Showing posts with label Equilibrium Seeking. Show all posts
Showing posts with label Equilibrium Seeking. Show all posts

Friday, October 17, 2008

Becker: The Economic Approach to Human Behavior

Becker, G., 1976. The Economic Approach to Human Behavior, University of Chicago Press.

Ch. 1: The Economic Approach to Human Behavior

“The following essays use an ‘economic’ approach in seeking to understand human behavior in a variety of contexts and situations. Although few persons would dispute the distinctiveness of an economic approach, it is not easy to states exactly what distinguished the economic approach from the sociological, psychological, anthropological, political or even genetical approaches” (3).

“Economics is said to be the study of (1) the allocation of material goods to satisfy material wants, (2) the market sector, and (3) the allocation of scarce means to satisfy competing ends” (3).

The first definition, according to Becker, is wrong because the logic of economics can be applied much more broadly than simply material goods. The third definition is the most broad, and does more to identify the nature of a problem to be solved and little to identify what it is that economists do. “All of these definitions of economics simply define the scope, and none tells us one iota about what the ‘economic’ approach is” (4). Becker argues that the economic approach, or method, is what makes this study unique, and not the subject-matter in question.

“Everyone recognizes that the economic approach assumes maximizing behavior more explicitly and extensively than other approaches…Moreover, the economic approach assumes the existence of markets that with varying degrees of efficiency coordinate the actions of different participants…Prices and other market instruments allocate the scarce resources within a society and thereby constrain the desires of participants and coordinate their actions. In the economic approach, these market instruments perform most, if not all, of the functions assigned to ‘structure’ in sociological theories…The preferences that are assumed to be stable do not refer to market goods and services, but to underlying objects of choice that are produced by each household using market goods and services…The combined assumptions of maximizing behavior, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as I see it” (5).

He then goes on to explain why these core assumptions of the economic approach are appropriate. Becker also explains how the economic approach can be applied to really any problem facing the social sciences. That being said, however, he ends this chapter by claiming that the economic approach provides a certain kind of knowledge about the world and that other approaches are quite useful in explaining different kinds of human behavior. In the end, there is a role for approaches that theorize actors to be rational maximizers with stable preferences operating in equilibrium seeking markets.

Thursday, September 25, 2008

Deutsch and Singer: Multiple Power Systems and International Stability

Deutsch, K. & Singer, J., 1964. Multiple Power Systems and International Stability. World Politics, 16(3), 390-406.

“In the classical literature of diplomatic history, the balance-of-power concept occupies a central position.” (390) This article explores the IV of the number of independent actors in a system against the DV of system stability.

“Stability may, of course, be considered from the vantage point of both the total system and the individual states comprising it. From the broader, or systemic, point of view, we shall define stability as the probability that the system retains all of its essential characteristics; that no single nation becomes dominant; that most of its members continue to survive; and that large-scale war does not occur. And from the more limited perspective of the individual nations, stability would refer to the probability of their continued political independence and territorial integrity without any significant probability of becoming engaged in a ‘war for survival.” (390-1)

There is a comparison between probabilistic concepts of stability and classical notions of stability, specifically that of Richardson. “Richardson’s stability referred simply to any set of conditions under which the system would return to its equilibrium state” (391). Kaplan’s definition of equilibrium is slightly different. In Richardson’s formulation, systems can be stable even if there is transition, like, for example, the increase of armament spending as a percentage of GDP as long as it’s consistent across countries. Kaplan is interested in being consistent with the variable that is the focus of the study.

The authors explore the amount of interactions that can possibly take place between different countries as the amount of poles increase in the international system. This obviously takes the form of an exponential growth curve.

Next, they explore the “Share of Attention” that can be offered by countries that is, “available for conflict” (396).

“Thus, if some minimum percentage of a nation’s external attention is required for that nation to engage in behavior tending toward armed conflict, and the increase in number of independent t actors diminishes that share that any nation can allocate to any other single actor, such an increase is likely to have a stabilizing effect upon the system” (400).

“In the long run, according to this model, even multi-polar systems operating under the rules of balance-of-power policies are shown to be self-destroying, but both in the short and the long run the instability of tight bipolar systems appears to be substantially greater. It seems plausible that, if the spread of nuclear weapons could be slowed down or controlled, a transition from the bipolar international system of the early 1950’s to an increasingly multipolar system in the 1960’s might by mankind some valuable time to seek some more dependable bases for world order” (406).

Monday, August 4, 2008

Gibson and Seventer: A Tale of Two Models

Gibson, B. & Van Seventer, D., 2000. A Tale of Two Models: comparing structuralist and neoclassical computable general equilibrium models for South Africa. International Review of Applied Economics, 14(2), 149-171.

“This paper compares two working models of the South African economy, an orthodox, neoclassical computable general equilibrium model in which savings drive investment, and a more structuralist, eclectic, model for which there is an independent investment function” (149).

“It is seen that the neoclassical model fully supports the principles of the `Washington Consensus’ while the structuralist model requires a far more heterodox set of policies to avoid slow growth or high inflation” (149).

They calibrate both models to the same SAM. The regional focus is South Africa.

They make a distinction between structuralist and neoclassical models. In neoclassical, or orthodox models, government spending is always a problem at the macro level: there is a clear inverse relationship between government spending and economic growth. Government spending can lead to, “…current account deficits, real exchange rate appreciation and an accelerated decline in export performance” (150).

Structuralist models make different assumptions, and do not rely solely on state-based explanations. “It is not typically assumed that resources are fully utilized in structuralist models, thereby opening a range of demand-side, employment generating policy options, options that have little relevance in the orthodox setting. “What makes a structuralist model structuralist is the specific and path-dependent character of the economy under study” (150).

