经济代写|宏观经济学代写Macroeconomics代考|ECON305

经济代写|宏观经济学代写Macroeconomics代考|What have we learned

We have gone over the basics of the Keynesian view of the business cycle, from its old IS-LM version to the modern canonical New Keynesian DSGE model. We saw the key role of imperfect price adjustment, leading to an upward-sloping aggregate supply curve, under which aggregate demand shocks have real consequences. We showed how imperfect competition and nominal (and real) rigidities are crucial for that. We saw how the Euler equation of consumption gives rise to the modern New Keynesian IS curve, while the Calvo model of price setting gives rise to the New Keynesian Phillips curve. Finally, we saw how we need to specify a policy rule (such as the Taylor rule) to close the model.
There is no consensus among macroeconomists as to whether the Keynesian or classical (RBC) view is correct. This is not surprising since they essentially involve very different world views in terms of the functioning of markets. Are market failures (at least relatively) pervasive, or can we safely leave them aside in our analysis? This is hardly the type of question that can be easily settled by the type of evidence we deal with in the social sciences.

Having said that, it’s important to stress the methodological convergence that has been achieved in macroeconomics, and that has hopefully been conveyed by our discussion in the last two chapters. Nowadays, essentially all of macro deals with microfounded models with rational agents, the difference being in the assumptions about the shocks and rigidities that are present (or absent) and driving the fluctuations. By providing a unified framework that allows policy makers to cater the model to what they believe are the constraints they face, means that the controversy about the fundamental discrepancies can be dealt, in a more flexible way within a unified framework. Imagine the issue of price rigidity, which is summarised by Calvo’s $\alpha$ coefficient of price adjustment. If you believe in no price rigidities, $\alpha$ has a specific value, if you think there are rigidities you just change the value. And nobody is going to fight for the value of $\alpha$, are they? Worst case scenario, you just run it with both parameters and look at the output. No wonder then that the DSGE models have become a workhorse, for example, in Central Banking.

经济代写|宏观经济学代写Macroeconomics代考|A model of job search

The specifics of the labour market have motivated the modelling of the process of job search. Obviously, how the market works depends on how workers look for a job. The theory of search tackles this question directly, though later on found innumerable applications in micro and macroeconomics.
Let’s start with the basic setup. Imagine a worker that is looking for a job, and every period (we start in discrete time), is made an offer $w$ taken from a distribution $F(w)$. The worker can accept or reject the offer. If he accepts the offer, he keeps the job forever (we’ll give away with this assumption later). If he rejects the offer he gets paid an unemployment compensation $b$ and gets a chance to try a new offer the following period. What would be the optimal decision? Utility will be described by the present discounted value of income, which the worker wants to maximise
$$\mathbb{E} \sum_{t=0}^{\infty} \beta^t x_t,$$
where $x=w$ if employed at wage $w$, and $x=b$ if unemployed and $\beta=\frac{1}{1+\rho}$. This problem is best represented by a value function that represents the value of the maximisation problem given your current state. For example, the value of accepting an offer with wage $w$ is
$$W(w)=w+\beta W(w) .$$
It is easy to see why. By accepting the wage $w$, he secures that income this period, but, as the job lasts forever, next period he still keeps the same value, so the second term is that same value discounted one period. On the other hand, if he does not accept an offer, he will receive an income of $b$ and then next period will get to draw a new offer. The value of that will be the maximum of the value of not accepting and the value of accepting the offer. Let’s call $U$ the value of not accepting ( $U$ obviously is motivated by the word unemployment):
$$U=b+\beta \int_0^{\infty} \max {U, W(w)} d F(w) .$$
Since,
$$W(w)=w /(1-\beta),$$
is increasing in $w$, there is some $w_R$ for which
$$W\left(w_R\right)=U .$$
The searcher then rejects the proposition if $w<w_R$, and accepts it if $w \geq w_R$. Replacing (16.4) in (16.5) gives
$$U=\frac{w_R}{(1-\beta)}$$

宏观经济学代考

经济代写|宏观经济学代写Macroeconomics代考|A model of job search

$$\mathbb{E} \sum_{t=0}^{\infty} \beta^t x_t,$$

$$W(w)=w+\beta W(w) .$$

$$U=b+\beta \int_0^{\infty} \max U, W(w) d F(w) .$$

$$W(w)=w /(1-\beta),$$

$$W\left(w_R\right)=U$$

$$U=\frac{w_R}{(1-\beta)}$$

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