This paper quantitatively examines the long-run macroeconomic effects of resource mis-allocation ... more This paper quantitatively examines the long-run macroeconomic effects of resource mis-allocation in an otherwise standard one-sector neoclassical growth model with heterogeneous firms being subject to progressive taxation as well as endogenous entry and exit decisions. Under a progressive fiscal policy rule, capital and labor inputs move from more productive firms to less productive establishments as the latter face a lower or negative tax rate. We find that since low-productivity firms use an inefficiently high level of productive resources when there are no entry and exit decisions, the overall production and aggregate productivity will fall as the tax progressivity rises. By contrast, more progressive taxation may raise the economy’s total output and aggregate productivity when endogenous entry and exit decisions are allowed and the household’s labor supply is postulated to be fixed. Our analysis therefore shows that the quantitative implications of progressive taxation are sensi...
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
On Indeterminacy and Growth under Progressive Taxation and Utility-Generating Government Spending
RePEc: Research Papers in Economics, Mar 1, 2016
ABSTRACT This paper examines the theoretical interrelations between equilibrium (in)determinacy a... more ABSTRACT This paper examines the theoretical interrelations between equilibrium (in)determinacy and economic growth in a one-sector representative-agent model of endogenous growth with progressive taxation of income and productive ow of public spending. We analyti-cally show that if the demand-side e¤ect of government purchases is weaker, the economy exhibits an indeterminate balanced-growth equilibrium and belief-driven growth uctua-tions when the tax schedule is regressive or su¢ ciently progressive. If the supply-side e¤ect of public expenditures is weaker, indeterminacy and sunspots arise under progressive in-come taxation. In sharp contrast to Keynesian-type stabilization policies, our analysis …nds that raising the tax progressivity may destabilize an endogenously growing economy with uctuations driven by agents'self-ful…lling expectations.
We examine the theoretical interrelations between progressive income taxation and macroeconomic (... more We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one-sector AK model of endogenous growth with utility-generating government purchases of goods and services. In sharp contrast to traditional Keynesian-type stabilization policies, progressive taxation operates like an automatic destabilizer that generates equilibrium indeterminacy and belief-driven fluctuations in our endogenously growing macroeconomy. Unlike the no-sustained-growth counterpart, this instability result is obtained regardless of (i) the degree of the public-spending preference externality and (ii) whether private and public consumption expenditures are substitutes, complements or additively separable in the household's utility function.
Despite using a variety of models and assumptions, the existing literature has overwhelmingly con... more Despite using a variety of models and assumptions, the existing literature has overwhelmingly concluded that education policy should be regressive. In this paper, we examine a two-period model in which the government may impose nonlinear taxes on both labour income and education expenditures. Individuals undertake education in the …rst period to increase their second-period wages. Our main result is that optimal education policy in our model is progressive. Speci…cally, if the government can commit, it is optimal for high-skill individuals to face a zero marginal tax rate on their education expenditures, while that for low-skill individuals is negative. If the government cannot commit, the optimal marginal tax rate on education expenditures by high-skill individuals is positive, while that for low-skill individuals remains negative.
This paper systematically examines the interrelations between a progressive income tax schedule a... more This paper systematically examines the interrelations between a progressive income tax schedule and macroeconomic (in)stability in an otherwise standard one-sector real business model with productive government spending. We analytically show that the economy exhibits indeterminacy and sunspots only if the equilibrium wage-hours locus is positively sloped and steeper than the household's labor supply curve. Unlike in the framework with useless public expenditures, a less progressive tax policy may operate like an automatic stabilizer that mitigates belief-driven cyclical ‡uctuations. Our quantitative analysis shows that this result is able to provide a theoretically plausible explanation for the discernible reduction in U.S. output volatility after the Tax Reform Act of 1986 was implemented.
We show that a one-sector real business cycle model with variable capital utilization and mild in... more We show that a one-sector real business cycle model with variable capital utilization and mild increasing returns-to-scale is able to generate qualitatively as well as quantitatively realistic aggregate ‡uctuations driven by news shocks to future consumption demand. In sharp contrast to many studies in the existing expectations-driven business cycle literature, our results do not rely on non-separable preferences or investment adjustment costs.