Orthodox modeling conceptions are derived from Dvarajan and Lewis (1990): “There are two sectors, traded and non-traded and three goods, counting imports. The exportable is not consumed at home and the home good is not exported” (151). “A second important assumption is that there is only one race and one class of consumers in the prototype version, even though there are 13 occupational categories, six income classes and four races in the base SAM” (151). “From the orthodox perspective, this model has many desirable properties.

The structuralist model takes time into account. In this way, it is dynamic and more useful than the static neoclassical model.

The authors find that the neoclassical model fits nicely with “Washington Consensus” conceptions of trade openness and taxation. The structuralist model is much more vague in its conclusions.

Devarajan et al.: Policy Lessons from Trade-Focused, Two-Sector Models

Devarajan, S., Lewis, J. & Robinson, S., 1990. Policy Lessons from Trade-Focused, Two-Sector Models. Journal of Policy Modeling, 12(4), 625-657.

These authors create a one country, two-sector, three good CGE trade model that is designed to be simple, or, in their words, minimalist. The benefits to this are clear: the CGE becomes much less of a black box. They call it the 1-2-3 model.

“The model has three actors: a producer, a household, and the rest of the world” (627).

“The 1-2-3 model is different from the standard neoclassical trade model with all goods tradable and all tradables perfect substitutes with domestic goods. The standard model, long a staple of trade theory, yields wildly implausible results in empirical applications” (630). One way to work around this is building on the word of Salter (1959) and Swan (1960) that separates tradables from non-tradables.

They claim that their 1-2-3 model is Walrasian, even though there are macro-level closures. “The additions of government, savings-investment, and the balance of trade are done in ways that retain the notion of flow equilibrium and do not strain the Walrasian paradigm” (642). They also highlight two different approaches on “macro closures”: in the first approach, macro-level factors are exogenous. “In the second approach, the CGE model is extended to include variables typically found in macro models…and to expand the notion of equilibrium to incorporate asset markets and expectations. The intent is to build CGE models that move beyond the Walrasian paradigm and directly incorporate macro phenomena” (642).

The started with the 1-2-3 model, then added macro-level factors like tariffs, subsidies, taxes, savings and investment. The addition of savings and investment brought up the need to discuss closure rules. Thus, a minimalist CGE model is built upon to make it more realistic.

Thursday, July 10, 2008

Hertel, et. al.: Distributional Effects of WTO Agricultural Reforms in Righ and Poor Countries

Hertel, Thomas W., Roman Keeney, Maros Ivanic, and L. Alan Winters. 2007. “Distributional effects of WTO agricultural reforms in rich and poor countries..” Economic Policy 22:289-336.

CGE contextualized, defined:
“General equilibrium, which dates back to Leon Walras (1834–1910), is one of
the crowning intellectual achievements of economics. It recognizes that there
are many markets and that they interact in complex ways so that, loosely
speaking, everything depends on everything else. Demand for any one good
depends on the prices of all other goods and on income. Income, in turn, depends
on wages, profits and rents, which depend on technology, factor supplies and
production, the last of which, in its turn, depends on sales (i.e., demand). Prices
depend on wages and profits and vice versa” (294).

CGE limitations:
“The models have their limitations, however. First, CGE simulations
are not unconditional predictions but rather ‘thought experiments’ about what
the world would be like if the policy change had been operative in the assumed
circumstances and year. The real world will doubtless have changed by the
time we get there. Second, while CGE models are quantitative, they are not
empirical in the sense of econometric modelling: they are basically theoretical,
with limited possibilities for rigorous testing against experience. Third, conclusions
about trade policy are very sensitive to the levels assumed for trade restrictions
in the base data. One can readily do sensitivity analysis on the parameter
values assumed for economic behaviour (as we have done in this paper), but
less so on the data because altering one element of the base data requires
compensating changes elsewhere in order to keep the national accounts and
social accounting matrix in balance. Of course, many of these criticisms apply
to other types of economic modelling and, therefore, while imperfect, CGE
models remain the preferred tool for analysis of global trade policy issues” (295)

Arrow and Debreu: Existence of an Equilibrium for a Competitive Economy

Arrow, KJ, and G Debreu. 1954. “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22:265-290.

Stemming from Walras: “It was assumed that each consumer acts so as to maximize his utility, each producer acts so as to maximize his profit, and perfect competition prevails, in the sense that each producer and consumer regards the prices paid and received as in- dependent of his own choices” (265).

On the need for these types of models: “Descriptively, the view that the competitive model is a reasonably accurate description of reality, at least for certain purposes” (265).

Results of this paper: “The main results of this paper are two theorems stating very general conditions under which a competitive equilibrium will exist” (266).

UPDATE:

"Walras did not, however, give any conclusive
arguments to show that the equations, as given, have a solution" (265)

Conrad: Computable General Equilibrium Models for Environmental Econnomics and Policy Analysis

Conrad, Klaus. 1999. “Computable General Equilibrium Models for Environmental Economics and Policy Analysis.” Pp. 1060-1088 in Handbook of environmental and resource economics.


“A CGE model is a system of linear and non-linear equations that is solved to simulate market equilibrium. It includes equations describing consumer and producer supply an demand behavior that are derived explicitly from conditions for profit or utility maximization, and market-clearing conditions in product and input markets. Unlike inter-industry input-output models and other earlier economy-wide planning models, household factor income and expenditures are linked in a theoretically appropriate manner” (1062).

