs with specific selected
  sectors (Russett, 1983)
• adding exogenous variables (trying to reduce
  specification error) a very reasonable approach
  prima facia (Russett, 1983 Domke,Eichenburg
  Kelleher, 1983 Duval and Mok, 1991)
• More elaborate statistical designs. (D, E, K)
• Questioning the nature and source of the tradeoff
  decision making process (Berry)

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Theory?

• Can it be that our theoretical articulation is
  erroneous?
• We need to examine the question starting with
  some very basic assumptions and see what we can
  deduce.
• Then we can turn to an empirical examination of
  tradeoffs

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Building Theory

• Let us start with the idea that we wish to
  ascertain the theoretical validity of the classic
  model.
• Can we support Equation (1) with a deductive
  framework?

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Deriving the Model

• We shall seek to derive Eq.1 from some simple
  axiomatic propositions. Therefore two consecutive
  budgets in yeart and yeart-1 are defined as
• 
  (2)
• 
  (3)

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Deriving the Model cont.

• Rearranging terms, defense spending is then
  defined as a function of total spending minus the
  other categories.
• (4)
• (5)

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Deriving the Model cont.

• A sector's percentage of the total federal budget
  indicates (at least to some degree) the relative
  change from one year to the next thus is
  fundamental to our loose notion of a tradeoff.
• Therefore calculating the change in defense
  spending from yeart-1 to yeart requires
  subtracting Equation 5 from Equation 4
• 
  (6)

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Deriving the Model cont.

• Rearranging terms we get
• 
  (7)

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Deriving the Model cont.

• In order to obtain the proportional (or
  percentage) change in defense spending, both
  sides are divided by defense spending at timet-1
• The step of multiplying both sides by 100 to
  convert proportions to percentages has been
  omitted for simplicity.
• 
  (8)

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Deriving the Model cont.

• Note that because of the axiomatic structure of
  the argument thus far, Equation 8 is in fact an
  identity!
• Equation (8) is true, based on some simple and
  non-controversial assumption.
• And on the face of it, Equation 8 does not equal
  Equation 1 the classic model

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Deriving the Model cont.

• Verification of the identity can be found by
  making it a regression equation (Equation 9)
• It is instructive to compare the classic model
  with the identity

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You Cant Get There from Here

• Further Equation 9 confirms that the classic
  model of Equation 1 is misspecified.
• The right hand sides of both equations do not
  match, yet they are comprised of nearly the same
  components.
• If you start with Equations 2 and 3 then, it
  would seem that, you can't get there Equation
  1 from here."

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Reconciling the models

• How do we reconcile the appeal of the classic
  model with the identity?
• Borrowing from classic algebraic techniques, let
  us see if we can find algebraic resolution to the
  problem.
• Hypothesis that B1, B2, and B3 equal the
  following.
• (10)
• (11)
• (12)

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• Substituting in the hypothetical quantities into
  the classic model, along with the other category,
  we get
• Canceling terms lets us convert the classic model
  other spending into the identity.

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What this means

• The coefficients of the classic model are in fact
  not fixed coefficients to be estimated but rather
  the variable ratios
• Tradeoffs are not statistically significant
  parameters, but rather the straightforward ratio
  of the two budget sectors in question.
• Thus our classic model has been a long fruitless
  search for a significant constant, when in fact
  the coefficient is by its very nature guaranteed
  to be a fluctuating ratio

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The tradeoff ratio

• As a result, we need only look at these ratios to
  ascertain if tradeoffs exist.
• Tradeoffs may be
• Stochastic (random)
• Systematic
• Fixed
• Exhibit temporal regularity - ARMA
• Exhibit drift
• Secular trends
• Only stochastic behavior means no tradeoff (or
  random trades)

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See Tables in Paper

• The ARIMA models test whether tradeoffs are
  stochastic, systematic or secular trends.
• As expected almost everything is systematic
• When we look at the deficit, this is less the case