Of the various reactions to our model, the one that has been most gratifying is its apparent influence on the modeling strategies of other researchers. Arrau (1990), Hamann (1992), Arrau and Schmidt-Hebbel (1993), Raffelhuschen (1989, 1993), Huang, He, Selo Imrohoroglu, and Thomas Sargent (1997), Altig and Carlstrom (1996), Heckman, Lochner, and Taber (1997, 1998), Hirte and Weber (1998), Schneider (1997), Fougere and Merette (1998,1999), Merette (1998), Lau (1999), Knudsen, Pedersen, Petersen, Stephensen, and Trier (1999), Bohringer, Pahlke, and Rutherford (1999), Malvar (1998), and Schmidt-Hebbel (1999) are examples in this regard. Equally gratifying, the model is starting to get attention in Washington. The Congressional Budget Office is now using the model to study both tax reform and privatizing social security and Joint Committee on Taxation of the U.S. Congress has included the model’s results in its recent analysis of the economic gains from tax reform (see the Joint Committee on Taxation 1997).

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## Monthly Archives: July 2014

Although Alan and I have never formally described our methods of double checking the code, after each modification of the model we subject it to a set of tests to make sure there are no misspecifications (bugs). One of these tests is checking that national saving is precisely zero in the long-run if there is neither population nor productivity growth. Another is to check that the economy sits in its initial steady state when one a) runs a transition, but b) specifies no policy change.

A third test is to check that each agent exactly exhausts her budget constraint at the end of her life and never violates her non negativity constraint with respect to labor supply. More info A fourth is to check that the government is satisfying its intertemporal budget constraint. And a fifth test is to confirm that alternative ways of running the exact same fiscal policy, such as taxing consumption via a retail sales tax or via a proportional income tax with 100 percent expensing, produce precisely the same economic results. Many of these checks are redundant; i.e., if any agent was off her budget constraint or if the government was off its budget constraint, the economy’s steady-state saving rate would not be zero when zero rates of population and productivity growth are assumed.

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Now if the economy is in a steady state initially, one can use steady-state values for evaluating such derivatives because the initial (pre-policy-change) position of the economy at any point in time is the steady state position. But what if the economy is moving along a transition path? Then the derivatives of economic variables at any particular point in time must be evaluated using the values of the economy’s initial (pre-policy-change) variables at that point in time. But how does one know these values unless one actually computes the economy’s dynamic equilibrium?

In general then, one can not use the calculus to study the impact of policy changes on the economy through time unless one computes the initial (pre-policy-change) transition path. But if one can compute the initial transition path (the transition path under the initial policy), one can also compute the new transition path (the transition path under the new policy) and compare them. So the calculus is really of no use. Furthermore, restricting oneself to evaluating derivatives for economies that are initially in a steady state is only valid for steady states that can be computed independent of the transition path.

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So I hooked up with Kent Smetters and Jan Walliser, who were both at the Congressional Budget Office, to add intragenerational heterogeneity to the model. We decided to follow very closely Fullerton and Rogers’ innovative approach of specifying 12 different human capital ability groups within each cohort. Kent and Jan did the yeoman’s job of reprogramming the A-К Model, after which we started writing papers on social security reform (Kotlikoff, Smetters, and Walliser 1997, 1998a, 1998b, and 1998c). During this period, I was also talking with Da i Altig who, together with Chuck Carlstrom, had done simulation work on a model that featured non differentiable budget constraints where the non differentiabilty arose from the discrete brackets of the federal income tax. I suggested that David team up with Alan, me, Kent, and Jan to work on a simulation study of U.S. tax reform that included non differentiable budget constraints as well as intragenerational heterogeneity. This collaboration resulted in Altig, et. al. (1997).

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The first version of the A-К Model had exogenous labor supply and proportional taxes. In the period right after the conference we teamed up with Jon Skinner to add variable labor supply, endogenous retirement, progressive taxes, and a lump-sum redistribution authority that could help us distinguish efficiency gains from intergenerational redistribution. This collaboration resulted in Auerbach, Kotlikoff, and Skinner (1983). In the midi 980s, Alan and I added investment incentives and quadratic costs of adjusting the capital stock. As a result, we had a model that we could use to see how intergenerational redistributions could be achieved via policy-induced asset market revaluations and how the stock market’s value would adjust in response to policy changes. We also added a social security system and, in a simplified version of the model, demographics, including the presence of children whose consumption entered in their parents’ utility functions when they were children. All of these features were included in our book Dynamic Fiscal Policy that we published in 1987 with Cambridge University Press.

