# Arithmetic of gender equality in Germany’s federal parliament

In an interview last week, Minister of Justice and Consumer Protection Katarina Barley expressed concern about the declining share of wmomen in the Germany's current federal parliament (see e.g. here). That share decreased from 36 percent to 30 percent after the most recent election. Barley suggests that this could imply “a step backwards in gender equality.”

I am skeptical, though. The figure below shows that no party in the current parliament reduced the share of women by 6 percentage points or more (which would be required to reduce the average share over all parties by 6 percentage points).

Instead, part of the decline seems to be explained by a compositional effect: Parties with a women's share below 36 percent won seats relative to parties with women's share above 36 percent. This is especially true for the FDP and the AfD that weren't in the previous parliament but also for the SPD that had a women's share of about 44 percent in the previous parliament but that also suffered losses in the most recent election. The vote share decline for the CDU-CSU (which, holding everything else equal, helps the women's share in parliament) is not enough to compensate for the other dynamics.

At a somewhat more technical level, we can decompose the change in women's share from parliaments 18 (the parliament from 2013-2017) to 19 (the current parliament) into two effects: First, holding current women's shares by party in parliament fixed, how did election results change the overall share (election effect)? Second, holding election results fixed, what's the effect of changes in women's shares by parties (gender composition effect)?

In other words, if $w_p^j$ denotes the women's share in each party in parliament $j$ and $v_p^j$ denotes the vote share of party $p$ in parliament $j$, then the difference in women's share in parliaments 18 and 19,
$\sum_p w_p^{19}v_p^{19} – \sum_p w_p^{18}v_p^{18}$
can be decomposed into
$\sum_p w_p^{19}(v_p^{19}-v_p^{18}) – \sum_p v_p^{18} (w_p^{18}-w_p^{19})$

The first sum denotes the election effect, while the second denotes the gender composition effect. Recall that the difference in overall women share is 6 percentage points. Using data from this election and last election, one can calculate the two sums above and find that the election effect and the gender composition effect each contribute about 3 percentage points to the total decline. Hence, about half of the total decline can be explained by election results in the most recent election.

To increase the share of women in parliament, it could suffice for the SPD to win voter shares back in the next election, or more generally, for parties with a high representation of women to win more seats. Recent results of the Green party in regional elections suggest that they might also improve their vote share in the next federal election. The share of women in parliament will most likely increase then, without any need to change electoral law (as was suggested by Barley).

# Emission trends in Germany

Given recent headlines about driving restrictions for diesel cars in several German cities, I was curious about patterns of nitrogen dioxide emissions across cities and over time in the underlying data. I find that current regulations don't have much bite because seasonal variation in emissions is large. Even at measuring stations with high average annual pollution, daily average pollution can fluctuate between 20 and 140 micro grams per cubic meter. Under the assumption that regulation is unchanged, I identify several cities and stations that were below the regulation limits in 2017 but are likely to exceed limits in 2018.

I downloaded emissions data from the website of the Umweltbundesamt (Federal Environmental Agency). As common with many German administrative sources, these data are difficult to access in bulk but, with some wrangling, one can get data on daily average and daily maximum emissions for each station going back to January 2017.

Keep in mind that there are two restrictions on nitrogen dioxide emissions (see for instance here):

• The daily maximum most not exceed 200 micro grams per cubic meter on more than 18 days per year
• The annual average must not exceed 40 micro grams per cubic meter

I will only discuss the latter as the 200 micro grams restriction does not appear to be restrictive in the data.

# Annual averages

How does annual average concentration look? The figure below plots annual averages in several large German cities. 2018 data are incomplete and not directly comparable to 2017 data. It does seem, however, that the average annual concentration over all stations in a city is typically below the maximum level of 40 micro grams per cubic meter (with the exception of Munich).

# Seasonal patterns

The annual average masks substantial heterogeneity over seasons, though. Berlin, Frankfurt and Hamburg display a clear seasonal pattern with higher concentration in the winter and lower concentration in the summer. Cologne and Munich have a slightly more suprising pattern with concentration typically being higher around quarter-ends. Average concentration over the past 30 days often exceeds the 40 micro grams limit.