Shoven and Whalley: Applying General Equilibrium

Shoven, John B, and John Whalley. 1992. Applying General Equilibrium. Cambridge University Press.

“A general equilibrium model of an economy can be best understood as one in which there are markets for each of N commodities, and consistent optimization occurs as part of equilibrium. Consumers maximize utility subject to their budget constraint, leading to demand-side specification of the model. Producers maximize profits, leading to the production-side specification. In equilibrium, market prices are such that the required equilibrium conditions hold. Demand equals supply for all commodities, and in the constant-returns-to-scale case zero-profit conditions are satisfied for each industry” (9).

“The applied general equilibrium models in operation today differ substantially from one another. Some are large-scale multipurpose models; others, small-scale issue-specific models. They vary in their country of application, use of functional forms, and treatment of such issues as time, foreign trade, and the government sector. Their use of data and parameter values also varies” (71).

“Although the general equilibrium model appropriate for any particular application depends largely on the policy issues being addressed, most applied models currently in use have a similar form. They are typically variants of static, two-factor models that have long been employed in public finance and international trade…Most models involve more than two goods, while aggregating the factors of production into two broad types—capital and labor” (92).

“Choice of the level of aggregation for an applied model is one of the more difficult design issues that any prospective modeler must confront. ON the one hand, there is the natural desire to make the model as detailed as possible in the belief that this will increase its realism. On the other hand, more detail is not always beneficial; much of it may prove superfluous to the issues at hand: (100).

Tuesday, July 8, 2008

Dellink: Modelling the Costs of Environmental Policy

Dellink, Rob B. 2005. Modelling the Costs of Environmental Policy: A Dynamic Applied General Equilibrium Assessment. Edward Elgar Publishing.

Different kinds of economic models:

Partial equilibrium models: “…describe those markets in an economy that are relevant for the analysis at hand” (13).

General equilibrium models: “…are similar to partial equilibrium models, with the main difference that general equilibrium models describe the entire economy” (13). See Ginsburg and Keyzer 1997.

Input-output models: “…can be regarded as simplified general equilibrium models, since they assume that substitution possibilities are absent” (13).

Neo-classical growth models: “…share their micro-economic foundation with general equilibrium models, but look at the development of the economy over time. Dynamic general equilibrium models are effectively neo-classical growth models” (14).

Endogenous growth models: “…emerged from neo-classical growth models, as many authors were dissatisfied with the fact that exogenously –given technological change is the driving force of economic growth in the neo-classical growth models. Therefore, models were developed that describe technological change endogenously” (14).

Neo-Keynesian models: “…are not based entirely on micro-economic theory, but rather on extrapolation of historic trends” (14).

There are three conditions that must be met for AGE models: zero profit, household income condition (that expenses can never be above income) and the market clearing condition.

UPDATE:

Different specifications of models:

Theoretical v. applied
Static v. dynamic
For dynamic: myopic for forward looking
Determistic v. stochastic
Calibrated v. estimated
Geographical scale
How integrated within sub-models
Tech progress: endogenous or exogenous (15-6)

Three basic conditions for AGEs:

Zero profit condition: “…under constant returns to scale the value of output has to equal the value of all inputs…firms that have a constant returns to scale production function and that operate under full competition will never be able to reap any excess profits. Note that this does not imply that there is no return to capital: capital is one of the inputs to production and receives a payment like all other inputs” (17).

Income condition: “Households cannot increase their expenditures above their income…Total income may stem from payments for the supply of labour and capital to the firms and from tax revenues” (17).

Market clearing condition: “For each good, the market clearing conditionhas to be satisfied, that is, total demand equals total supply. For the primary production factors, labour and capital, this means that total demand for these goods must be equal to the total amount available” (17).

“Applied general equilibrium models are generalized input-output models, where substitution is allowed and prices are determined within the model. They can be seen as a system of non-linear equations, which can be solved simultaneously. The essence of AGEs is that prices of all goods are determined within the model such that all the conditions stated above are satisfied simultaneously. The economy can be described in the AGE model as a set of balances: for every demand there is a supply” (18).

Monday, May 12, 2008

Adelman and Robinson: Income Distribution Policy in Developing Countries

Adelman, Irma, Sherman Robinson and World Bank. (1978). Income distribution policy in developing countries : a case study of Korea. Stanford, Calif.: Published for the World Bank [by] Stanford University Press.

This work begins by explicitly wanting to move the development debate away from a trickle-down economic approach to an approach that focuses more heavily on distribution.

“The model has five essential distinguishing features. It solves for prices endogenously in both factor and product markets. Its solution is based on achieving a measure of consistency among the results of individual optimizing behavior by a large number of actors…It incorporates income distribution, monetary phenomena, inflation, and foreign trade. It is dynamic, with imperfect intertemporal consistency. And, finally, it allows for varying principles of market clearing and institutional behavior” (3).

“The model operates by simulating the operation of factor and product markets with profit-maximizing firms and utility-maximizing households. It can thus be characterized as a computable general-equilibrium (CGE) model and is broadly in the neoclassical tradition, though it has a number of disequilibrium, non-neoclassical features. The overall model consists of a static, within-period adjustment model linked to a dynamic, intertemporal-adjustment model” (3).

“Basically, what differentiates our model from other multisectoral models is that it solves endogenously for wages and prices in a multifactor, multiconsumer, multiproduct world in which firm and consumer behavior is based on the optimization of separate objective functions. These features are emphasized in the simple CGE model” (19).

