经济代写|宏观经济学代写Macroeconomics代考|The costs of inflation

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经济代写|宏观经济学代写Macroeconomics代考|The costs of inflation

The Sidrauski model shows that inflation does not affect the equilibrium. But somehow we do not believe this result to be correct. On the contrary, we believe inflation is harmful to the economy. In their celebrated paper, Bruno and Easterly (1996) found that, beyond a certain threshold inflation was negatively correlated with growth, a view that is well established among practicioners of monetary policy. This result is confirmed by the literature on growth regressions. Inflation always has a negative and significant effect on growth. In these regressions it may very well be that inflation is capturing a more fundamental weakness as to how the political system works, which may suggest that for these countries it is not as simple as “choosing a better rate of inflation”.

However, to make the point on the costs of inflation more strongly, we notice that even disinflation programs are expansionary. This means that the positive effects of lowering inflation are strong, so much so that they even undo whatever potential costs a disinflation may have. Figures 19.6 and 19.7 show all recent disinflation programs for countries that had reached an inflation rate equal to or higher than $20 \%$ in recent years. The figure is split in two panels, those countries that implemented disinflation with a floating regime and those that used some kind of nominal anchor (typically the exchange rate), and shows the evolution of inflation (monthly) in 19.6 and GDP (quarterly) in 19.7 since the last time they reached $20 \%$ anual inflation. The evidence is conclusive: disinflations are associated with higher growth.

So what are these costs of inflation that did not show up in the Sidrausky model? There has been a large literature on the costs of inflation. Initially, these costs were associated with what were dubbed shoe-leather costs: the cost of going to the bank to get cash (the idea is that the higher the inflation, the lower your demand for cash, and the more times you needed to go to the bank to get your cash). This was never a thrilling story (to say the least), but today, with electronic money and credit cards, simply no longer makes any sense. On a more benign note we can grant it tries to capture all the increased transaction costs associated with running out (or low) of cash.

Other stories are equally disappointing. Menu costs (the idea that there are real costs of changing prices) is as uneventful as the shoe-leather story. We know inflation distorts tax structures and redistributes incomes across people (typically against the poorest in the population), but while these are undesirable consequences they on their own do not build a good explanation for the negative impact of inflation on growth.

经济代写|宏观经济学代写Macroeconomics代考|The Tommasi model: Inflation and competition

So the problem with inflation has to be significant and deep. An elephant in the room that seems difficult to see. Tommasi (1994) provides what we believe is a more plausible story based on the role of inflation in messing up the price system. Tommasi focuses on a well-known fact: increases in inflation increase the volatility in relative prices (this occurs naturally in any model where prices adjust at different times or speed). Tommasi argues that relative prices changes, not only generate economic inefficiencies but also change the relative power of sellers and purchasers pushing the economy away from its competitive equilibrium. To see this, let’s draw from our analysis of search discussed in Chapter 16.

Imagine a consumer that is searching for a low price. Going to a store implies finding a price, the value of which can be described by
$$
r W(p)=(\bar{x}-p)+\rho[U-W(p)] .
$$
Having a price implies obtaining a utility $\bar{x}-p$. If relative prices were stable, the consumer could go back to this store and repurchase, but if relative prices change, then this price is lost. This occurs with probability $\rho$. If this event occurs, the consumer is left with no offer (value $U$ ). The $\rho$ parameter will change with inflation and will be our object of interest. If the consumer has no price, he needs to search for a price with cost $C$ and value $U$ as in
$$
r U=-C+\alpha \int_0^{\infty} \max (0, W(p)-U) d F(p)
$$
Working analogously as we did in the case of job search, remember that the optimal policy will be determined by a reservation price $p_R$. As this reservation price is the one that makes the customer indifferent between accepting or not accepting the price offered, we have that $r W\left(p_R\right)=\bar{x}-p_R=r U$, which will be handy later on. Rewrite (19.57) as
$$
W(p)=\frac{\bar{x}-p+\rho U}{r+\rho}
$$
Subtracting $U$ from both sides (and using $r U=\bar{x}-p_R$ ), we have
$$
W(p)-U=\frac{\bar{x}-p+\rho U}{r+\rho}-U=\frac{\bar{x}-p-r U}{r+\rho}=\frac{p_R-p}{r+\rho} .
$$
We can now replace $r U$ and $W(p)-U$ in (19.58) to obtain
$$
\bar{x}-p_R=-C+\frac{\alpha}{r+\rho} \int_0^{p_{\Omega}}\left(p_R-p\right) d F(p)
$$
or, finally,
$$
p_R=C+\bar{x}-\frac{\alpha}{r+\rho} \underbrace{\int_0^{p_n}\left(p_R-p\right)}_{(+)} d F(p) .
$$
The intuition is simple. The consumer is willing to pay up to his valuation of the good $\bar{x}$ plus the search cost $C$ that can be saved by purchasing this unit. However, the reservation price falls if there is expectation of a better price in a new draw.

