Essays on Macroeconomic Policies

This thesis deals with two issues in macroeconomic policies: The size of government expenditure multiplier on GDP, and optimal dynamic income taxation.;Chapter 2 concerns the effectiveness of government expenditure when the economy is up against the zero lower bound on the nominal interest rate. (This chapter is coauthored with R. Anton Braun.) There are two ways to approach this issue. One is to use data from historical episodes of very low interest rates and to quantify the effect of changes in government expenditure on GDP; Other is to use an economic model as an approximation of the reality and to measure the consequences of changes in fiscal policy in the model. Those studies that follows the latter approach have found government expenditure multiplier significantly higher than one. We demonstrate that a big fraction of such a large multiplier is due to the bias introduced by inaccuracy of the common solution method. After correcting these biases, however, the government purchases multiplier for output is still well above one.;The rest of this thesis is devoted to the analysis of optimal income taxation. One important role of income tax is to provide social insurance to income fluctuations. The dynamic Mirrleesian taxation literature attempts at understanding desirable properties of income taxes in view of insurance provision, by solving dynamic mechanism design problems. Chapter 3 develops a tool to numerically solve dynamic mechanism design problems where private information is persistent. Chapter 4 uses this tool to analyze an optimal income tax system when people endogenously accumulate their skills. Chapter 3, which is coauthored with Kenichi Fukushima, considers a dynamic mechanism design problem in which the agent's hidden type follows an N-state Markov chain. We show that if the Markov chain's transition probabilities are mixtures of K (less than or equal to N) densities whose mixture proportions encapsulate the dependence on the previous state, there exists a well-behaved recursive formulation of the problem with K, as opposed to N, continuous state variables. This result makes it possible to formulate computationally tractable models in which the hidden type process contains both persistent and transitory components, each of which can take many distinct values.;In Chapter 4 I use the method developed in Chapter 3 and consider dynamic Mirrleesian optimal income taxation when people endogenously accumulate their skills over the life cycle. I formulate the optimal taxation problem with a history-dependent tax system as a dynamic direct mechanism design problem in which people's skills (human capital) and their human capital investment are private information. Compared to the case where skills follow an exogenous stochastic process, skill endogeneity adds two tradeoffs: One between the skill accumulation incentive and insurance, and the other between current labor income and future high skills. I quantify how these tradeoffs alter implications on optimal allocation and taxes, deriving those from models with and without human capital accumulation that are calibrated to the U.S. data. In the endogenous skill model an optimal allocation exhibits lower lifetime labor income inequality and higher lifetime consumption inequality than in the exogenous skill model, implying a smaller redistribution from the rich to the poor which is necessary to encourage human capital investment.