“The discussion of the model is organized around the activities of firms as buyers of factors and sellers of output and the activities of consumers as suppliers of factors and buyers of output. The circular flow identities which require that no income and no outputs be unaccounted for, is maintained in the model not only by production adjustments (as in other models), but also by price and factor income modifications. It is this feature that distinguishes CGE models from other economy-wide models” (20).

Friday, May 2, 2008

Cuddington, et. al.: Disequilibrium Macroeconomics in Open Economies

Cuddington, John T., Per-Olov Johansson and Karl-Gustaf Löfgren. (1984). Disequilibrium macroeconomics in open economies. Oxford, England: B. Blackwell.

This work examines fixed-price models, where prices are exogenously imposed on the model.

Backhaus: From Walras to Pareto

Backhaus, Jürgen G. and J. A. Hans Maks. (2006). From Walras to Pareto. New York: Springer. http://www.loc.gov/catdir/toc/fy0704/2006923764.html
http://www.loc.gov/catdir/enhancements/fy0819/2006923764-d.html

Walras was the predecessor to Pareto as the chair of Political Economy at the University of Lausanne.

This is an edited volume that explores both Walras and Pareto, but not together. Actually, it’s quite strange. There is a useful chapter from my perspective that deals with Walras and philosophy of social science issues. In this chapter, the author, Jan van Daal, positions Walras as understanding that his general equilibrium model was an ideal-type model, and that there is a continuum that runs through pure economics, to applied economics to social economics and then through theories of family and government.

UPDATE:

From the van Daal chapter:

Walras separated his thinking on science into Pure and Applied. van Daal presents a 2x2 box with pure and applied on the x axis and nature/person on the y axis (person is then separated into person viz. nature and person viz. person).

He then situates Walras' main texts. Pure Economics occupies the box where Pure science and Nature interact.

Fisher: Disequilibrium Foundations of Equilibrium Economics

Fisher, Franklin M. (1983). Disequilibrium foundations of equilibrium economics. Cambridge [Cambridgeshire] ; New York: Cambridge University Press. http://www.loc.gov/catdir/description/cam022/82025105.html
http://www.loc.gov/catdir/toc/cam026/82025105.html

What does equilibrium mean in an economic setting in any case? Why would the study of equilibrium be of interest? Some people say that the study is uninformative because if the economy is in some way in disequilibrium, then the study of economics is theoretically off the mark. We can say that a market is in equilibrium if we define equilibrium so narrowly that it doesn’t explain much of anything. We can also say that an economy is in equilibrium if we endow agents with quasi-omniscient abilities.

There is much more to this analysis that specifically explores the nature of economic modeling vis-à-vis economic stability, equilibrium and disequilibrium in the first chapter that will not be touched on in this abstract.

From the beginning of chapter 2: “In my view, there have been four major developments in the history of modern stability analysis. These are (1) the realization that the subject was one which had to be studied in a context with a formal dynamic structure; (2) the realization that global, rather than simply local, results could be obtained; (3) the introduction of non-tâtonnement processes; and (4) closely related to this, the insight that attention paid to specifying the disequilibrium processes involved could lead to far more satisfactory results than could be obtained by restricting the excess demand functions” (19).

In chapter 2, Fisher explores the concept of tâtonnement. Stability analysis began with Samulson and Hicks. These, “…observed that the subject could only be rigorously studied in a framework specifying the equations of motion of the system when not in equilibrium”. Hicks suggested that Walras’ theory of tâtonnement be formalized which was realized through, “…a set of price adjustment equations that formed the basis for nearly all later work” (20).

Fisher highlights problems with the basic equilibrium equation (20), and argues that there are flaws. For example, he believes that in reality, it is impossible to translate, for example, excess demand into efficient price changes. He goes on to claims that the auctioneer who adjusts prices according to the prevailing sentiment of the consumers in the room is, “…at best an inconvenient fiction” (21).

There is also embedded in the above equation assumptions about consumers wanting to take action when their demand doesn’t agree with the dictated price, as well as their ability to take action. “…so that, even though the excess demand involved may be for a good dated in the far future, 1990 toothpaste, for example, individuals who will want that good in the far future begin immediately to attempt to acquire it” (22). “I shall refer to this as the ‘Present Action Postulate.’ It is implicit in the entire stability literature, although seldom explicitly stated. Perhaps this is because it need not be faced explicitly as long as we remain in a world in which the adjustment of prices to equilibrium can be safely supposed to take place before the dates on any commodities…come due and all acquisitions must be made before any are needed for consumption or production – the Arrow-Debreu world in which all markets and trades occur at the beginning of time and never again. Elegant as such a model is, however, it is not truly satisfactory when applied to real economies developing over time” (22).

Tâtonnement: The Lyapounov Second Method is explored. It requires a rest point, which is, “…a point at which the process does not move. In the models we shall be considering, rest points are in one-to-one correspondence with points that are in some sense also economic equilibria…” (24). “A rest point is said to be globally stable if the system converges to it from every set of initial conditions. This, of course, is a very strong property. In particular, if there is more than one rest point, then no particular rest point can be globally stable in this sense since if the process begins at some other rest point it will never leave it” (24). The next term introduced is that of an adjustment process: “An adjustment process…is said to be globally stable if, for any set of initial conditions, there is a rest point to which the system converges. The difference, of course, is that it doesn’t have to be the same rest point for all initial conditions” (25). “Finally, it is useful to distinguish this from the definition of the quasi-stability of an adjustment process. For convenience of language, let us suppose that the variables involved are prices only…Starting with any initial condition, consider an infinite sequence of prices. Such a sequence may not have a limit…but it may nevertheless have one or more limit points (roughly, points to smaller and smaller neighborhoods of which the sequence keeps returning). If every limit point of every such sequence is a rest point of the adjustment process, then that process is said to be quasi-stable” (25).

