Readings Available through Online University Libraries

  • Robert Hall, “Intertemporal Substitution in Consumption,” JPE, April 1988, 96(2), 339-357.

  • Hansen, L.P., with K.J. Singleton, “Stochastic Consumption, Risk Aversion, and the Temporal Behavior of Asset Returns,” Journal of Political Economy, (April 1983), 91(2): 249-265.

  • Gollier, C., and Kimball, M., 2018. ”Toward a Systematic Approach to the Economic Effects of Uncertainty: Characterizing Utility Functions,” Journal of Risk and Insurance, 85(2) (May), 397-430.

  • Gollier, C., and Kimball, M., 2018. “New Methods in the Classical Economics of Uncertainty: Comparing Risks,” Geneva Risk and Insurance Review, 43(1), 5-23.

  • Kimball, M., 2014. “The Effect of Uncertainty on Optimal Control Models in the Neighborhood of

    a Steady State,” Geneva Risk and Insurance Review 39 (March 2014), 2-39.

  • Kimball, M. and Weil, P., 2009: “Precautionary Saving and Consumption Smoothing across Time

    and Possibilities,” Journal of Money, Credit and Banking, 41 (March-April), pp. 245-284.

  • Elmendorf, E. and Kimball, M., 2000: “Taxation of Labor Income and the Demand for Risky

    Assets,” International Economic Review, 41 (August), 801–832.

  • Barsky, B., Juster, F. T., Kimball, M. and Shapiro, M., 1997: “Preference Parameters and Be-

    havioral Heterogeneity: An Experimental Approach in the Health and Retirement Study,” Quarterly Journal of Economics, (May), 537–579.

  • Carroll, C. and Kimball, M., 1996: “On the Concavity of the Consumption Function,” Economet- rica, 64 (July), 981–992.

  • Kimball, M., 1993: “Standard Risk Aversion,” Econometrica (May), 589–611.

  • Kimball, M., 1990: “Precautionary Saving in the Small and in the Large,” Econometrica (January),

    53–73.

  • Kimball, M., 1989: “The Effect of Demand Uncertainty on a Precommitted Monopoly Price,”

    Economics Letters, 30 (September), 1–5.

  • Kimball, M. and Mankiw, N. G., 1989: “Precautionary Saving and the Timing of Taxes,” Journal

    of Political Economy, 97 (August), 863–879.

Linked Readings

Spring 2021

Risk

Time

  • Take-Home Exam #4 (Due at noon on Wednesday, April 7): (Part A) Apply the Symmetry Theorem to Long and Plosser (1983) “Real Business Cycles” (in the JPE). You do not need to be formal. Just point out what the symmetries are (there is more than one dimension’s worth of symmetries) so I can understand what you are pointing to. (Part B) Use arguments based on Taylor expansions to derive the continuous-time stochastic Bellman equation with one state variable following a diffusion (and the only other component to the state variable vector being time). The point is to see how you can get there through another path than L’Hopital’s rule.

Reading Assignments

Risk: One- and Two-Period Models

  • Kimball, M., 1990: ``Precautionary Saving in the Small and in the

    Large,'' Econometrica (January), 53--73.

  • Kimball, M., 1993: ``Standard Risk Aversion,'' Econometrica

    (May), 589--611.

  • Elmendorf, E. and Kimball, M., 2000: ``Taxation of Labor Income

    and the Demand for Risky Assets,'' International Economic

    Review, 41 (August), 801--832.

  • Kimball, M. and Weil, P., 2009: ``Precautionary Saving and Consumption Smoothing across Time and Possibilities,'' Journal of Money, Credit and Banking, 41 (March-April), pp. 245-284

  • Kimball, M., 1989: ``The Effect of Demand Uncertainty on a

    Precommitted Monopoly Price,'' Economics Letters, {\bf 30}

    (September), 1--5.

  • Gollier, C., and Kimball, M., 2018.  ``New Methods in the Classical Economics of Uncertainty: Comparing Risks," Geneva Risk and Insurance Review, 43(1), 5-23.

  • Gollier, C., and Kimball, M., 2018.  "Toward a Systematic Approach to the Economic Effects of Uncertainty:  Characterizing Utility Functions," Journal of Risk and Insurance, 85(2) (May), 397-430.

