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 Although this data is a bit out of date, the trend should be interesting regardless.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 Spearmanâ€™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 citiesâ€™ 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.