To me this illustrates how annual averages are not really helpful. It's like having one hand in freezing water and one hand in boiling water, fine on average, but really missing the point.

Drilling down a bit further, we can evaluate data by measuring station to see where concentration within a city is most severe and driving restrictions are most likely. For my home town of Cologne, concentration is (naturally) highest at stations closer to the city center (Turiner Str and clevischer Ring).

# Stations at increased risk of nearby-driving restrictions

Because of the aforementioned seasonalities, average annual concentration remains an unsatisfying measure. Nevertheless, under the assumption that average annual concentration continues to be the measure of choice, I was curious about stations most likely to exceed the 40 micro grams limit this year. To get a quick sense before 2018 is complete, I computed average annual concentration by station from Nov 11, 2017 to Nov 10, 2018. All of the top 15 places exceeded the 40 micro grams limit in 2017 already and continue to do so in 2018.

## # A tibble: 15 x 3
##    Stationsname                     Mean2017 MeanNov17ToNov18
##    <chr>                               <dbl>            <dbl>
##  1 Stuttgart Am Neckartor               73.0             76.7
##  2 Stuttgart Hohenheimer Straße         68.8             70.7
##  3 München/Landshuter Allee             78.2             60.5
##  4 Hamburg Habichtstraße                57.9             59.4
##  5 B Neukölln-Silbersteinstr.           48.7             58.9
##  6 Köln Clevischer Ring 3               62.1             57.4
##  7 Kiel-Theodor-Heuss-Ring              56.8             56.3
##  8 Ludwigsburg Friedrichstraße          50.8             55.8
## 10 Nürnberg/Von-der-Tann-Straße         42.6             53.8
## 11 Reutlingen Lederstraße-Ost           59.5             53.5
## 13 B Neukölln-Karl-Marx-Str. 76         49.5             53.1
## 14 Heilbronn Weinsberger Straße-Ost     56.5             52.8
## 15 Mannheim Friedrichsring              44.7             52.5


# New stations likely above the limit by year-end 2018

A few places did not exceed the limit in 2017 but are on track to exceed the limit in 2018. Expect debates about driving restrictions to pick up there.

## # A tibble: 9 x 3
##   Stationsname                    Mean2017 MeanNov17ToNov18
##   <chr>                              <dbl>            <dbl>
## 1 Mainz-Rheinallee                    35.9             46.8
## 2 Kassel-Fünffenster-Str.             38.8             46.2
## 3 Fulda-Petersberger Str.             39.4             44.5
## 4 Leipzig Lützner Str. 36             37.1             44.2
## 5 Norderstedt                         39.4             44.0
## 6 Saarbrücken-Verkehr                 36.5             43.9
## 7 Karlsruhe Reinhold-Frank-Straße     39.3             43.9
## 8 Bremen Verkehr 1                    39.2             43.2
## 9 Offenbach-Untere Grenzstraße        37.8             43.2


# Housing valuations in Germany (part 2)

How is the German housing market doing? In my second take on this question, I compare rent to purchase prices for apartments in Germany.

A common measure of valuation, the buy-to-annual rent ratio relates purchase price to annual rent (excluding utilities) for comparable apartments, that is, ideally, apartments of the same size, amenities and location. From an investor's perspective, the ratio answers the question: How many years does it take until my investment is amortized (excluding issues of taxation, maintenance, …), keeping rent fixed?

To compute the price-to-rent ratio, I group apartments by city and size and compute the mean purchase prices and annual rent in each group. I keep only groups with at least 10 apartments listed for rent and 10 apartments listed for purchase. The mean price-to-rent ratio is about 25.

A first result, illustrated in the figure below, is that the price-to-rent ratio increases in apartment size, so it seems that it is relatively better to rent rather than to buy larger apartments right now (unless purchase and rental listings differ more in other characteristics for larger apartments than for smaller ones).

How do the big cities do? To illustrate, I focus on apartments with living space between 80 and 110 square meters. Munich and Frankfurt are about on par with price-to-rent ratios above 30, while buying seems relatively more attractive in Hamburg or Cologne.

