13.4 The Data

The data set is provided by the Gutachterausschuß für Grundstückswerte in Berlin, an expert commission for Berlin's real estate market. The commission collects information on all real estate transactions in Berlin in a data base called Automatisierte Kaufpreissammlung.

Here, we use data for 1502 sales of detached single-family houses in a district of Berlin for the years 1980 to 1999, stored in M D *BASE . Besides the price, we observe the size of the lot, the floor space, and the age of the house. The data set XFGhouseprice contains the log price observations for all 80 quarters. There are at most $N=43$ observations in any quarter. The following lines of XploRe code

  Y = read("XFGhouseprice.dat")
  Y[1:20,41:44]

can be used to take a look at the entries of XFGhouseprice. Every column gives the observations for one quarter. Thus, in columns 41 to 44 we find the observations for all quarters of 1990. If less than 43 transactions are observed in a quarter the remaining entries are filled with the missing value code NaN. Only in the first quarter of the year 1983 we observe 43 transactions.

The corresponding data set XFGhousequality contains the observed characteristics of all houses sold. They are ordered in the following way: each column contains all observations for a given quarter. Remember that for every house we observe log size of the lot, log size of the floor space and age. The first three rows of a column refer to the first house in $t$, the next three to the second house and so on.

Let us look at the characteristics of the first two observations in 1990:1. Just type the following lines in the XploRe input window

X = read("XFGhousequality.dat")
X[1:6,41]'

After compiling, you get the output

[1,]   6.1048   4.7707  53  6.5596  5.1475  13

The size of the lot for the second house is about 706 square meters (just take the antilog). The size of the floor space is 172 square meters and the age is 13 years.

The following table shows summary statistics of our Berlin house price data.

     "========================================================="
     " Summary statistics for the Berlin house price data      "
     "========================================================="
     " Sample for 80 quarters with 1502 observations           "
     "                                                         "
     "     Observations per period                             "
     "     ----------------------------------------------------"
     "        Minimum =  4    Average = 18.77    Maximum = 43  "
     "                                                         "
     "     Transaction prices (in thousand DM)                 "
     "     ----------------------------------------------------"
     "        Minimum =  100.00      Average   = 508.46        "
     "        Maximum = 1750.01      Std. Dev. = 197.92        "
     "                                                         "
     "     Size of the lot (in square meters)                  "
     "     ----------------------------------------------------"
     "        Minimum =  168.00      Average   = 626.18        "
     "        Maximum = 2940.00      Std. Dev. = 241.64        "
     "                                                         "
     "     Size of the floor space (in square meters)          "
     "     ----------------------------------------------------"
     "        Minimum =  46.00       Average   = 144.76        "
     "        Maximum = 635.00       Std. Dev. = 48.72         "
     "                                                         "
     "     Age of the building (in years)                      "
     "     ----------------------------------------------------"
     "        Minimum =   0          Average   = 28.59         "
     "        Maximum = 193          Std. Dev. = 21.58         "
     "========================================================="

XFGsssm1.xpl

Not surprisingly for detached houses there are large differences in the size of the lot. Some houses were new in the period of the sale while one was 193 years old. That is a good example for the potential bias of the average price per quarter as a price index. If we do not control explicitly for depreciation we might obtain a low price level simply because the houses sold in a quarter were old.

Nevertheless, the average price per quarter can give an indication of the price level. Figure 13.1 shows the average price per quarter along with confidence intervals at the 90% level. Instead of the average price, we could also calculate an average adjusted price, where the most important characteristic is used for the adjustment. Such adjustment is attained by dividing the price of every house by--for example--the respective size of the lot. However, even in that case we would control only for one of the observed characteristics. In our model we will control for all of the observed characteristics.

Figure 13.1: Average price per quarter, units are Deutsche Mark (1 DM $\approx$ 0.511 EURO). Confidence intervals are calculated for the 90% level.

XFGsssm2.xpl