It has recently been shown that incorporating "keeping up with the Joneses" preferences into a pr... more It has recently been shown that incorporating "keeping up with the Joneses" preferences into a prototypical two-ability-type optimal nonlinear taxation model leads to higher marginal income tax rates for both types of agents. Speci…cally, the high-skill type faces a positive marginal income tax rate, rather than zero as in the conventional case. In this paper, agents'utility functions are postulated to exhibit "habit formation in consumption" such that the prototypical two-abilitytype optimal nonlinear taxation model becomes a dynamic analytical framework. We show that if the government can commit to its future …scal policy, the presence of consumption habits does not a¤ect the standard results on optimal marginal income tax rates. By contrast, if the government cannot pre-commit, the highskill type will face a negative marginal income tax rate, whereas the e¤ect of habit formation on the low-skill type's marginal tax rate is ambiguous.
This paper examines the interrelations between the sectoral composition of government spending an... more This paper examines the interrelations between the sectoral composition of government spending and macroeconomic (in)stability in a two-sector real business cycle model with positive productive externalities in investment and a balanced-budget fiscal policy rule, whereby endogenous public expenditures are financed by the distortionary constant tax rate. Under the benchmark parameterization, our model always exhibits indeterminacy and sunspots provided the tax rate does not exceed a critical value. When the tax rate is raised to a higher level, a sufficiently high public-consumption share can destabilize the macroeconomy by generating belief-driven cyclical fluctuations. We also find that saddle-path stability and equilibrium uniqueness will prevail when the household's labor supply elasticity is not higher than a threshold level. In addition, analytical proofs for each of the aforementioned quantitative results are provided.
It has been widely known that neoclassical growth models with su¢cient increasing returns in prod... more It has been widely known that neoclassical growth models with su¢cient increasing returns in production may feature indeterminacy. This note shows that investment adjustment costs increase the required degree of increasing returns for indeterminacy to arise. Under empirically plausible levels of investment adjustment costs, we need implausibly large degree of increasing returns to generate indeterminacy.
This paper examines the quantitative implications of government fiscal policy in a discrete-time ... more This paper examines the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits local indeterminacy, we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10-cycles, quasi-periodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability, suggesting a unique equilibrium, while the true nonlinear model exhibits global indeterminacy. This result implies that stabilization policies designed to suppress sunspot fluctuations near the steady state may not prevent sunspots, cycles, or chaos in regions away from the steady state. Overall, our results highlight the importance of using a model's nonlinear equilibrium conditions to fully investigate global dynamics.
We examine the theoretical interrelations between progressive income taxation and macroeconomic (... more We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one-sector real business cycle model with utility-generating government purchases of goods and services. When private and public consumption expenditures are complements in the household utility and the tax schedule is progressive, we analytically show that the economy exhibits indeterminacy and sunspots if and only if the degree of government-spending preference externality is higher than a critical threshold. Unlike traditional Keynesian-type stabilization policies, raising the tax progressivity may destabilize this version of our model by generating endogenous cyclical ‡uctuations. Moreover, the economy always displays saddle-path stability and equilibrium uniqueness under utility substitutability between private and public consumptions and progressive taxation.
This paper examines an in…nite-horizon model of dynamic nonlinear income taxation in which there ... more This paper examines an in…nite-horizon model of dynamic nonlinear income taxation in which there exists a small probability that the government cannot commit to its future tax policy. In this "loose commitment" environment, we …nd that even a little uncertainty over whether the government can commit yields substantial e¤ects on the optimal dynamic nonlinear income tax system. Under an empirically plausible parameterization, numerical simulations show that highskill individuals must be subsidized in the short run, despite the government's redistributive objective, unless the probability of commitment is higher than 98%. Loose commitment also reverses the short-run welfare e¤ects of changes in most model parameters. In particular, all individuals are worse-o¤, rather than better-o¤, in the short run when the proportion of high-skill individuals in the economy increases. Finally, our main …ndings remain qualitatively robust to a setting in which loose commitment is modelled as a Markov switching process.
This paper addresses the question as to whether it is optimal to use separating or pooling nonlin... more This paper addresses the question as to whether it is optimal to use separating or pooling nonlinear income taxation when the government cannot commit to its future tax policy. We also compare the levels of social welfare attainable under these tax systems versus that in the autarkic equilibrium. Both two-period and infinite-horizon settings are considered. Under empirically plausible parameter values, separating taxation is optimal in the two-period model, whereas autarky is optimal when the time horizon is infinite. The effects of varying the degree of wage inequality, the populations of low-skill and high-skill workers, and the discount rate are explored as well. For reasonable changes in these parameters, separating taxation remains optimal in the two-period model, while autarky remains optimal in the infinite-horizon model. Pooling is not optimal in either the two-period or infinite-horizon models for all parameter changes considered.
