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1 Structure of DSGE models 2 Advantages and disadvantages of DSGE modeling 3 Schools of DSGE modeling 4 Example 5 Controversy 6 References

Dynamic equilibrium A system in dynamic equilibrium is a particular example of a system in a steady state. In a steady state the rate of inputs is equal to the rate of outputs so that the composition of the system is unchanging in time. For example, a lake is in a steady state when water flows in at the same rate as water flows out. The term dynamic equilibrium is used in thermodynamics for systems involving reversible reactions. It is said that the rate of the forward reaction is equal to the rate of the backward reaction. Both reactions do in fact occur, but to such a minuscule extent that changes in composition cannot be observed. For example, in a new bottle of cola the concentration of carbon dioxide in the liquid phase has a particular value. If half the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever decreasing rate and the partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached. At that point a molecule of CO2 may leave the liquid phase, but then another molecule of CO2 will pass from the gas to the liquid. At equilibrium the rate of loss of CO2 is equal to the rate of gain. In this case, the equilibrium concentration of CO2 in the liquid is given by Henry's law, which states that the solubility of a gas in a liquid is directly proportional to

the partial pressure of that gas above the liquid. This relationship is written as where k is a temperature-dependent constant, p is the partial pressure and c is the concentration of the dissolved gas in the liquid. Thus, the partial pressure of CO2 in the gas has increased until Henry's law is obeyed. The concentration of carbon dioxide in the liquid has decreased and the drink has lost some of its fizz. Henry's law may be derived by setting the chemical potentials of carbon dioxide in the two phases to be equal to each other. Equality of chemical potential defines chemical equilibrium. Other constants for dynamic equilibrium involving phase changes include partition coefficient and solubility product. Raoult's law defines the equilibrium vapor pressure of an ideal solution. Dynamic equilibria can also exist in a homogeneous system. A simple example occurs with acid-base equilibria such as the "dissociation" of acetic acid, in aqueous solution. CH3CO2H CH3CO2- + H+ At equilibrium the concentration quotient, K, the acid dissociation constant, is constant (subject to some conditions)

In this case, the forward reaction involves the liberation of some protons from acetic acid molecules and the backward reaction involves the formation of acetic acid molecules when an acetate ion accepts a proton. Equilibrium is attained when the sum of chemical potentials of the species on the left-hand side of the equilibrium expression is equal to the sum of chemical potentials of the species on the right-hand side. At the same time the rates of forward and backward reactions are equal to each other. Equilibria involving the formation of chemical complexes are also dynamic equilibria and concentrations are governed by the stability constants of complexes. Dynamic equilibria can also occur in the gas phase as, for example, when nitrogen dioxide dimerizes. 2NO2 N2O4;

Dynamic stochastic general equilibrium Dynamic stochastic general equilibrium modeling (abbreviated DSGE or sometimes SDGE or DGE) is a branch of applied general equilibrium theory that is increasingly influential in contemporary macroeconomics. The DSGE methodology attempts to explain aggregate economic phenomena, such as economic growth, business cycles, and the effects of monetary and fiscal policy, on the basis of macroeconomic models derived from microeconomic principles. One of the main reasons

macroeconomists have begun to build DSGE models is that unlike more traditional macroeconometric forecasting models, DSGE macroeconomic models should not, inprinciple, be vulnerable to the Lucas critique (Woodford, 2003, p. 11; Tovar, 2008, p. 15).

Structure of DSGE models As their name indicates, DSGE models are dynamic, studying how the economy evolves over time. They are also stochastic, taking into account the fact that the economy is affected by random shocks such as technological change, fluctuations in the price of oil, or errors in macroeconomic policy-making. This contrasts with the static models studied in Walrasian general equilibrium theory, applied general equilibrium models and computable general equilibrium models. Traditional macroeconometric forecasting models used by central banks in the 1970s, and even today, estimated the dynamic correlations between prices and quantities in different sectors of the economy, and often included thousands of variables. Since DSGE models are technically more difficult to solve and analyze, they tend to abstract from so many sectoral details, and include far fewer variables: just a few variables in theoretical DSGE papers, or on the order of a hundred variables in the experimental DSGE forecasting models now being constructed by central banks. What DSGE models give up in sectoral detail, they attempt to make up in logical consistency, because they are founded

on microeconomic principles of constrained decisionmaking. Therefore, DSGE models must spell out the following aspects of the economy. •

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Preferences: the objectives of the agents in the economy must be specified. For example, households might be assumed to maximize a utility function over consumption and labor effort. Firms might be assumed to maximize profits. Technology: the productive capacity of the agents in the economy must be specified. For example, firms might be assumed to have a production function, specifying the amount of goods produced, depending on the amount of labor and capital they employ. Technological constraints on agents' decisions might also include costs of adjusting the capital stock, the level of employment, or the price level. Institutional framework: the institutional constraints under which economic agents interact must be specified. In many DSGE models, this might simply mean that agents make their choices within some exogenously imposed budget constraints, and that prices are assumed to adjust until markets clear. It might also mean specifying the rules of monetary and fiscal policy, or even how policy rules and budget constraints change depending on a political process.

