## 经济代写|宏观经济学代写Macroeconomics代考|Using calibration to explain income differences

We have seen in Chapter 2 that a major issue in growth empirics is to assess the relative importance of factor accumulation and productivity in explaining differences in growth rates and income levels. A different empirical approach to this question is calibration, in which differences in productivity are calculated using imputed parameter values that come from microeconomic evidence. As it is closely related to the methodology of growth accounting, we discuss it here. (We will see later, when discussing business cycle fluctuations, that calibration is one of the main tools of macroeconomics, when it comes to evaluating models empirically.)

One of the main contributions in this line of work is a paper by Hall and Jones (1999). In their approach, they consider a Cobb-Douglas production function for country $i$,
$$Y_i=K_i^\alpha\left(A_i H_i\right)^{1-\alpha},$$
where $K_i$ is the stock of physical capital, $H_i$ is the amount of human capital-augmented labour and $A_i$ is a labour-augmenting measure of productivity. If we know $\alpha, K_i$ and $H_i$, and given that we can observe $Y$, we can back out productivity $A_i$ :
$$A_i=\frac{Y_i^{\frac{1}{1-\alpha}}}{K_i^{\frac{a}{1-a}} H_i} .$$
But how are we to know those?
For human capital-augmented labour, we start by assuming that labour $L_i$ is homogeneous within a country, and each unit of it has been trained with $E_i$ years of schooling. Human capital-augmented labour is given by
$$H_i=e^{\phi\left(E_i\right)} L_i .$$
The function $\phi(E)$ reflects the efficiency of a unit of labour with $E$ years of schooling relative to one with no schooling $(\phi(0)=0) . \phi^{\prime}(E)$ is the return to schooling estimated in a Mincerian wage regression (i.e. a regression of log wages on schooling and demographic controls, at the individual level). As such, we can run a Mincerian regression to obtain $H_i$. (Hall and Jones do so assuming that different types of schooling affect productivity differently.)

How about physical capital? We can compute it from data on past investment, using what is called the perpetual inventory method. If we have a depreciation rate $\delta$, it follows that
$$K_{i, t}=(1-\delta) K_{i, t-1}+I_{i, t-1}$$

## 经济代写|宏观经济学代写Macroeconomics代考|Growth regressions

Another approach to the empirics of economic growth is that of growth regressions – namely, estimating regressions with growth rates as dependent variables. The original contribution was an extremely influential paper by Robert Barro (1991), that established a canonical specification. Generally speaking, the equation to be estimated looks like this:
$$g_{i, t}=\mathbf{X}{i, t}^{\prime} \beta+\alpha \log \left(y{i, t-1}\right)+c_{i, t},$$
where $g_{i, t}$ is the growth rate of country $i$ from period $t-1$ to period $t, \mathbf{X}{i, t}^{\prime}$ is a vector of variables that one thinks can affect a country’s growth rate, both in steady state (i.e. productivity) and along the transition path, $\beta$ is a vector of coefficients, $y{i, t-1}$ is country is output in the previous period $t-1, \alpha$ is a coefficient capturing convergence, and $\epsilon_{i, t}$ is a random term that captures all other factors omitted from the specification.

Following this seminal contribution, innumerable papers were written over the subsequent few years, with a wide range of results. In some one variable was significant; in others, it was not. Eventually, the results were challenged on the basis of their robustness. Levine and Renelt (1991), for example, published a paper in which they argued no results were robust. The counterattack was done by a former student and colleague of Barro, Sala-i-Martin (1997), that applied a similar robustness check to all variables used by any author in growth regressions, in his amusingly titled paper, “I Just Ran Two Million Regressions”. He concluded that, out of the 59 variables that had shown up as significant somewhere in his survey of the literature, some 22 seem to be robust according to his more lax, or less extreme, criteria (compared to Levine and Renelt’s). These include region and religion dummies, political variables (e.g. rule of law), market distortions (e.g. black market premium), investment, and openness.

## 经济代写|宏观经济学代写Macroeconomics代考|Using calibration to explain income differences

$$Y_i=K_i^\alpha\left(A_i H_i\right)^{1-\alpha},$$

$$A_i=\frac{Y_i^{\frac{1}{1-\alpha}}}{K_i^{\frac{\alpha}{1-\alpha}} H_i} .$$

$$H_i=e^{\phi\left(E_i\right)} L_i .$$

Mincerian 工资回归中估计的学校教育回报（即在个人层面上对学校教育和人口控制的对数工资回归) 。

$$K_{i, t}=(1-\delta) K_{i, t-1}+I_{i, t-1}$$

## 经济代写|宏观经济学代写Macroeconomics代考|Growth regressions

$$g_{i, t}=\mathbf{X} i, t^{\prime} \beta+\alpha \log (y i, t-1)+c_{i, t},$$

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