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|The costs of inflation

Sidrauski 模型表明通货膨胀不会影响均衡。但不知何故,我们不相信这个结果是正确的。相反,我们认为通货膨胀对经济有害。Bruno 和 Easterly(1996 年)在他们著名的论文中发现,超过某个阈值后,通胀与增长呈负相关,这一观点在货币政策实践者中得到了很好的证实。有关增长回归的文献证实了这一结果。通货膨胀总是对增长产生负面和显着的影响。在这些倒退中,通货膨胀很可能正在抓住政治体系运作方式的更根本性弱点,这可能表明对于这些国家而言,它并不像“选择更好的通货膨胀率”那么简单。

然而,为了更加强调通货膨胀的成本,我们注意到即使是反通货膨胀计划也是扩张性的。这意味着降低通货膨胀的积极影响非常大,以至于它们甚至可以抵消通货紧缩可能带来的任何潜在成本。图 19.6 和 19.7 显示了针对通货膨胀率达到或高于通货膨胀率的国家的所有近期反通货膨胀计划20%最近几年。该图分为两个面板,那些通过浮动机制实施反通货膨胀的国家和那些使用某种名义锚定(通常是汇率)的国家,并显示了 19.6 的通货膨胀(月度)和 GDP(季度)的演变19.7 自从他们上次到达20%年度通货膨胀。证据确凿:通货紧缩与更高的增长有关。

那么这些没有出现在 Sidrausky 模型中的通货膨胀成本是多少?有大量关于通货膨胀成本的文献。最初,这些成本与所谓的鞋皮成本有关:去银行取现金的成本(这个想法是通货膨胀率越高,您对现金的需求越低,您需要去银行的次数越多去银行取现金)。这从来都不是一个激动人心的故事(至少可以这么说),但今天,有了电子货币和信用卡,就再也没有任何意义了。从更温和的角度来看,我们可以承认它试图捕捉与现金用完(或低)相关的所有增加的交易成本。

其他故事同样令人失望。菜单成本(改变价格会产生实际成本的想法)就像鞋皮的故事一样平淡无奇。我们知道通货膨胀会扭曲税收结构并在人们之间重新分配收入(通常针对人口中最贫穷的人),但尽管这些都是不良后果,但它们本身并不能很好地解释通货膨胀对增长的负面影响。

经济代写|宏观经济学代写Macroeconomics代考|The Tommasi model: Inflation and competition

因此,通货膨胀的问题必须是重大而深刻的。房间里的大象似平很难看到。Tommasi (1994) 根据通货膨胀在扰乱价格体系中的作用,提供了一个我们认为更合理的故事。 Tommasi 专注于一个众所周知的事实:通货膨胀的增加会增加相对价格的波动性(这在 价格以不同时间或速度调整的任何模型中自然发生)。Tommasi 认为,相对价格的变化 不仅会导致经济效率低下,还会改变买卖双方的相对力量,从而将经济推离竞争均衡。 为了解这一点,让我们借鉴第 16 章中讨论的搜索分析。
想象一下正在寻找低价的消费者。去商店意味着找到一个价格,其价值可以描述为
$$
r W(p)=(\bar{x}-p)+\rho[U-W(p)]
$$
有价格意味看获得效用 $\bar{x}-p$. 如果相对价格稳定,消费者可以回到这家商店重新购买, 但如果相对价格发生变化,那么这个价格就会丟失。这有可能发生 $\rho$. 如果发生此事件, 消费者将得不到任何报价 (价值 $U$ ). 这 $\rho$ 参数将随着通货膨胀而变化,并将成为我们感 兴趣的对象。如果消费者没有价格,他需要寻找有成本的价格 $C$ 和价值 $U$ 如在
$$
r U=-C+\alpha \int_0^{\infty} \max (0, W(p)-U) d F(p)
$$
与我们在求职案例中所做的类似,请记住最优策略将由保留价格决定 $p_R$. 由于此保留价 格使客户对接受或不接受所提供的价格无动于衷,因此我们有 $r W\left(p_R\right)=\bar{x}-p_R=r U$ ,稍后会派上用场。将 (19.57) 重写为
$$
W(p)=\frac{\bar{x}-p+\rho U}{r+\rho}
$$
减去 $U$ 从双方 (并使用 $r U=\bar{x}-p_R$ ),我们有
$$
W(p)-U=\frac{\bar{x}-p+\rho U}{r+\rho}-U=\frac{\bar{x}-p-r U}{r+\rho}=\frac{p_R-p}{r+\rho} .
$$
我们现在可以更换 $r U$ 和 $W(p)-U$ 在 (19.58) 中得到
$$
\bar{x}-p_R=-C+\frac{\alpha}{r+\rho} \int_0^{p_{\Omega}}\left(p_R-p\right) d F(p)
$$
或者,最后,
$$
p_R=C+\bar{x}-\frac{\alpha}{r+\rho} \underbrace{\int_0^{p_n}\left(p_R-p\right)}_{(+)} d F(p) .
$$
直觉很简单。消费者愿意支付他对商品的估价 $\bar{x}$ 加上搜索成本 $C$ 可以通过购买本机来节 省。但是,如果预期在新开奖中有更好的价格,则保留价会下降。

经济代写|宏观经济学代写Macroeconomics代考

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