The book moves to a non-tâtonnement trade model: “One such development was the abandonment of the tâtonnement assumption of no trading out of equilibrium which had wound up in a dead end and the introduction of what are rather inelegantly called ‘non-tâtonnement’ processes. Since that is not a very informative name, I shall refer to them as ‘trading processes.’ It is important to remember that, while this stage of development permits trading out of equilibrium, most of the work to be discussed does not permit consumption or production to take place until equilibrium has been reached. One must think of participants as swapping titles to commodity stocks while prices…adjust. Only after the music stops do people go home and enjoy what they have.” (25).

There is an examination of the Edgewood process, which is seen as being inadequate.

The Hahn Process is then explored. “The central assumption of the Hahn Process is as follows. At any one time, after trade has taken place, there may of course be either unsatisfied demand or unsatisfied supply for some commodity, say, apples. However, we suppose that markets are sufficiently well organized that there are not both. In other words, there may be people who wish to sell apples at the current prices and cannot or there may be people who wish to buy apples at the current price and cannot, but there are not, after trade, simultaneously both unsatisfied sellers and unsatisfied buyers” (31).

“Note the different roles played by utilities in the Edegeworth and Hahn Processes. In the Edgeworth Process, the utilities actually achieved by individuals…rise while trading is going on. In the Hahn Process, target utilities—the utilities which they would achieve if they could complete their transactions—fall out of equilibrium. One way of looking at it is to say that in disequilibrium plans are not all compatible and that, in the Hahn Process, the adjustment is such that people have to lower their expectations until equilibrium is reached and everyone can in fact attain the utility he anticipates” (32). One key assumption of the Hahn Process is that no one ever runs out of money.

It continues down the path of micro-economic analysis.

The book concludes that, when producers and consumers take their decisions in a state of market disequilibrium, the model will eventually fall into equilibrium (hence the title). This model avoids some of the crucial misgivings of other models, specifically the tâtonnement model which necessarily needs to make large cuts in demand, which is unrealistic.

I skipped much of the middle of this book, its focus on micro-analysis and the equations.

Wednesday, April 30, 2008

Malinvaud: The Theory of Unemployment Reconsidered

Malinvaud, Edmond. (1985). The theory of unemployment reconsidered (2nd ed.). New York, NY, USA: B. Blackwell.

“Eight years after the first edition of this book, its main message still stands, namely that the microeconomic theory of fixed-price general equilibrium has direct significance for the macroeconomic theory of involuntary unemployment” (vii).

“Before I proceed, I must make it clear why general equilibrium analysis is a proper approach to the study of unemployment. Indeed, most economists nowadays strongly abject to such an idea. The objection comes from a misunderstanding of what general equilibrium analysis really is. Economists have been brought up to think that the very notion of equilibrium implies that, for each commodity, supply must equal demand, which of course cannot be the case for labour if some involuntary unemployment remains. But a general equilibrium is an abstract construct that has no logical obligation to assume equality between supply and demand” (4-5). “The classical development of economic theory and the dominant role played by the Walrasian system explain why many people are not reluctant to accept that the name ‘equilibrium’ could be applied outside of this system. Some of these people, often irritated by the highbrow mathematical theory that was built around the concept of competitive equilibrium, claim that such a concept is hopelessly inadequate to any real problem. Others speak as if the Walrasian equilibrium was not an abstraction but almost a real situation that would prevail if no disturbance occurred.” (5).

The rest of the book attempts to apply this general equilibrium seeking model to the issue of unemployment and policy.

Walras: Elements of Pure Economics

Walras, Léon. (1954). Elements of pure economics. London,: Published by Allen and Unwin.

Walras spends a bit of the first section of his book exploring a definition for political economy, as well as distinguishing between art, science and ethics. “There is a theory of wealth, that is, a theory of exchange and value in exchange, which is a science, and a theory of the production of wealth, that is, a theory of agriculture, industry and trade, which is an art…that political economy may be considered both as an explanation of what is and as a programme of what ought to be. Now, what ought to be, should be considered as such either from the point of view of expediency or material well-being, or from the point of view of equity or justice. What ought to be from the point of view of material well-being is the concern of applied science or art; while what ought to be from the point of view of justice is the concern of moral science or ethics.” (60).

Then goes on to explain what value in exchange is, distinguished between a person an a thing, adds that when a thing has value and is scarce, then it is exchangeable, explains that markets exist for the exchange of these things, that the price of the things being exchanged is similar to gravity in that it is a natural force, explains that, like gravity, we can affect it (decrease/increase supply/demand), then wonders why we would abstractly theorize about the interaction in the market when we can use mathematical language to more efficiently represent it.

“Only useful things limited in quantity can be produced by industry and all things that industry produces are scarce…In fact we may be certain that industry does nothing but produce scarce things and that it endeavors to produce them all” (73).

The book then goes on to methodically lay out the structure of economic interactions between purchasers and sellers. There are assumptions of rationality on the parts of the individuals, either utility or profit. Then, because these assumptions are reached, market clearing behavior takes over. Also, a socially optimum price is reached, a socially optimum level of production and utility are also reached.

*skipped much text

“Let…be the quantities of final products which consumers need to hold as reserves in kind; let…be the quantities of consumers’ goods and services they need to have on hand in the form of cash reserves; and let…be the quantity of new capital goods evaluated in numéraire which consumers require in the form of money savings. Altogether these quantities make up a fund of working or circulating capital for consumption” (377).

