Rent and GDP Increases

23 Feb 2017

There have been lots of news stories written about the raising rents all across the US, but I wondered how much of this was being driven by economic growth. I grabbed rent data from 2014 from apartmentlist.com and GDP growth between 2013 and 2014 from wikipedia. Although this data is a bit out of date, the trend should be interesting regardless.

The dataset had information for both one and two bedroom units, and you can see a trend for each below. Notably, the trend is quite weak. Cities that have been in the news a lot, like San Francisco, San Jose, Denver, and Vancouver, lay quite a bit above the trend with one bedroom apartment rents increasing faster than GDP growth. But lesser written-about cities, like Hartford, Houston, and Atlanta are also increasing faster than GDP.

The information for the fits can be found below. Both show weak (but significant) correlations. I used the Spearman’s rho to quantify the correlation and the statsmodels package in python to fit a linear least squares model to the data.

Spearman correlation = 0.38, pvalue = 0.00309695
                                    OLS Regression Results                            
        ==============================================================================
        Dep. Variable:                      y   R-squared:                       0.097
        Model:                            OLS   Adj. R-squared:                  0.081
        Method:                 Least Squares   F-statistic:                     6.109
        Date:                Wed, 15 Feb 2017   Prob (F-statistic):             0.0165
        Time:                        11:33:17   Log-Likelihood:                -125.25
        No. Observations:                  59   AIC:                             254.5
        Df Residuals:                      57   BIC:                             258.7
        Df Model:                           1                                         
        Covariance Type:            nonrobust                                         
        ==============================================================================
                         coef    std err          t      P>|t|      [95.0% Conf. Int.]
        ------------------------------------------------------------------------------
        Intercept      1.6813      0.644      2.611      0.012         0.392     2.971
        x              0.3569      0.144      2.472      0.016         0.068     0.646
        ==============================================================================
        Omnibus:                       15.535   Durbin-Watson:                   1.986
        Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.533
        Skew:                           1.194   Prob(JB):                     0.000156
        Kurtosis:                       4.195   Cond. No.                         11.2
        ==============================================================================

        Warnings:
        [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
        
Spearman correlation = 0.38, pvalue = 0.0032529
                                    OLS Regression Results                            
        ==============================================================================
        Dep. Variable:                      y   R-squared:                       0.096
        Model:                            OLS   Adj. R-squared:                  0.080
        Method:                 Least Squares   F-statistic:                     6.044
        Date:                Wed, 15 Feb 2017   Prob (F-statistic):             0.0170
        Time:                        11:33:23   Log-Likelihood:                -126.94
        No. Observations:                  59   AIC:                             257.9
        Df Residuals:                      57   BIC:                             262.0
        Df Model:                           1                                         
        Covariance Type:            nonrobust                                         
        ==============================================================================
                         coef    std err          t      P>|t|      [95.0% Conf. Int.]
        ------------------------------------------------------------------------------
        Intercept      0.8829      0.663      1.333      0.188        -0.444     2.210
        x              0.3652      0.149      2.458      0.017         0.068     0.663
        ==============================================================================
        Omnibus:                       10.421   Durbin-Watson:                   1.880
        Prob(Omnibus):                  0.005   Jarque-Bera (JB):               10.446
        Skew:                           0.846   Prob(JB):                      0.00539
        Kurtosis:                       4.176   Cond. No.                         11.2
        ==============================================================================

        Warnings:
        [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
        

As a sanity check, I took a look at the one bedroom and two bedroom price increases plotted against eachother.

There is a strong correlation between them, but with an offset from unity. Two bedroom apartments generally increase slower than one bedroom apartments.

Finally, I mapped out the top cities’ increase in one and two bedroom apartment rentals, along with GDP growth.

This was a relatively simple analysis of only one year of data from some of the cities in the US. I would love to repeat this with better data for more years and see how trends change over time.