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After contemplating for a couple of days the embarrassment of showing up at the conference with no paper, it suddenly struck us that this same procedure used to solve for steady states might work in solving for the economy’s exact transition path. In the case of the solving for the transition path one would guess the time-path of the amount of capital relative to labor demanded by firms, use this path to calculate a time-path of factor payments, and then use this time-path of factor payments to determine a time-path of the supply of capital relative to labor. If one found a time-path of demands of capital relative to labor that equaled the time-path of the supply of these factors, one would have calculated a dynamic equilibrium.

At this point, we had two questions left to worry about: How should we handle the fact that our economy had no terminal period? And, would our procedure of solving for the transition path converge? To deal with the terminal period issue, we decided to assume that the economy reached a steady state at a date that was sufficiently far off in the future that the economy would, indeed, have plenty of time to reach that steady state. Thus, in forming our initial guess of the time-path of the demand for capital relative to labor and in updating this guess, we assumed that the value of this ratio was constant from year 150 onward; i.e., we guessed the same value of this ratio for years after 150 as for year 150.

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Knowing that the fiscal policies matter a lot in the long run raised the ante in studying the transition, particularly the duration of the transition. If the long-run took forever to reach, then knowing the economy’s ultimate position wasn’t particularly useful. On the other hand, if the transition to the economy’s final destination was very quick, then steady-state analysis would suffice. Either way one would need to compute transition paths.

Summers (1981) and Seidman (1983), following the lead of Miller and Upton (1974), took a stab at this by computing transition paths based on the assumption of myopic expectations, specifically the assumption that agents assume that current factor prices will prevail at all future dates. This approach seems appealing on first thought, but not on second or third thought. First, one has to ask why agents would consider simply current, as opposed to past, factor prices in thinking about future factor prices. Second, if one permits agents to think about past factor prices, how many past prices should one let agents consider?

Third, what should one assume about the way agents weigh current and past factor prices in forming expectations about future factor prices? Fourth, should one value agent’s well being based on the actual time-path of factor prices that prevails or the one that agents mistakenly assume will prevail? And fifth, how do agents consider fiscal actions taken today, such as a tax cut, that necessitate future fiscal actions, like a spending cut, to satisfy the government’s intertemporal budget constraint? Ignoring general equilibrium feedback effects on factor prices is one thing. But assuming that agents think the government can borrow indefinitely to pay its bills is something else again.

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Mathematically, a three-period life-cycle model gives rise to a third- or higher order non linear difference for which there are, in general, no known analytical solutions. The problem becomes even more complicated in dealing with 55 generations. In the A-К Model agents consider factor prices and, thus, capital-labor ratios, over their entire lifetimes. Hence, the youngest agent at any point in time is considering, among other things, the factor prices and capital-labor ratio that will prevail 55 years in the future.

But this agent knows that the capital-labor ratio 55 years in the future will be determined, in part, by the labor supply of the youngest agent in the economy in that year. This youngest agent 55 years hence will, in turn, be considering factor prices and, thus, capital-labor ratios, over the following 55 years. In sum, the economic decisions of the youngest agent alive this year depend on 110 capital-labor ratio; i.e., the A-К Model entails, roughly speaking, a 110th order non linear difference equation for the economy’s key state variable — it’s ratio of capital to labor.

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The revolutions underway in macroeconomics and public finance were concomitant with the revolution in the access of academic economists to high speed computers. Although PCS did not yet exist, computer programs could be punched onto computer cards and run on university mainframes. John Shoven and John Whalley were perhaps the first public finance economists to demonstrate the potential power of this new technology to study economies in general equilibrium. They showed how Harberger’s model of the corporate income tax could be expanded to include multiple industries, each facing its own effective rate of corporate income taxation, and solved, using Scarfs algorithm, on the computer.

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The Rational Expectations Revolution made the entire profession think more about dynamics, particularly about the dynamics of neoclassical (micro-based) models. The foundation for considering models of economic change over time had, of course, been laid in previous decades by Domar, Harrod, Koopmans, Samuelson, Solow, Diamond, Phelps, Stiglitz, Cass, Shell, Sidrausky, Tobin, Uzawa and numerous other growth theorists. So most of the theoretical machinery was well in place by the time Diamond, Feldstein, Stiglitz, Sheshinski and other public finance economists started v l dressing the issue of the dynamic impacts of various fiscal policies.