“Furthermore, let…be the quantities of newly produced final products, raw materials and new capital goods in stock and on display which producers need to have on reserve in kind’ and let…be the quantities of final products, raw materials, capital goods and productive services which these same producers require in the form of cash reserves. These quantities make up a fund of working or circulation capital for production” (377). “These two revolving funds added together…constitute the economy’s circulating capital…” (377).

“Finally, in order to come still more closely to reality, we must drop the hypothesis of an annual market period and adopt in its place the hypothesis of a continuous market. Thus, we pass from the static to the dynamic state. For this purpose, we shall now suppose that the annual production and consumption, which we had hitherto represented as a constant magnitude for every moment of the year under consideration, change from instant to instant along with the basic data of the problem” (380).

“Every hour, nay, every minute, portions of these different classes of circulating capital are disappearin and reappearing. Personal capital, capital goods proper and money also disappear and reappear, in a similar manner, but much more slowly. Only landed capital escapes this process of renewal. Such is the continuous market, which is perpetually tendin towards equilibrium without ever actually attaining it, because the market has no other way of approaching equilibrium except by groping, and, before the goal is reached, it has to renew its efforts and start over again, all the basic data of the problem, e.g. the initial quantities possessed, the utilities of goods and services, the technical coefficients, the excess of income over consumption, the workin capital requirements, etc., having changed in the meantime. Viewed in this way, the market is like a lake agitated by the wind, where the water is incessantly seeking its level without ever reaching it. But whereas there are days when the surface of a lake is almost smooth, there never is a day when the effective demand for products and services equals their effective supply and when the selling price of products equals the cost of the productive services used in making them” (380).

Friday, April 25, 2008

Ginsburgh & Keyzer: The Structure of AGE Models

Ginsburgh, Victor and Michiel Keyzer. (1997). The structure of applied general equilibrium models. Cambridge Mass.: MIT Press.

“This book describes the structure of general equilibrium models. It is written for the researcher who intends to construct or study applied general equilibrium (AGE models and has a special interest in their theoretical background. Both general equilibrium theory and AGE modeling continue to be active fields of research, but the styles of presentation differ greatly. Whereas the applied model builder often finds the style of theoretical papers inaccessible, the theoretician can hardly recognize the concepts he is used to in the list of equations of applied models. The main purpose of the book is to present the theoretical models in a unified way and to indicate how the main concepts can find their way into applications” (xiii).

The book then goes on to do this in an apparently thorough way.

UPDATE:

"Profit-maximizing behavior has been questioned in two respects: Do producers have access to all the information that they need to optimize? Is profit maximization a rational rule of conduct for the owners of the firm? With respect to the first issue, in reality producers are obviously faced with uncertainty about their external environment...and about their own production set...Therefore, in applications, one maintains profit maximization but accounts for uncertainty by restricting the production set through additional constraints. For example, one excludes highly unreliable techniques or limits the options for substitution" (41-2).

"In the literature, general equilibrium models are presented in very different ways. Some are written in terms of excess demand, as in section 1.3, others in terms of welfare programs, as in section 1.4" (91). "When the structure of the model is changed, say, to introduce international trade, taxes, or external effects, or when some assumptions are relaxed, such as allowing for nonconvexities, one format is usually best suited for proofs of existence of equilibrium; another should possibly be used for analysis of efficiency, and yet others for applied work and for computation. However, it should be stressed that all formats describe the same model and lead to the same equilibrium solutions" (91).

Basic format of CGE: Goods and Factors: economy is separated into goods and factors; Production Sets: every producer supplies a single good, every good requires factors; Endowments: factors are owned by consumers; Utility: consumers have utility that is continuous, strictly quasiconcave and nonsatiated (109-10).

"We will consider that a model is written in CGE format when it is specified as a system of simultaneous equations consisting of commodity balances...for goods and factors, price equations...for goods and budget equations..." (110).

Adelman & Robinson: Macroeconomic Adjustment and Income Distribution

Adelman, Irma and Sherman Robinson. (1988). "Macroeconomic adjustment and income distribution : Alternative models applied to two economies". Journal of Development Economics, 29(1), 23-44. http://www.sciencedirect.com:80/science/article/B6VBV-45NHVST-10/1/8f843dd9b8dd40cd989877c99456f484\par

This paper attempts to rectify a disagreement about the distributional capabilities that resulted from two earlier CGE model deployments.

“In the development literature, CGE models trace their lineage back to the input-output based multisector models widely applied to problems of planning in developing countries in the 1960s. While firmly based on the foundations of Walrasian general equilibrium theory, a CGE model can also be seen as a logical culmination of a trend in the planning model literature to add more and more substitutability and non-linearity to the basic input-output model. A CGE model works by: (1) specifying the various actors in the economy (for example, firms, households, government, and the rest of the world); (2) describing their motivation and behavior (utility maximization for consumers and profit maximization for firms); (3) specifying the institutional structure, including the nature of market interactions (competitive markets for goods and labor); and (4) solving for the equilibrium values of all endogenous variables. The model simulates the working of a market economy and solves for a set of prices…that clears all markets…The model is highly non-linear with neoclassical production expenditure functions, and incorporates a variety of substitution possibilities in production and demand” (25).

These models were initially used to examine how tax structures effected a Walrasian economic system. This base has been built upon by modelers, who have added to it more “structural” features that are not a part of neoclassical economic theory. The paper goes on in much detail to examine CGE models. I stopped here.

