2. Spending Tradeoffs slide 1 A Hitchhiker ’ s Guide to Guns vs Butter A multimedia presentation on specification error that will sail “like bricks don’t”

3. Spending Tradeoffs slide 2 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.

4. Spending Tradeoffs slide 3 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 sector ’ s share of the budget increases, it would seem to come at some other sector ’ s share (as measured in percentage terms.)

5. Spending Tradeoffs slide 4 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

6. Spending Tradeoffs slide 5 The confirmation of tradeoffs In the classic model represented by Equation (1) the existence of tradeoffs is confirmed by a significant negative coefficient for B 2 Researchers have attempted to ‘ repair ’ this model by examining different spending categories and adding other factors to control for specification error.

7. Spending Tradeoffs slide 6 The Record of the Classic Model It simply doesnt pan out in real life… 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.

8. Spending Tradeoffs slide 7 The Puzzle Why should what seems so intuitively obvious be unsupported by the literature?

9. Spending Tradeoffs slide 8 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)

10. Spending Tradeoffs slide 9 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

11. Spending Tradeoffs slide 10 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?

12. Spending Tradeoffs slide 11 Deriving the Model We shall seek to derive Eq.1 from some simple axiomatic propositions. Therefore two consecutive budgets in year t and year t ‑ 1 are defined as (2) (3)

13. Spending Tradeoffs slide 12 Deriving the Model – cont. Rearranging terms, defense spending is then defined as a function of total spending minus the other categories. (4) (5)

14. Spending Tradeoffs slide 13 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 year t ‑ 1 to year t requires subtracting Equation 5 from Equation 4: (6)

15. Spending Tradeoffs slide 14 Deriving the Model – cont. Rearranging terms we get: (7)

16. Spending Tradeoffs slide 15 Deriving the Model – cont. In order to obtain the proportional (or percentage) change in defense spending, both sides are divided by defense spending at time t-1 The step of multiplying both sides by 100 to convert proportions to percentages has been omitted for simplicity. (8)

17. Spending Tradeoffs slide 16 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

18. Spending Tradeoffs slide 17 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

19. Spending Tradeoffs slide 18 Tradeoff Identity Model ModelConstant B 0 Total Spending B 1 Health B 2 Other B 3 Adj. r 2 Durbin- Watson Tradeoff Identity (Eq. 9) 0.01.0 1.00NA (a)(a)(NA) Other Sectors Omitted -1.133.805-9.146-.671.71 (-.35)(8.95)(-3.07) Classic Tradeoff Model Classic Model (Equation 1) -2.5301.518-.067-.721.48 (-.84)(9.29)(-.48) Other Sectors Included -1.3811.384-.094-.535.811.67 (1.51)(10.19)(-.84)(-4.49)

20. Spending Tradeoffs slide 19 You Can ’ t 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."

21. Spending Tradeoffs slide 20 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 B 1, B 2, and B 3 equal the following. (10) (11) (12)

22. Spending Tradeoffs slide 21 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.

23. Spending Tradeoffs slide 22 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

24. Spending Tradeoffs slide 23 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)

25. Spending Tradeoffs slide 24 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

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