Advantages and disadvantages of DSGE modeling By specifying preferences (what the agents want), technology (what the agents can produce), and institutions (the way they interact), it is possible (in principle, though challenging in practice) to solve the DSGE model to predict what is actually produced, traded, and consumed. In principle, it is also possible to make valid predictions about the effects of changing the institutional framework. In contrast, as Robert Lucas pointed out, such a prediction is unlikely to be valid in traditional macroeconometric forecasting models, since those models are based on observed past correlations between macroeconomic variables. These correlations can be expected to change when new policies are introduced, invalidating predictions based on past observations. Given the difficulty of constructing accurate DSGE models, most central banks still rely on traditional macroeconometric models for short-term forecasting. However, the effects of alternative policies are increasingly studied using DSGE methods. Since DSGE models are constructed on the basis of assumptions about agents' preferences, it is possible to ask whether the policies considered are Pareto optimal, or how well they satisfy some other social welfare criterion derived from preferences (Woodford, 2003, p. 12).

Schools of DSGE modeling At present two competing schools of thought form the bulk of DSGE modeling. •

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Real business cycle (RBC) theory builds on the neoclassical growth model, under the assumption of flexible prices, to study how real shocks to the economy might cause business cycle fluctuations. The paper of Kydland and Prescott (1982) is often considered the starting point of RBC theory and of DSGE modeling in general. The RBC point of view is surveyed in Cooley (1995). New-Keynesian DSGE models build on a structure similar to RBC models, but instead assume that prices are set by monopolistically competitive firms, and cannot be instantaneously and costlessly adjusted. The paper that first introduced this framework was Rotemberg and Woodford (1997). Introductory and advanced textbook presentations are given by Galí (2008) and Woodford (2003). Monetary policy implications are surveyed by Clarida et al. (1999).

Example The European Central Bank (ECB) has developed a DSGE model, often called the Smets-Wouters model, which it uses to analyze the economy of the Eurozone as a whole (in other words, the model does not analyze individual European countries separately). The model is intended as

an alternative to the Area-Wide Model (AWM), a more traditional empirical forecasting model which the ECB has been using for several years. The ECB webpage that describes the Smets-Wouters model also discusses the advantages of building a DSGE model instead of relying on more traditional methods. The equations in the Smets-Wouters model describe the choices of three types of decision makers: households, who choose how much to work, to consume, and to invest; firms, which choose how much labor and capital to employ; and the central bank, which controls monetary policy. The parameters in the equations were estimated using Bayesian statistical techniques so that the model approximately describes the dynamics of GDP, consumption, investment, prices, wages, employment, and interest rates in the Eurozone economy. In order to accurately reproduce the sluggish behavior of some of these variables, the model incorporates several types of frictions that slow down adjustment to shocks, including sticky prices and wages, and adjustment costs in investment.

Controversy Critics, such as Willem Buiter, have argued that DSGE models can be misleading. In his blog for the Financial Times, Buiter has argued that DSGE models rely excessively on an assumption of complete markets, and are unable to describe the highly nonlinear dynamics of economic fluctuations, making training in 'state of the art'

macroeconomic modeling 'a privately and socially costly waste of time and resources'.[1] N. Gregory Mankiw, regarded as one of the founders of New Keynesian DSGE modeling, has also argued that 'New classical and new Keynesian research has had little impact on practical macroeconomists who are charged with ... policy. ... From the standpoint of macroeconomic engineering, the work of the past several decades looks like an unfortunate wrong turn.'[2] Replying to Mankiw, Michael Woodford argues that DSGE models are commonly used by central banks today, and have strongly influenced policy makers like Ben Bernanke. However, he argues that what is learned from DSGE models is not so different from traditional Keynesian analysis: 'It is true that the modeling efforts of many policy institutions can reasonably be seen as an evolutionary development within the macroeconomic modeling program of the postwar Keynesians; thus if one expected, with the early New Classicals, that adoption of the new tools would require building anew from the ground up, one might conclude that the new tools have not been put to use. But in fact they have been put to use, only not with such radical consequences as had once been expected.'[3]