##                City medianPriceToRent
## 1           München             32.62
## 2 Frankfurt am Main             31.09
## 3            Berlin             28.01
## 4           Hamburg             26.92
## 5              Köln             25.95
## 6         Stuttgart             22.11


Where are price-to-rent ratios highest? Perhaps surprisingly, the top 10 miss a few big cities and include a few unexpected ones (Rostock, Solingen?). In each of these cities, one can buy an apartment for the equivalent of 30 years of rent (without purchase fees, maintenance and such). To put these values in perspective, note that they are about on par with average price-to-rent ratios in cities such as Los Angeles, Seattle or Boston (see here).

##             City medianPriceToRent
## 1         Lübeck             38.94
## 2       Landshut             36.80
## 3        Rostock             36.43
## 4  Halle (Saale)             36.01
## 5       Erlangen             35.42
## 7        München             32.62
## 8       Solingen             32.56
## 9         Coburg             31.42
## 10       Leipzig             31.27


To provide more context, it would be nice to compare these values to historical price-to-rent ratios in Germany, data that I don't have. Overall, it seems fair to say, though, that buying does not seem like an attractive investment in many places as yields are very poor. Of course, buying comes with other non-monetary utility and benefits which might still make buying a good choice for some.

# Housing valuations in Germany (part 1)

How is the German housing market doing? This morning, Zeit-Online reported results of a recent survey suggesting that most people looking for houses consider a price range of between EUR 200,000 and EUR 400,000. The price range aligns relatively well with German median income, yet, it is difficult to find housing in that price range close to the big cities (the article portrays a family that is willing to take on a 2 hour daily commute to find housing that price range).

To get a sense of valuations, I’m starting a series of posts about housing in Germany. I focus on apartments rather than houses (the apartment market seems more liquid and has more observations of listings).

In the first post, I am trying to get a quick sense of how much apartment rents are driven by apartment characteristics versus location characteristics. I start with a simple model of monthly apartment rent as a function of living space, the number of rooms, whether or not the apartment has a balcony, a garden or a kitchen. The idea is that the above apartment characteristics (to the extent available) can be viewed as fundamentals and are unrelated to location characteristics. Of course, location is important and can also provide quality of life. You can think of this post as trying to decompose rents in a part given by apartment quality and a part that might reflect location quality.

I omit the model details here, but the model explains about 70% of the variation in apartment rents. For each apartment, I compute the fundamental apartment rent as the prediced value from my model above.

The figure below shows the distribution of actual rent and rent based on fundamental value. As one can see, fundamental rent is often higher than actual rent.

How is this difference between actual and fundamental rent distributed across regions? The figure below shows results. In particular, it shows by how much actual rent deviates from fundamental rent (in percent). Positive values mean actual rent is above fundamental rent and negative values mean the opposite.
Not surprisingly, renting in cities is more expensive conditional on fixed apartment characteristics. You can clearly see Munich, Frankfurt, Stuttgart, Cologne and Berlin on the map.

Which are the cities with the highest share of apartments that are listed at least 50% above fundamental value? The top 25 are in the table below and they do include the usual suspects, in particular Munich and its surrounding region. It’s interesting to note that Cologne appears to have a much higher share of those fundamentally overvalued apartment listings than its neighboring city Dusseldorf. Does that suggest higher quality of life in Cologne?

##                               City ShareMorethan50
## 1                          München            0.76
## 2                  München (Kreis)            0.48
## 3                Starnberg (Kreis)            0.48
## 4         Fürstenfeldbruck (Kreis)            0.47
## 5                Frankfurt am Main            0.45
## 6                        Stuttgart            0.44
## 7                  Lörrach (Kreis)            0.43
## 8                            Fürth            0.35
## 9                       Heidelberg            0.35
## 10                            Köln            0.35
## 11                  Dachau (Kreis)            0.34
## 12                Miesbach (Kreis)            0.33
## 13                        Nürnberg            0.33
## 14                          Berlin            0.31
## 15                        Würzburg            0.31
## 16               Ebersberg (Kreis)            0.29