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zdpMiV_3b1y-?u%YR^ZyA+M!VrEb09VexB=A?w<9cJl5L#&)#Q<2na8;rT{tbl~V8#s3&U2G!i#nv-K=I{+u|g^i*#YUaO{hvWVv1hfIY*~qFN}wk zRL(|4UMCl>fu0JG#`G=x!yfn4$d3JY$rt^{5?WjuZ8c z;`EOC&P-i-{2spyxd$s_eu93|lnAZ@=dCJ0^F?7pA(7rkj_faTkH_y(4+C1B5X?UK z1Yb+&EbZ%@W_v0ZOX=#?)W)V1IynK5BfQ(w0>NI;p>@MUf)Bsep;6Si#` zf;|U06@{gTC|o7HT2L712hVC?dTGj3uT$rRuQ1lofdKH6ytuuV)7;v2Y%M=SI+!_D zC#G=)89U#C{>E7N5OJ)pO)Y9?k4v0+U|~EOP(uvHE3zXHT65_a!}%L9`<4@yNiXh< z4}k1FAyysOf)$PNPCov0#X~#coQ>{~|JM0R*GCVFqd}W^yNA38=E*<#>-eMB5$^4X zC;j(xN0sT<+ezkksjn6!)qmp}=saQePj3jA!ett8Hp#v{Q88T+DY}&5XsNL+N;KYb z508%c+A+q6bFCY=I|J@l5snPYFb_r#rYql|-3eL{(F9Gmk<9N*8?L*-og*VE+$%Y+ z!T8d*xW5hf=smQ7#HRUQ%~0A&1SQI6%7=oysFc%G?-Jb~=xLyY7T5z;1r+XFoaTpl zqz4RLinICVfI=DNtzN=#Fzj?02^ z17u0Iq(9HR;JHXR^G&Aenmk6YkS2(X@f6nOB0@AaVtP zJA*N0B(o=NSY^IgDUYAWDI8uyWXw0v_uE4DqdFcd^eV9Tl@)}Tth|^Npm(r6V|!|t z1hQ#xO9{S~QSi(rf3`中,我们研究了McCall工作搜寻模型 {cite}`McCall1970`作为理解失业和劳动者决策的一种方式。 -该模型的一个不现实特征是每份工作都是永久性的。 +在之前的模型中,我们假设工作是永久性的,这不太符合现实。 -在本讲座中,我们通过引入工作离职来扩展McCall模型。 +本讲座将通过引入离职的可能性来使McCall模型更加贴近现实。 -一旦引入离职,个体就会将: +一旦引入离职,个体会有不同的考虑: -* 失去工作视为资本损失,以及 -* 失业期视为寻找可接受工作的*投资* +* 失业不仅仅是一个暂时状态,而是随时可能发生的资本损失 +* 失业期间的工作搜寻成为寻找下一份工作的*投资* -另一个小的补充是引入效用函数以使劳动者偏好更加复杂。 +我们还将引入效用函数来更好地刻画劳动者的偏好。 -我们需要以下导入: +让我们首先导入所需的包: -```{code-cell} ipython +```{code-cell} ipython3 import matplotlib.pyplot as plt import matplotlib as mpl FONTPATH = "fonts/SourceHanSerifSC-SemiBold.otf" @@ -93,13 +94,13 @@ from quantecon.distributions import BetaBinomial ### 工资过程 -目前我们将放弃在{doc}`基础模型 `中保持的状态过程和工资过程的分离。 +为了简化模型,我们不再像{doc}`基础模型 `那样将状态过程和工资过程分开。 -特别是,我们简单地假设工资报价$\{ w_t \}$是独立同分布的,具有共同的分布$q$。 +我们直接假设工资报价$\{w_t\}$是从一个共同分布$q$中独立抽取的。 -可能的工资值集合用$\mathbb W$表示。 +我们用$\mathbb W$表示所有可能的工资值集合。 -(稍后我们将回到具有驱动随机结果的独立状态过程$\{s_t\}$,因为这种表述在更复杂的模型中通常更方便。) +(在后面的章节中,我们会重新引入独立的状态过程$\{s_t\}$来驱动随机结果,因为这种方式在处理更复杂的模型时会更加方便。) ### 时间安排和决策 @@ -115,7 +116,7 @@ from quantecon.distributions import BetaBinomial 1. 获得效用$u(w_e)$,并且 1. 以某个(小的)概率$\alpha$被解雇。 -如果当前*失业*,劳动者要么接受要么拒绝当前报价$w_t$。 +如果当前*失业*,劳动者可以接受或拒绝当前报价$w_t$。 如果他接受,则立即以工资$w_t$开始工作。 @@ -166,11 +167,11 @@ h(w) = \max \left\{ v(w), \, u(c) + \beta \sum_{w' \in \mathbb W} h(w') q(w') \ 方程{eq}`bell1_mccall`表达了以工资$w_e$就业的价值,包括: * 当前报酬$u(w_e)$加上 -* 考虑到$\alpha$被解雇概率的贴现预期报酬 +* 考虑到$\alpha$被解雇概率的贴现预期价值 方程{eq}`bell2_mccall`表达了失业且手中有报价$w$的价值,作为两个选项的最大值:接受或拒绝当前报价。 -接受使劳动者转为就业,因此获得报酬$v(w)$。 +接受使劳动者转为就业,因此获得价值$v(w)$。 拒绝导致失业补偿和明天的失业。 @@ -238,12 +239,11 @@ v(w) = u(w) + \beta 然后我们可以确定劳动者的最优行为。 从{eq}`bell2_mccall`中,我们看到失业个体接受当前报价$w$如果$v(w) \geq u(c) + \beta d$。 +这表明接受工作的价值超过了继续搜索的预期价值。 -这意味着接受的价值高于拒绝的预期价值。 - -显然$v$(至少是弱)随$w$增加,因为个体永远不会因更高的工资报价而变得更差。 +由于更高的工资报价不会让个体更差,$v$是关于$w$的(弱)递增函数。 -因此,我们可以将最优选择表达为接受工资报价$w$当且仅当: +这意味着个体的最优策略可以用一个保留工资来表示 - 当且仅当工资报价$w$超过某个临界值时接受工作: $$ w \geq \bar w @@ -253,13 +253,14 @@ $$ ### 求解贝尔曼方程 -我们将使用与{doc}`第一个工作搜寻讲座 `中相同的迭代方法来求解贝尔曼方程。 +我们将采用与{doc}`第一个工作搜寻讲座 `相同的迭代方法来求解贝尔曼方程。 -这里这包括: +具体步骤如下: -1. 对$d$和$v$做出猜测 -1. 将这些猜测代入{eq}`bell02_mccall`和{eq}`bell01_mccall`的右侧 -1. 从这个规则更新左侧,然后重复 +1. 首先对$d$和$v$的值进行初始猜测 +1. 将这些猜测值代入{eq}`bell02_mccall`和{eq}`bell01_mccall`右侧的表达式 +1. 计算得到新的左侧值,并用这些新值更新猜测 +1. 重复以上步骤直到收敛 换句话说,我们使用以下规则进行迭代: @@ -283,7 +284,7 @@ v_{n+1}(w) = u(w) + \beta 如前所述,系统总是收敛到真实解---在这种情况下,是满足{eq}`bell02_mccall`和{eq}`bell01_mccall`的$v$和$d$。 -(可以通过Banach压缩映射定理获得证明。) +(可以通过巴拿赫压缩映射定理获得证明。) ## 实现 @@ -295,15 +296,15 @@ v_{n+1}(w) = u(w) + \beta 默认效用函数是CRRA效用函数: -```{code-cell} python3 +```{code-cell} ipython3 @jit def u(c, σ=2.0): return (c**(1 - σ) - 1) / (1 - σ) ``` -另外,这是一个基于BetaBinomial分布的默认工资分布: +另外,这是一个基于Beta-二项分布的默认工资分布: -```{code-cell} python3 +```{code-cell} ipython3 n = 60 # w的n个可能结果 w_default = np.linspace(10, 20, n) # 10到20之间的工资 a, b = 600, 400 # 形状参数 @@ -311,9 +312,9 @@ dist = BetaBinomial(n-1, a, b) q_default = dist.pdf() ``` -这是我们的McCall模型与离职的jitted类: +这是我们的McCall模型与离职的即时编译类: -```{code-cell} python3 +```{code-cell} ipython3 mccall_data = [ ('α', float64), # 工作离职率 ('β', float64), # 贴现因子 @@ -351,7 +352,7 @@ class McCallModel: 然后我们将当前迭代作为近似解返回。 -```{code-cell} python3 +```{code-cell} ipython3 @jit def solve_model(mcm, tol=1e-5, max_iter=2000): """ @@ -387,7 +388,7 @@ def solve_model(mcm, tol=1e-5, max_iter=2000): 我们将使用代码中的默认参数化。 -```{code-cell} python3 +```{code-cell} ipython3 mcm = McCallModel() v, d = solve_model(mcm) h = u(mcm.c) + mcm.β * d @@ -409,7 +410,7 @@ plt.show() 这是一个函数`compute_reservation_wage`,它接受`McCallModel`的实例并返回相关的保留工资。 -```{code-cell} python3 +```{code-cell} ipython3 @jit def compute_reservation_wage(mcm): """ @@ -431,7 +432,9 @@ def compute_reservation_wage(mcm): ## 参数的影响 -在下面的每个实例中,我们将向你展示一个图形,然后要求你在练习中重现它。 +现在我们将研究保留工资如何随不同参数变化。 + +对于每个参数,我们会展示一副图,并在练习中让你动手来重现这些图形。 ### 保留工资和失业补偿 @@ -485,7 +488,7 @@ def compute_reservation_wage(mcm): 关于水平轴上的值,使用: -```{code-cell} python3 +```{code-cell} ipython3 grid_size = 25 c_vals = np.linspace(2, 12, grid_size) # 失业补偿 beta_vals = np.linspace(0.8, 0.99, grid_size) # 贴现因子 @@ -499,9 +502,9 @@ alpha_vals = np.linspace(0.05, 0.5, grid_size) # 离职率 :class: dropdown ``` -这是第一个图。 +这是第一幅图。 -```{code-cell} python3 +```{code-cell} ipython3 mcm = McCallModel() w_bar_vals = np.empty_like(c_vals) @@ -521,9 +524,9 @@ ax.legend() plt.show() ``` -这是第二个图。 +这是第二幅图。 -```{code-cell} python3 +```{code-cell} ipython3 fig, ax = plt.subplots() for i, β in enumerate(beta_vals): @@ -538,9 +541,9 @@ ax.legend() plt.show() ``` -这是第三个图。 +这是第三幅图。 -```{code-cell} python3 +```{code-cell} ipython3 fig, ax = plt.subplots() for i, α in enumerate(alpha_vals): @@ -556,4 +559,4 @@ plt.show() ``` ```{solution-end} -``` \ No newline at end of file +```