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Avoiding root-finding in the Krusell-Smith algorithm simulation
Bakota, Ivo
This paper proposes a novel method to compute the simulation part of the Krusell-Smith (1997, 1998) algorithm when the agents can trade in more than one asset (for example, capital and bonds). The Krusell-Smith algorithm is used to solve general equilibrium models with both aggregate and uninsurable idiosyncratic risk and can be used to solve bounded rationality equilibria and to approximate rational expectations equilibria. When applied to solve a model with more than one financial asset, in the simulation, the standard algorithm has to impose equilibria for each additional asset (find the market-clearing price), for each period simulated. This procedure entails root-finding for each period, which is computationally very expensive. I show that it is possible to avoid this rootfinding by not imposing the equilibria each period, but instead by simulating the model without market clearing. The method updates the law of motion for asset prices by using Newton-like methods (Broyden’s method) on the simulated excess demand, instead of imposing equilibrium for each period and running regressions on the clearing prices. Since the method avoids the root-finding for each time period simulated, it leads to a significant reduction in computation time. In the example model, the proposed version of the algorithm leads to a 32% decrease in computational time, even when measured conservatively. This method could be especially useful in computing asset pricing models (for example, models with risky and safe assets) with both aggregate and uninsurable idiosyncratic risk since methods which use linearization in the neighborhood of the aggregate steady state are considered to be less accurate than global solution methods for these particular types of models.
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Firm leverage and wealth inequality
Bakota, Ivo
This paper studies the effects of a change in firm leverage on wealth inequality and macroeconomic aggregates. The question is studied in a general equilibrium model with a continuum of heterogeneous agents, life-cycle, incomplete markets, and idiosyncratic and aggregate risk. The analysis focuses on the particular change in firm leverage that occurred in the U.S. during the 1980s, when firm leverage increased significantly, and subsequently has been dropping since the early 1990s. In the benchmark model, an increase in firm leverage of the size that occurred during the 1980s increases capital accumulation by 5.38%, decreases wealth inequality by 1.07 Gini points and decreases government revenues by 0.11% of output. An increase in firm leverage increases average after-tax returns on savings, as firm debt has beneficial tax treatment. This increases the saving rates of all households, and disproportionately increases the saving rates of relatively poorer households. Consequently, the model implies that the increase in firm leverage did not contribute to rising inequality in the U.S. in the 1980s, but rather the opposite, that the reduction in leverage from the early 1990s to 2008 has contributed to rising wealth inequality. Furthermore, I show that if the model abstracts from beneficial tax treatment of corporate debt, the change in leverage has only minor effects on macro aggregates and inequality, despite having significant implications for asset prices. This is consistent with the previous result in the literature showing that the Modigliani-Miller theorem approximately holds in the heterogeneous agents model with imperfect markets.
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Wealth inequality in dynamic stochastic general equilibrium models
Troch, Tomáš ; Stráský, Josef (advisor) ; Gregor, Martin (referee)
in English In my diploma thesis I propose a dynamic stochastic general equilibrium model to describe economic inequality. The model combines two approaches that were traditionally used to model inequality - first, it features two classes of agents that differ in their ownership of capital and second, each class consists of heterogeneous agents who are subject to uninsurable idiosyncratic shocks. This combination allows the two classes to behave in a fundamentally different way while maintaining the individual character of agents in the economy - a feature that has not been modeled before but which adequately describes the empirical reality. I show that the model with classical RBC structure and a single wage underestimates the observed inequality. When the wage differential is introduced through different taxation of the two classes, the model matches empirical inequality much better. Further I argue that the government can significantly reduce inequality at a relatively small cost in terms of output lost. Finally using Theil coefficient decomposition, I show how much of the total inequality is attributable to between-class and within-class inequalities.
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