This article examines the welfare implications of some basic structural features of the U.S. tax ... more This article examines the welfare implications of some basic structural features of the U.S. tax code. The authors consider the tax deductibility of depreciation and the practice of taxing labor income differently than capital income. Their results show that long-run welfare and output can be improved by a policy of "accelerated depreciation," whereby the depreciation rate for tax purposes exceeds the rate of economic depreciation. This policy increases the tax on pure profits relative to other types of capital income. The authors also find that the benefits of applying separate tax rates to labor and capital income tend to be minimal over a range of typical depreciation tax policies.
Eusepi (2009, International Journal of Economic Theory 5, pp. 9-23) analytically …nds that a one-... more Eusepi (2009, International Journal of Economic Theory 5, pp. 9-23) analytically …nds that a one-sector real business cycle model may exhibit positive co-movement between consumption and investment when the equilibrium wage-hours locus is positively-sloped and steeper than the household's labor supply curve. However, we show that this condition does not imply expectations-driven business cycles will emerge in Eusepi's model. Speci…cally, a positive news shock about future productivity improvement leads to an aggregate recession whereby output, employment, consumption and investment all fall in the announcement period.
This paper examines the quantitative interrelations between sectoral composition of public spendi... more This paper examines the quantitative interrelations between sectoral composition of public spending and equilibrium (in)determinacy in a two-sector real business cycle model with positive productive externalities in investment. When government purchases of con-sumption and investment goods are set as constant fractions of their respective sectoral output, we show that the public-consumption share plays no role in the models local dynamics, and that a su ¢ ciently high public-investment share can stabilize the economy against endogenous belief-driven cyclical uctuations. When each type of government spending is postulated as a constant proportion of the economys total output, we nd that there exists a trade-o ¤ between public consumption versus investment expenditures
This paper quantitatively examines the long-run macroeconomic effects of resource mis-allocation ... more This paper quantitatively examines the long-run macroeconomic effects of resource mis-allocation in an otherwise standard one-sector neoclassical growth model with heterogeneous firms being subject to progressive taxation as well as endogenous entry and exit decisions. Under a progressive fiscal policy rule, capital and labor inputs move from more productive firms to less productive establishments as the latter face a lower or negative tax rate. We find that since low-productivity firms use an inefficiently high level of productive resources when there are no entry and exit decisions, the overall production and aggregate productivity will fall as the tax progressivity rises. By contrast, more progressive taxation may raise the economy’s total output and aggregate productivity when endogenous entry and exit decisions are allowed and the household’s labor supply is postulated to be fixed. Our analysis therefore shows that the quantitative implications of progressive taxation are sensi...
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
On Indeterminacy and Growth under Progressive Taxation and Utility-Generating Government Spending
RePEc: Research Papers in Economics, Mar 1, 2016
ABSTRACT This paper examines the theoretical interrelations between equilibrium (in)determinacy a... more ABSTRACT This paper examines the theoretical interrelations between equilibrium (in)determinacy and economic growth in a one-sector representative-agent model of endogenous growth with progressive taxation of income and productive ow of public spending. We analyti-cally show that if the demand-side e¤ect of government purchases is weaker, the economy exhibits an indeterminate balanced-growth equilibrium and belief-driven growth uctua-tions when the tax schedule is regressive or su¢ ciently progressive. If the supply-side e¤ect of public expenditures is weaker, indeterminacy and sunspots arise under progressive in-come taxation. In sharp contrast to Keynesian-type stabilization policies, our analysis …nds that raising the tax progressivity may destabilize an endogenously growing economy with uctuations driven by agents'self-ful…lling expectations.
We examine the theoretical interrelations between progressive income taxation and macroeconomic (... more We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one-sector AK model of endogenous growth with utility-generating government purchases of goods and services. In sharp contrast to traditional Keynesian-type stabilization policies, progressive taxation operates like an automatic destabilizer that generates equilibrium indeterminacy and belief-driven fluctuations in our endogenously growing macroeconomy. Unlike the no-sustained-growth counterpart, this instability result is obtained regardless of (i) the degree of the public-spending preference externality and (ii) whether private and public consumption expenditures are substitutes, complements or additively separable in the household's utility function.
