经济代写|宏观经济学代写Macroeconomics代考|ECON6002

Doug I. Jones

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经济代写|宏观经济学代写Macroeconomics代考|Changes in government expenditures

Suppose now that at time 0 there is an unanticipated and permanent increase in spending from $g^L$ to $g^H$. From (18.17) it follows that tax revenue adjusts instantaneously to its new (and higher) value:
$$\tau^{\prime}=\phi^{\prime} y=r d_0+g^H, \quad t \geq 0 .$$
The adjustment takes place via an increase in the tax rate $\phi$, to a higher level $\phi^{\prime}$. Since revenues increases one-to-one with government spending, fiscal deficit does not change. Hence, an unanticipated and permanent increase in spending has no impact on the deficit nor on government debt.
How about temporary shocks? Suppose that the economy is in the initial steady-state described above, with revenue given by (18.17). At time 0 , there is an unanticipated and temporary increase in spending:
$$g_t= \begin{cases}g^H, & 0 \leq t0. First compute the revenue path. Expression (18.16) becomes$$
\phi=\frac{r d_0+r \int_0^{\infty} g_t e^{-r t} d t}{y} .
$$Combining (18.21) and (18.22) we have that revenue rises immediately to the level given by:$$
\tau^{\prime \prime}=\phi^{\prime \prime} y=r d_0+g^H\left(1-e^{-r T}\right)+g^L e^{-r T}, \quad t \geq 0 .
$$where \phi^{\prime \prime}>\phi is now the new and constant tax rate. Note that, quite naturally, the increase in the tax rate is lower under the temporary increase in spending than under the permanent increase:$$
\phi^{\prime}-\phi^{\prime \prime}=\frac{\left(g^H-g^L\right) e^{-r T}}{y}>0 .
$$Next, compute the path for the fiscal deficit. Plugging (18.23) into (18.1) we have$$
\dot{d}_t=r\left(d_t-d_0\right)+\left(g^H-g^L\right) e^{-r T}, \quad 0 \leq t0 .
$$经济代写|宏观经济学代写Macroeconomics代考|Countercyclical fiscal policy The pattern we have just established gives us a standard framework for thinking about how fiscal policy should respond to fluctuations: you should run deficits when expenditure needs are unusually high, and compensate with surpluses when they are relatively low. In short, the logic of tax smoothing provides a justification for running a countercyclical fiscal policy, based on long-run intertemporal optimisation. This basic principle can be even stronger under plausible alternative assumptions, relative to what we have imposed so far. Consider, for instance, the case of a loss function for the deadweight loss of taxes that depends uniquely on the tax rate (i.e. eliminating the factor y_t that multiplies \ell(\cdot) in (18.3) above). Then it is easy to see that the FOC is$$
\ell^{\prime}\left(\frac{\tau_t}{y_t}\right) \frac{1}{y_t}=\lambda,
$$which means that the tax rate should be higher in booms and lower in recessions. The same happens if, plausibly, distortions are higher in recessions. { }^2 Or if government expenditure has a higher value in recessions than in booms – say, because of unemployment insurance. All of these changes further strengthen the countercyclical nature of fiscal policy. 宏观经济学代考 经济代写|宏观经济学代写Macroeconomics代考|Changes in government expenditures 现在假设在时间 0 有一个意外的和永久性的支出增长来自 g^L 到 g^H. 从 (18.17) 可以看出，税收收入会立即调整到新 的 (和更高的) 值:$$
\tau^{\prime}=\phi^{\prime} y=r d_0+g^H, \quad t \geq 0 .
$$调整是通过提高税率进行的 \phi, 更上一层楼 \phi^{\prime}. 由于收入与 政府支出一对一增长，财政赤字没有变化。因此，支出的 意外和永久性增加不会对赤字或政府债务产生影响。 临时冲击怎么样? 假设经济处于上述初始稳定状态，收入 由 (18.17) 给出。在时间 0，支出出现意外的临时增加. 经济代写|宏观经济学代写Macroeconomics代考|Countercyclical fiscal policy 我们刚刚建立的模式为我们提供了一个思考财政政策应该 如何应对波动的标准框架：当支出需求异常高时，你应该 保持赤字，当支出需求相对较低时，你应该用盈余来弥 补。简而言之，税收平滑的逻辑为运行基于长期跨期优化 的反周期财政政策提供了理由。 相对于我们目前所施加的假设，在合理的替代假设下，这 一基本原则可能更加强大。例如，考虑仅取决于税率的税 收无谓损失的损失函数的情况 (即消除因素 y_t 乘以 (\cdot) 在 上面的 (18.3) 中) 。那么很容易看出FOC是$$
\ell^{\prime}\left(\frac{\tau_t}{y_t}\right) \frac{1}{y_t}=\lambda,


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