A Hitchhiker ’ s Guide to Guns vs Butter

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

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.

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.)

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

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 B2 • Researchers have attempted to ‘repair’ this model by examining different spending categories and adding other factors to control for specification error.

6. The Record of the Classic Model • It simply doesntpan 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.

7. The Puzzle • Why should what seems so intuitively obvious be unsupported by the literature?

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)

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

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?

11. 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)

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

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 yeart‑1 to yeart requires subtracting Equation 5 from Equation 4: • (6)

14. Deriving the Model – cont. • Rearranging terms we get: • (7)

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 timet-1 • The step of multiplying both sides by 100 to convert proportions to percentages has been omitted for simplicity. • (8)

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

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. 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."

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 B1, B2, and B3 equal the following. • (10) • (11) • (12)

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.

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

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)

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