Despite using a variety of models and assumptions, the existing literature has overwhelmingly con... more Despite using a variety of models and assumptions, the existing literature has overwhelmingly concluded that education policy should be regressive. In this paper, we examine a two-period model in which the government may impose nonlinear taxes on both labour income and education expenditures. Individuals undertake education in the …rst period to increase their second-period wages. Our main result is that optimal education policy in our model is progressive. Speci…cally, if the government can commit, it is optimal for high-skill individuals to face a zero marginal tax rate on their education expenditures, while that for low-skill individuals is negative. If the government cannot commit, the optimal marginal tax rate on education expenditures by high-skill individuals is positive, while that for low-skill individuals remains negative.
This paper systematically examines the interrelations between a progressive income tax schedule a... more This paper systematically examines the interrelations between a progressive income tax schedule and macroeconomic (in)stability in an otherwise standard one-sector real business model with productive government spending. We analytically show that the economy exhibits indeterminacy and sunspots only if the equilibrium wage-hours locus is positively sloped and steeper than the household's labor supply curve. Unlike in the framework with useless public expenditures, a less progressive tax policy may operate like an automatic stabilizer that mitigates belief-driven cyclical ‡uctuations. Our quantitative analysis shows that this result is able to provide a theoretically plausible explanation for the discernible reduction in U.S. output volatility after the Tax Reform Act of 1986 was implemented.
We show that a one-sector real business cycle model with variable capital utilization and mild in... more We show that a one-sector real business cycle model with variable capital utilization and mild increasing returns-to-scale is able to generate qualitatively as well as quantitatively realistic aggregate ‡uctuations driven by news shocks to future consumption demand. In sharp contrast to many studies in the existing expectations-driven business cycle literature, our results do not rely on non-separable preferences or investment adjustment costs.
It has recently been shown that incorporating "keeping up with the Joneses" preferences into a pr... more It has recently been shown that incorporating "keeping up with the Joneses" preferences into a prototypical two-ability-type optimal nonlinear taxation model leads to higher marginal income tax rates for both types of agents. Speci…cally, the high-skill type faces a positive marginal income tax rate, rather than zero as in the conventional case. In this paper, agents'utility functions are postulated to exhibit "habit formation in consumption" such that the prototypical two-abilitytype optimal nonlinear taxation model becomes a dynamic analytical framework. We show that if the government can commit to its future …scal policy, the presence of consumption habits does not a¤ect the standard results on optimal marginal income tax rates. By contrast, if the government cannot pre-commit, the highskill type will face a negative marginal income tax rate, whereas the e¤ect of habit formation on the low-skill type's marginal tax rate is ambiguous.
This paper examines the interrelations between the sectoral composition of government spending an... more This paper examines the interrelations between the sectoral composition of government spending and macroeconomic (in)stability in a two-sector real business cycle model with positive productive externalities in investment and a balanced-budget fiscal policy rule, whereby endogenous public expenditures are financed by the distortionary constant tax rate. Under the benchmark parameterization, our model always exhibits indeterminacy and sunspots provided the tax rate does not exceed a critical value. When the tax rate is raised to a higher level, a sufficiently high public-consumption share can destabilize the macroeconomy by generating belief-driven cyclical fluctuations. We also find that saddle-path stability and equilibrium uniqueness will prevail when the household's labor supply elasticity is not higher than a threshold level. In addition, analytical proofs for each of the aforementioned quantitative results are provided.
It has been widely known that neoclassical growth models with su¢cient increasing returns in prod... more It has been widely known that neoclassical growth models with su¢cient increasing returns in production may feature indeterminacy. This note shows that investment adjustment costs increase the required degree of increasing returns for indeterminacy to arise. Under empirically plausible levels of investment adjustment costs, we need implausibly large degree of increasing returns to generate indeterminacy.
This paper examines the quantitative implications of government fiscal policy in a discrete-time ... more This paper examines the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits local indeterminacy, we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10-cycles, quasi-periodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability, suggesting a unique equilibrium, while the true nonlinear model exhibits global indeterminacy. This result implies that stabilization policies designed to suppress sunspot fluctuations near the steady state may not prevent sunspots, cycles, or chaos in regions away from the steady state. Overall, our results highlight the importance of using a model's nonlinear equilibrium conditions to fully investigate global dynamics.
