Analysis

Overview

This section tests a hypothesis whether university towns have their housing prices less effected by recessions, using a t-test. The test compares the ratio of the mean housing price in the quarter of the recession bottom to the quarter before the recession starts between university and non-university towns. (price_ratio = recession_bottom / quarter_before_recession).

Data cleaning and processing are described in the previous section.

This project is based on assignments from Introduction to Data Science in Python by University of Michigan on Coursera

The analysis for this project was performed in Python.

Finding Recession Start, End and Bottom

In order to test the hypothesis whether university towns have their housing prices less effected by recessions, we first need to define what we mean by recession.

A recession is defined as starting with two consecutive quarters of GDP decline, and ending with two consecutive quarters of GDP growth.

A recession bottom is the quarter within a recession which had the lowest GDP.

We then proceed by finding the recession start, recession end and recession bottom in the data. We will use these figures for calculating the ratios of the mean housing prices discussed above.

The following function returns the year and quarter of the recession start time as a string value in a format such as 2005Q3:

def get_recession_start():
    
    gdp = gdp_lead_lag()
    gdp['Recession Start Dummy'] = 0
    gdp['Recession Start Dummy'][(gdp['Change in GDP'] < 0) & (gdp['Lead Change in GDP'] < 0)] = 1
    recession_start = gdp[gdp['Recession Start Dummy'] == 1]
    recession_start = recession_start.reset_index(drop = True)
    recession_start = recession_start['Quarter'].iloc[0]
    
    return recession_start

print(get_recession_start())

The results show that the recession started in 2008Q3.

The next function returns the year and quarter of the recession end time as a string value in a format such as 2005Q3:

def get_recession_end():
    
    gdp = gdp_lead_lag()
    recession_start = get_recession_start()    
    
    # Ensure that recession end comes after recession start
    gdp['Recession Start Dummy'] = np.nan
    gdp['Recession Start Dummy'][gdp['Quarter'] == recession_start] = 1
    gdp['Recession Start Dummy'] = gdp['Recession Start Dummy'].ffill()
    
    # Impose additional conditions to identify recession end
    gdp['Recession End Dummy'] = np.nan
    gdp['Recession End Dummy'][(gdp['Change in GDP'] > 0) & (gdp['Lagged Change in GDP'] > 0)] = 1
    recession_end = gdp[(gdp['Recession Start Dummy'] == 1) & (gdp['Recession End Dummy'] == 1)]
    recession_end = recession_end.reset_index(drop = True)
    recession_end = recession_end['Quarter'].iloc[0]
    
    return recession_end

print(get_recession_end())

The results show that the recession ended in 2009Q4.

The next function returns the year and quarter of the recession bottom as a string value in a format such as 2005Q3:

def get_recession_bottom():

    # Load GDP data
    gdp = load_gdp_data()
    
    # Get recession start and end and delete data outside of the recession period
    start = get_recession_start()
    end = get_recession_end()
    gdp['Start'] = np.nan
    gdp.Start[gdp.Quarter == start] = 1
    gdp.Start = gdp.Start.ffill()
    gdp['End'] = np.nan
    gdp.End[gdp.Quarter == end] = 1
    gdp.End = gdp.End.bfill()
    recession = gdp[(gdp.Start == 1) & (gdp.End == 1)]
    
    # Find the quarter during which min(GDP) was reached while in recession
    recession = recession[recession.GDP == recession.GDP.min()]
    recession = recession.reset_index(drop = True)
    recession = recession.Quarter.iloc[0]
    
    return recession

print(get_recession_bottom())

The results show that the recession bottom was reached in 2009Q2.

The t-test

First, we calculate the decline (or growth) in housing prices between the recession start and recession bottom. Then we run a t-test to determine whether such price declines in university towns are statistically significantly different from the declines in non-university towns. The t-test returns whether the null hypothesis (that the two groups are the same) is rejected as well as the p-value of the confidence.

The following function returns a tuple (different, p, better) where “different” = True if the the p-value of the t-test p < 0.01 (we reject the null hypothesis), or “different” = False if otherwise (we cannot reject the null hypothesis). The value for “better” is either “university town” or “non-university town” depending on which has a higher mean price ratio (which is equivalent to a reduced market loss).

def run_ttest():   
    
    # Create university towns dummy
    u_towns = get_list_of_university_towns()
    u_towns = u_towns[['State', 'RegionName']]
    u_towns['U_Town'] = 1
    u_towns = u_towns.set_index(['State', 'RegionName'])
    
    # Merge university towns with housing prices by state and region name
    x = convert_housing_data_to_quarters()
    x = x.merge(u_towns, how = 'left', left_index = True, right_index = True)
    x.U_Town[x.U_Town.isnull()] = 0
    
    # Analyze trends in housing values
    start = get_recession_start()
    bottom = get_recession_bottom()
    y = x[[start, bottom, 'U_Town']]
    y['Change'] = y['2009Q2'] / y['2008Q3']
    
    ut = y[y['U_Town'] == 1]['Change'].dropna()
    not_ut = y[y['U_Town'] == 0]['Change'].dropna()
    t = ttest_ind(ut, not_ut)
    p = t[1]
    
    different = False
    if p < 0.01:
        different = True
    
    better = 'university town'
    if ut.mean() < not_ut.mean():
        better = 'non-university town'
        
    return (different, p, better)

print(run_ttest())

Results

The resulting tuple is (True, 0.0031, ‘university town’), which means that the null hypotheses (the two groups are the same) is rejected with the p-value of 0.0031. This result implies that university towns experienced smaller housing price declines during the recession of 2008-2009 compared to non-university towns.