**Python** is a powerful and easy to use programming language. It has a large community of developers and given its open source nature, you can find many solutions, scripts, and help all over the web. It is easy to learn and code, and faster than other high-level programming languages...and did I mention it is *free* because it is **open source**

**IPython** is a very powerful extension to Python that provides:
Powerful interactive shells (terminal and Qt-based).

- A browser-based notebook with support for code, text, mathematical expressions, inline plots and other rich media.
- Support for interactive data visualization and use of GUI toolkits.
- Flexible, embeddable interpreters to load into your own projects.
- Easy to use, high performance tools for parallel computing.

I use Canopy on OSX, so the rest of this tutorial will assume you are using that distribution. Everything that is done should work on any distribution that has the required packages, since the Python scripts should run (in rinciple) on any of these distributions.

We will use IPython as our computing environment.

Once you have your Python distribution installed you'll be ready to start working. You have two options:

- Open the Canopy program and work there
- From the Terminal prompt (command-line in Windows) execute one of the following commands:
`ipython`

`ipython qtconsole`

`ipython notebook`

While they are all using IPython, each has its advantages and disadvantages. You should to play with them to get a better feeling of which you want to use for which purpose. In my own research I usually use a text editor (TextMate) and the `ipython qtconsole`

. Although after seeing the power of Ipython's notebooks (see this excellent and in-depth presentation by its creators), I might consider shifting towards the notebook. As you will see, this might prove an excellent environment to do research, homework, replicate papers, etc.

You can pass some additional commands to `ipython`

in order to change colors and rendering of plots. I usually use `ipython qtconsole --color=linux --pylab=inline`

. You can create profiles to manage many options within IPython.

Let's start by running some simple commands at the prompt to do some simple computations.

In [ ]:

```
1+1-2
```

In [ ]:

```
3*2
```

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```
3**2
```

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```
-1**2
```

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```
3*(3-2)
```

In [ ]:

```
3*3-2
```

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```
1/2
```

In [ ]:

```
from __future__ import division
1/2
```

It is a good idea to include this among the packages to be imported by default

So what else can we do? Where do we start if we are new? You can use `?`

or `help()`

to get help.

In [ ]:

```
?
```

In [ ]:

```
help()
```

`mycommand`

you can use `help(mycommand)`

, `mycommand?`

or `mycommand??`

to get information about how it is used or even see its code.

In [ ]:

```
help(sum)
```

In [ ]:

```
sum?
```

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```
sum??
```

We can print information

In [ ]:

```
print 'Hello World!'
```

We can also create variables, which can be of various types

In [ ]:

```
a=1
b=2
a+b
```

`a`

and `b`

now hold numerical values we can use for computing

In [ ]:

```
c=[1,2]
d=[[1,2],[3,4]]
print 'c=%s' % c
print 'd=%s' % d
```

Notice that we have used `%s`

and `%`

to let Python know we are passing a string to the print function.

What kind of variables are `c`

and `d`

? They look like vectors and matrices, but...

In [ ]:

```
print 'a*c=%s' % (a*c)
print 'b*d=%s' % (b*d)
```

In [ ]:

```
c*d
```

`c`

and `d`

as list objects

In [ ]:

```
type(c)
```

In [ ]:

```
type(d)
```

In [ ]:

```
type(a)
```

Luckily Python has a powerful package for numerical computing called Numpy.

In order to use a package in Python or IPython, say `mypackage`

, you need to import it, by executing

```
import mypackage
```

After executing this command, you will have access to the functions and objects defined in `mypackage`

. For example, if `mypackage`

has a function `squared`

that takes a real number `x`

and computes its square, we can use this function by calling `mypackage.squared(x)`

. Since the name of some packages might be too long, your can give them a nickname by importing them instead as

```
import mypackage as myp
```

so now we could compute the square of `x`

by calling `myp.squared(x)`

.

We will see various packages that will be useful to do computations, statistics, plots, etc.

IPython has a command that imports Numpy and Matplotlib (Python's main plotting package). Numpy is imported as `np`

and Matplotlib as `plt`

. One could import these by hand by executing

```
import numpy as np
import matplotlib as plt
```

but the creators of IPython have optimized the interaction between these packages by running the following command:

`%pylab`

In [ ]:

```
%pylab?
```

I do recommend using the `--no-import-all`

option in order to ensure you do not contaminate the namespace. Instead it might be best to use

```
%pylab --no-import-all
%matplotlib
```

In [ ]:

```
%matplotlib?
```

In [ ]:

```
%pylab --no-import-all
%matplotlib inline
```

In [ ]:

```
np?
```

Let us now recreate `c`

and `d`

, but as Numpy arrays instead.

In [ ]:

```
ca=np.array(c)
da=np.array(d)
print 'ca=%s' % ca
print 'da=%s' % da
```

In [ ]:

```
cm=np.matrix(c)
dm=np.matrix(d)
print 'cm=%s' % cm
print 'dm=%s' % dm
```

*wonderful* feature of IPython, which is not avalable if Python)

In [ ]:

```
cm.shape
```

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```
ca.shape
```

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```
dm.
da.
```

Let's try again some operations on our new arrays and matrices

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```
cm*dm
```

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```
ca*da
```

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```
ca.dot(da)
```

We can create special matrices using Numpy's functions and classes

In [ ]:

```
print np.ones((3,4))
print np.zeros((2,2))
print np.eye(2)
print np.ones_like(cm)
```

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```
np.random
```

In [ ]:

```
x0=0
x=[x0]
[x.append(x[-1]+np.random.normal()) for i in range(500)]
plt.plot(x)
plt.title('A simple random walk')
plt.xlabel('Period')
plt.ylabel('Log Income')
plt.show()
```

We have used some of the functions in Python, Numpy and Matplotlib. But what if we wanted to create our own functions? It is very easy to do so in Python. There are two ways to define functions. Let's use them to define the CRRA utility function $u(c)=\frac{c^{1-\sigma}-1}{1-\sigma}$ and the production function $f(k)=Ak^\alpha$.

The first method is as follows:

In [ ]:

```
def u(c,sigma):
'''This function returns the value of utility when the CRRA
coefficient is sigma. I.e.
u(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1
and
u(c,sigma)=ln(c) if sigma==1
Usage: u(c,sigma)
'''
if sigma!=1:
u=(c**(1-sigma)-1)/(1-sigma)
else:
u=np.log(c)
return u
```

This defined the utility function. Let's plot it for $0< c\le5$ and $\sigma\in\{0.5,1,1.5\}$

In [ ]:

```
c=np.linspace(0.1,5,100)
u1=u(c,.5)
u2=u(c,1)
u3=u(c,1.5)
plt.plot(c,u1,label=r'$\sigma=.5$')
plt.plot(c,u2,label=r'$\sigma=1$')
plt.plot(c,u3,label=r'$\sigma=1.5$')
plt.xlabel(r'$c_t$')
plt.ylabel(r'$u(c_t)$')
plt.title('CRRA Utility function')
plt.legend(loc=4)
plt.show()
```

In [ ]:

```
def u(c,sigma=1):
'''This function returns the value of utility when the CRRA
coefficient is sigma. I.e.
u(c,sigma)=(c**(1-sigma)-1)/(1-sigma) if sigma!=1
and
u(c,sigma)=ln(c) if sigma==1
Usage: u(c,sigma=value), where sigma=1 is the default
'''
if sigma!=1:
u=(c**(1-sigma)-1)/(1-sigma)
else:
u=np.log(c)
return u
```

In [ ]:

```
sigma1=.25
sigma3=1.25
u1=u(c,sigma=sigma1)
u2=u(c)
u3=u(c,sigma=sigma3)
plt.plot(c,u1,label=r'$\sigma='+str(sigma1)+'$')
plt.plot(c,u2,label=r'$\sigma=1$')
plt.plot(c,u3,label=r'$\sigma='+str(sigma3)+'$')
plt.xlabel(r'$c_t$')
plt.ylabel(r'$u(c_t)$')
plt.title('CRRA Utility function')
plt.legend(loc=4)
plt.show()
```

Write the function for the production function. Can you generalize it so that we can use it for aggregate, per capita, and per efficiency units without having to write a function for each?

`lambda`

notation, which allows you to define functions in one line or without giving the function a name.

In [ ]:

```
squared= lambda x: x**2
squared(2)
```

Let's write a script that prints "Hello World!"

In [ ]:

```
%%file?
```

In [ ]:

```
%%file helloworld.py
#!/usr/bin/env python
# coding=utf-8
'''
My First script in Python
Author: Me
E-mail: [email protected]
Website: http://me.com
GitHub: https://github.com/me
Date: Today
This code computes Random Walks and graphs them
'''
'''
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
'''
print 'Hello World!'
```

Let's run that script

In [ ]:

```
%run helloworld.py
```

Write a simple script that simulates and plots random walks. In particular, create a function randomwalk(x0,T,mu,sigma) that simulates the random walk starting at $x_0=x0$ until $t=T$ where the shock is distributed $\mathcal{N}(\mu,\sigma^2)$

In [ ]:

```
import time
time.sleep(60*5)
print "It's time"
```

In [ ]:

```
import pandas as pd
```

*wdimobile.csv* and *wdigdppc.xlsx* and import it into python by issuing the following command:

In [ ]:

```
dfincome=pd.read_csv('./WDI/wdigdppc.csv', skiprows=2)
dfmobile=pd.read_excel('./WDI/wdimobile.xls', skiprows=2)
```

Now you should have a *data frame* with the data you downloaded.

Let's see what they look like...

In [ ]:

```
dfincome
```

In [ ]:

```
dfmobile
```

**data frames** look like spreadsheets or data tables. Columns have names that can be used to call the data, e.g.

In [ ]:

```
dfmobile.columns
```

In [ ]:

```
dfmobile['Country Code']
```

In [ ]:

```
growth=np.log(dfincome['2005'])-np.log(dfincome['2000'])
```

In [ ]:

```
growth
```

In [ ]:

```
dfincome['growth']=np.log(dfincome['2005'])-np.log(dfincome['2000'])
```

In [ ]:

```
dfincome[['Country Code','growth']]
```

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```
dfincome.set_index('Country Code', inplace=True)
```

In [ ]:

```
growth=np.log(dfincome['2005'])-np.log(dfincome['2000'])
growth.name='growth'
growth
```

Let's delete the growth column from dfincome

In [ ]:

```
dfincome.drop('growth',axis=1, inplace=True)
```

Let's compute the growth of cell phone subscription for the period 2000-2005

In [ ]:

```
dfmobile.set_index('Country Code',inplace=True)
growthmobile=np.log(dfmobile['2005'])-np.log(dfmobile['2000'])
```

In [ ]:

```
growthmobile.name='mobile'
```

In [ ]:

```
growthmobile
```

Let's see the descriptive stats for each growth process

In [ ]:

```
growth.describe()
```

In [ ]:

```
growthmobile.describe()
```

In [ ]:

```
growthmobile.ix[growthmobile==np.inf]
```

In [ ]:

```
growthmobile.ix[growthmobile==np.inf]=np.nan
```

In [ ]:

```
growthmobile.describe()
```

Let's compute the correlation between between both growth rates

In [ ]:

```
growth.corr(growthmobile)
```

In [ ]:

```
mydata=pd.merge(growth.reset_index(),growthmobile.reset_index())
mydata
```

Second, we use the pd.concat command that concatenates series or data frames into data frames.

In [ ]:

```
grates=pd.concat([growth,growthmobile],axis=1)
grates
```

Now let's import the *statsmodels* module to run the regression.

In [ ]:

```
import statsmodels.api as sm
import statsmodels.formula.api as smf
from IPython.display import Latex
```

In [ ]:

```
mod = sm.OLS(mydata['growth'],sm.add_constant(mydata['mobile']), missing='drop').fit()
mod.summary2()
```

In [ ]:

```
mod = smf.ols(formula='growth ~ mobile', data=mydata[['growth','mobile']], missing='drop').fit()
mod.summary2()
```

In [ ]:

```
mod = smf.ols(formula='growth ~ mobile', data=grates, missing='drop').fit()
mod.summary2()
```

In [ ]:

```
mysummary=mod.summary2()
Latex(mysummary.as_latex())
```

Using Pandas and Statsmodels write a Python script that:

- Downloads and opens the data from the Penn World Tables (PWT) versions 7.1 and 8.0
- Using the data from the PWT estimate the contribution of technological progress, TFP, by using the growth accounting framework studied in class.
- Using the data from the PWT calibrate productivity difference using the framework studied in class.
- Using the data from the PWT replicate the MRW analysis.

Some additional useful tools:

- LaTeX Output
- Plotting

In [ ]:

```
%%latex
\begin{eqnarray}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{eqnarray}
```

Some examples of plots...

In [ ]:

```
dfincome[[str(i) for i in range(1990,2013)]].loc['USA'].plot()
```

In [ ]:

```
plt.scatter(grates.growth,grates.mobile)
```

In [ ]:

```
from pandas.io import wb
wb.search('cell*')
```