We examine the theoretical interrelations between progressive income taxation and macroeconomic (... more We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one-sector real business cycle model with utility-generating government purchases of goods and services. When private and public consumption expenditures are complements in the household utility and the tax schedule is progressive, we analytically show that the economy exhibits indeterminacy and sunspots if and only if the degree of government-spending preference externality is higher than a critical threshold. Unlike traditional Keynesian-type stabilization policies, raising the tax progressivity may destabilize this version of our model by generating endogenous cyclical ‡uctuations. Moreover, the economy always displays saddle-path stability and equilibrium uniqueness under utility substitutability between private and public consumptions and progressive taxation.
This paper examines an in…nite-horizon model of dynamic nonlinear income taxation in which there ... more This paper examines an in…nite-horizon model of dynamic nonlinear income taxation in which there exists a small probability that the government cannot commit to its future tax policy. In this "loose commitment" environment, we …nd that even a little uncertainty over whether the government can commit yields substantial e¤ects on the optimal dynamic nonlinear income tax system. Under an empirically plausible parameterization, numerical simulations show that highskill individuals must be subsidized in the short run, despite the government's redistributive objective, unless the probability of commitment is higher than 98%. Loose commitment also reverses the short-run welfare e¤ects of changes in most model parameters. In particular, all individuals are worse-o¤, rather than better-o¤, in the short run when the proportion of high-skill individuals in the economy increases. Finally, our main …ndings remain qualitatively robust to a setting in which loose commitment is modelled as a Markov switching process.
This paper addresses the question as to whether it is optimal to use separating or pooling nonlin... more This paper addresses the question as to whether it is optimal to use separating or pooling nonlinear income taxation when the government cannot commit to its future tax policy. We also compare the levels of social welfare attainable under these tax systems versus that in the autarkic equilibrium. Both two-period and infinite-horizon settings are considered. Under empirically plausible parameter values, separating taxation is optimal in the two-period model, whereas autarky is optimal when the time horizon is infinite. The effects of varying the degree of wage inequality, the populations of low-skill and high-skill workers, and the discount rate are explored as well. For reasonable changes in these parameters, separating taxation remains optimal in the two-period model, while autarky remains optimal in the infinite-horizon model. Pooling is not optimal in either the two-period or infinite-horizon models for all parameter changes considered.
This article examines the welfare implications of some basic structural features of the U.S. tax ... more This article examines the welfare implications of some basic structural features of the U.S. tax code. The authors consider the tax deductibility of depreciation and the practice of taxing labor income differently than capital income. Their results show that long-run welfare and output can be improved by a policy of "accelerated depreciation," whereby the depreciation rate for tax purposes exceeds the rate of economic depreciation. This policy increases the tax on pure profits relative to other types of capital income. The authors also find that the benefits of applying separate tax rates to labor and capital income tend to be minimal over a range of typical depreciation tax policies.
Eusepi (2009, International Journal of Economic Theory 5, pp. 9-23) analytically …nds that a one-... more Eusepi (2009, International Journal of Economic Theory 5, pp. 9-23) analytically …nds that a one-sector real business cycle model may exhibit positive co-movement between consumption and investment when the equilibrium wage-hours locus is positively-sloped and steeper than the household's labor supply curve. However, we show that this condition does not imply expectations-driven business cycles will emerge in Eusepi's model. Speci…cally, a positive news shock about future productivity improvement leads to an aggregate recession whereby output, employment, consumption and investment all fall in the announcement period.
This paper examines the quantitative interrelations between sectoral composition of public spendi... more This paper examines the quantitative interrelations between sectoral composition of public spending and equilibrium (in)determinacy in a two-sector real business cycle model with positive productive externalities in investment. When government purchases of con-sumption and investment goods are set as constant fractions of their respective sectoral output, we show that the public-consumption share plays no role in the models local dynamics, and that a su ¢ ciently high public-investment share can stabilize the economy against endogenous belief-driven cyclical uctuations. When each type of government spending is postulated as a constant proportion of the economys total output, we nd that there exists a trade-o ¤ between public consumption versus investment expenditures
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