Time: Multiperiod Models

  • Kimball, M., 1988: ``Farmers' Cooperatives as Behavior Towards

    Risk,'' American Economic Review, 78 (March), 224--232.

  • Kimball, M. and Mankiw, N. G., 1989: ``Precautionary Saving and

    the Timing of Taxes,'' Journal of Political Economy, 97

    (August), 863--879.

  • Carroll, C. and Kimball, M., 1996: ``On the Concavity of the

    Consumption Function,'' Econometrica, 64 (July), 981--992.

  • Kimball, M., 1990: “Precautionary Saving and the Marginal Propensity to Consume.” Get it at this link.

  • Joe Lupton’s dissertation using capitalization of the habit burden

  • Laurie Pounder’s “Life-Cycle Consumption Examined”: Part 1 of applying the Merton model (with its scale symmetry), plus the capitalization symmetry to Health and Retirement Study data.

  • Laurie Pounder’s “High and Low Savers? Circumstances, Patience and Cognition”: Part 2 of applying the Merton model (with its scale symmetry), plus the capitalization symmetry to Health and Retirement Study data—this time as a benchmark from which reality departs.

  • On Perturbation Methods: Kimball, M., “The Effect of Uncertainty on Optimal Control Models in the Neighbourhood of a Steady State,” Geneva Risk and Insurance Review 2014 Mar;39(1):2-39. (Link to ungated PubMed version.)

Resources

Things I Should Have Said about Rederiving the Classic Arrow-Pratt Theory

  1. Around w, I should have written that greater central risk aversion around w implies greater diffidence around w, and greater diffidence around w implies greater local Arrow-Pratt risk aversion at w. If true for all w, one can close the loop, since then (but not if only for one value of w) greater Arrow-Pratt risk aversion implies greater central risk aversion around all w. 
  2. The integral to get the implication that greater central risk aversion implies greater diffidence is very closely related to the picture I drew.
  3. According to Polya’s principle in “How to Solve It” of building up one’s human capital by solving easier problems before banging one’s head too long against harder problems without such preparation, it would be a great idea to literally solve the differential equation (that is the counterpart with an = sign) before trying to “integrate” the differential inequality by rewriting terms as the derivative of the integral of something and doing monotonic transformations. 
  4. An easy way to get the implication that m>0 in the derivation of the condition for central risk aversion would be to define central risk aversion with two inequalities: Ms. 2 wants less than or equal to 1 unit of the risky asset if Ms 1 wants less than or equal to 1 unit. Nevertheless, the math problem of what happens if m is negative in the case we did is of some interest. 
  5.  The mathematical reference for this class is R. Tyrrell Rockafellar’s wonderful book Convex Analysis.  I strongly recommend it to you (and put the Amazon link in the last sentence). Tyrrell gives this statement of the separating hyperplane theorem on p. 97:

Theorem 11.3. Let C_1 and C_2 be non-empty convex sets in R^n. In order that there exists a hyperplane separating C_1 and C_2 properly [that is, without C_1 and C_2 both being contained in the hyperplane], it is necessary and sufficient that [the relative interior of] C_1 and [the relative interior of] C_2 have no point in common.

The key clarification is in the concept of “relative interior.” Here is what Tyrrell says about relative interiors in p. 44:

In the case of convex sets, the concept of interior can be absorbed into a more convenient concept of relative interior. This concept is motivated by the fact that a line segment or triangle embedded in R^3 does have a natural interior of sorts which is not truly an interior in the sense of the whole metric space R^3. The relative interior of a convex set C in R^n, which we denote by ri C, is defined as the interior which results when C is regarded as a subset of its affine hull aff C. 

The concept of “affine hull” is probably somewhat more familiar, but here is what Tyrrell says about that on page 6:

Corrollary 1.4.1. Every affine subset of R^n is an intersection of a finite collection of hyperplanes. …

Obviously, the intersection of an arbitrary collection of affine sets is again affine. Therefore, given any S [that is a subset of] R^n there exists a unique smallest affine set containing S (namely the intersection of the collection of affine sets M such that M [is a superset of] S). This set is called the affine hull of S and is denoted aff S. It can be proved, as an exercise, that aff S consists of all the vectors [that can be formed by arbitrary linear combination of elements of S with weights that can each individually be any real number, but collectively must sum to 1].