Hahn: On Non-Walrasian Equilibria

Hahn, Frank. (1978). "On Non-Walrasian Equilibria". Review of Economic Studies, 45(139), 1. http://search.ebscohost.com/login.aspx?direct=true&db=buh&AN=4624761&site=ehost-live\par

“I shall call an economy non-Walrasian whenever the trading possibilities of agents cannot be described as the set of trades which at given prices make the value of purchases no greater than the value of sales” (1). Non-Walrasian economics is important to understand, mostly because Walrasian economics can’t fully explain current economic systems. Hahn highlights two difficulties when using Walrasian economic analysis: what happens when one wants to highlight and explore an economy that is not in equilibrium and secondly, that the perfect competition postulate is empirically wrong (1).

Robinson: Multisectoral Models

Robinson, Sherman. (1988). "Multisectoral Models". In Hollis Burnley Chenery, T. N. Srinivasan & Jere R. Behrman (Eds.), Handbook of development economics (pp. 3 v. in 4). Amsterdam ; New YorkNew York, N.Y., U.S.A.: North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.

There are three main ways that Robinson identifies that can be used to classify different CGE models. The first is by highlighting the mathematical structure of the model. The second is by what policy is the focus of the model. The third is by the theoretical foundation of the model (886).

The author firstly explains how CGE models grew out of linear modeling work completed before the 1970s. “In the early 1970s, work was started on a new type of non-linear, multisectoral model which sought to simulate the workings of a market economy, solving for both market prices and quantities simultaneously. These computable general equilibrium (CGE) models can be seen as a natural outgrowth of input-output and LP models, adding neoclassical substitutability in production and demand, as well as an explicit system of market prices and a complete specification of the income flows in the economy. The first developing country application was Adelman and Robinson (1978), which started an extensive literature” (888).

Robinson then goes on to identify four important solution techniques that were developed in the late 70s.

“One can classify models along a continuum running from analytic to applied. Analytic models are designed to explore the implications of various sets of theoretical postulates, with as few assumptions as possible about the magnitudes of parameters” (891). “Typically, stylized numerical models are more complex than analytic models, since wider applicability is desired and simplicity is no longer required. Stylized numerical models nonetheless tend to stay close to their underlying analytic models. Since the goal is to explore particular causal mechanisms, simplicity is desirable. Stylized models are still a long way from models which seek to capture in a realistic way the variety of important effects that might impinge on a particular policy problem facing a particular country” (892). “Applied models differ from stylized models in two important ways. First, they broaden further the range of stylized facts that are incorporated. Second, they seek to capture important features of a particular economy or situation. For example, while a styli9zed model can represent a number of similar countries…an applied model would be built for a particular country. By including more institutional detail, applied models are more specific and narrow” (892).

“In general, analytic models do not yield specific policy recommendations” (893).

“While multisector models applied to developing countries are Walrasian and neoclassical in spirit, most modelers quickly abandoned many of the strong assumptions of neoclassical theory when faced with the problem of capturing the stylized facts characterizing these economies. The assumptions of perfect competition, perfectly functioning markets with flexible prices, and free mobility of products and factors are not sustainable in actual economies. Instead, modelers have incorporated a variety of ‘structuralist’ rigidities into their models that seek to capture non-neoclassical behavioral relations, macro imbalances, and institutional rigidities characteristic of developing countries” (894).

“One problem is that applied modelers often seek to draw on strands of theory outside the paradigm of Arrow-Debreu general equilibrium theory. The concept of equilibrium imbedded in the neo classical general equilibrium model underlying all multisector models its that of flow equilibrium in product and factor markets. There are additional equilibrium concepts that one might want to capture in a model, reflecting different underlying analytical theories. A second concept is that of equilibrium in aggregate ‘financial’ or ‘nominal’ flows, which define3d a notion of macro equilibrium—the heart of Keynesian macroeconomics. A third concept is that of equilibrium in asset markets, defining another form of macro equilibrium. Fourth, there is inter-temporal equilibrium involving expectations—adaptive, rational, consistent, or whatever—in an explicitly dynamic framework. The four equilibrium concepts are not independent, and it is an open question how adequate are theoretical and empirical models that only include one or two of them.” (895).

At the end of 895-6, Robinson addresses the issue of non-Walrasian models and equilibrium seeking components. He concludes that they may be just as equilibrium seeking, but that there is just a different equilibrium being sought that is no more or less rigorous than the Walrasian alternative.

“The CGE framework requires a complete specification of both the supply and demand sides of all markets, including gall the nominal magnitudes in the circular flow” (906). On page 907, Robinson outlines the simplest structure of a Walrasian CGE. It starts, at its most basic level, with producers and households. These two actors then are assumed to maximize utility or profits. They respond to signals, in the most basic case, to prices. Finally, the structure of the interaction of the units must be specified. This can become much more complex as models grow, and other actors can be imposed.

This, however, does not fully make a CGE. “With the specification of the agents, their motivation and the institutional constraints under which they interact, a general equilibrium model is still not completely determined. One must also define ‘equilibrium conditions’ which are ‘system constraints’ that must be satisfied, but that are not taken into account by any agent in making his decisions. Formally, an equilibrium can be defined as a set of signals such that the resulting decisions of all agents jointly satisfy the system constraints. The signals represent the equilibrating variables of the model. For example, a market equilibrium in a competitive model is defined as a set of prices and associated quantities such that all excess demands are zero. In a market economy, prices are the equilibrating variables that vary to achieve market clearing.

“As discussed earlier, the definition of equilibrium conditions is a fundamental property of a model. The specification of equilibrating variables and of system constraints that characterize and equilibrium can be seen as a simplifying device that providers a way to describe the results of the workings of an actual economy. For example, instead of specifying prices as equilibrating variables to achieve market clearing, one could instead try to model price determination explicitly, specifying ‘disequilibrium’ price adjustment rules to describe how prices change over time. Such a specification is theoretically very difficult to implement—indeed, event to define—and completely unnecessary if one is willing to accept the market-clearing system constraints under flexible prices as a reasonable description of the final result of such a process within the time period described by the model” (908).

A neoclassical, closed-economy CGE is described.

“Within the framework of the CGE model, one can distinguish three kinds of structuralist models” (913). These different structural aspects, or additions, to traditional neoclassical CGE models are to correct for variance and error. The first remains theoretically close to neoclassical modeling. In this structural addition, there are substitution elasticities that are imposed and is termed “elasticity structuralist” (914). Secondly, there is the “micro-structuralist” version of the model which, “assumes that various markets do not work properly or are not present at all. Instead, there are assumed to be restrictions on factor mobility, rigid prices, rationing and neoclassical disequilibrium in one or more important markets” (914). Thirdly, there is the “macro-structural” model (914). This approach emphasizes, “…achieving equilibrium among various macro aggregates; in particular, savings and investment, exports and imports and government expenditure and revenue” (914).

UPDATE:

“One problem is that applied modellers often seek to draw on strands of theory outside the paradigm of Arrow-Debreu general equilibrium theory. The concept of equilibrium imbedded in the neoclassical general equilibrium model underlying all multisectoral models is that of flow equilibrium in product and factor markets. There are additional equilibrium concepts that one might want to capture in a model, reflecting different underlying analytical theories. A second concept is that of equilibrium in aggregate ‘financial’ or ‘nominal’ flows, which defines a notion of macro equilibrium—the heart of Keynesian macroeconomics. A third concept is that of equilibrium in asset markets, defining another form of macro equilibrium. Fourth, there is intertemporal equilibrium involving expectations—adaptive, rational, consistent, or whatever—in an explicitly dynamic framework. The four equilibrium are not independent, and it is an open question how adequate are theoretical and empirical models that only include one or two of them” (895).

“There is as yet no acceptable reconciliation of micro and macro theory, and the Walrasian model is an uneasy host for incorporating macro phenomena” (896).

Thursday, April 24, 2008

Taylor: Socially Relevant Policy Analysis

Taylor, Lance. (1990). Socially relevant policy analysis : structuralist computable general equilibrium models for the developing world. Cambridge, Mass.: MIT Press.

This edited volume is designed to promote the use and development of structural CGE models. The first chapter by Taylor is of interest to me. In that chapter, Taylor outlines structural CGE models and distinguishes them from neoclassical CGE (or Walrasian) models.

“The emphasis here is on ‘structuralist’ models, which account for only some of the CGEs. Their perspective is broader than that of other, more ‘neoclassical’ constructs. Lustig (1988) nicely summarizes the ideas around which they are build: ‘Structuralist thought considers that structural characteristics (the repetition is appropriate) of the economy are fundamental to its behavior. Among the structural factors are the distribution of income and wealth, tenancy relationships on the land, the type and degree of specialization in foreign trade, the density of chains of production, the degree of concentration in markets, control of the means of production by distinct types of actors (the private sector, the state, or transnational capital), the functioning of financial intermediaries, and penetration of technical advance, as well as sociopolitical factors associated with the extent of organization of the working class and other influential sectors and classes, the geographical and sectoral distribution of the population, and its level of skills” (1).

Some general guides for a structural model of the economy: economic institutions (classes, states, corporations, for example) are not price takers; the flow is typically from investment, exports and fiscal demand (all predetermined) to income distribution, import/exports and savings; the money supply adjusts relatively statically to inflation; financial intermediation is an important driver; imported intermediate goods required to support domestic production; and development is not balanced (2-3).

“How are these views about the economy built into a model? Structuralists’s [sic] practice has five key features. First, they begin their analysis by singling out economically relevant sets of people and institutions and specifying how they fit into available data on income and wealth distributions. In Adelman and Robinson’s (1989) phrase, they create an ‘extended functional distribution’ based on the institutional structure of the economy at hand. Each set of economic actors typically is related to a functional category of the income distribution…or a production sector; it ahs different behavior patterns and partial controls over the system. In practice, a group, a class, or institution may be labeled by specific income flows rather than membership in an identifiable cluster of firms or individuals, but that is a shortcut. The justification for taking it is the belief that actions both of legal persons such as the state, or corporate sector and of real households reflect their positions in the economic system as revealed by their principal income source. They interact according to behavioral rules the modeler specifies, with consequent repercussions on macroeconomic equilibrium” (3).

“Startin from such notions of economic structure and institutions or class runs counter to neoclassical practice. Economists presently in the ‘mainstream’ devote their time to ‘deriving’ macro behavioral functions from stylized optimization exercises that individual persons, firms, and even the government are supposed to undertake. If clever, the analyst can fold the separate optimizations into a Pareto first-, second-, or nth-best equilibrium that can be represented as the extreme value of a social welfare function. A harmonious, welfare-maximizing economy (perhaps with a few ‘distortions’ to be removed) represents the mainstream version…More adventurous neoclassicals may build in rent-seeking bureaucrats and other obstructions, but few go far in trying to bring class and economic power into their models through the rational agent back door” (4).

Second distinction: money flows in terms of prices and monetary terms, not real terms.

Third: “…different prices are under varying degrees of control by distinct groups in the economy…the models herein postulate that power plays a role in price formation” (5).

Fourth: substitution based on price occurs, but it is not core to the models.

Fifth: “…their behavior [the models] depends crucially upon their description of causal linkages in the macroeconomic system” (6).