# Nudging Nutrition: Lessons from the Danish “Fat Tax”

Christian M. Dahl111Department of Economics, University of Southern Denmark.
Nadja van ’t Hoff11footnotemark: 1 Giovanni Mellace11footnotemark: 1 Sinne
Smed222Department of Food and Resource Economics, University of Copenhagen.

( Version: August 28, 2024.
)

###### Abstract

In October 2011, Denmark introduced the world’s first and, to date, only tax
targeting saturated fat. However, this tax was subsequently abolished in
January 2013. Leveraging exogenous variation from untaxed Northern-German
consumers, we employ a difference-in-differences approach to estimate the
causal effects of both the implementation and repeal of the tax on consumption
and expenditure behavior across eight product categories targeted by the tax.
Our findings reveal significant heterogeneity in the tax’s impact across these
products. During the taxed period, there was a notable decline in consumption
of bacon, liver sausage, salami, and cheese, particularly among low-income
households. In contrast, expenditure on butter, cream, margarine, and sour
cream increased as prices rose. Interestingly, we do not observe any
difference in expenditure increases between high and low-income households,
suggesting that the latter were disproportionately affected by the tax. After
the repeal of the tax, we do not observe any significant decline in
consumption. On the contrary, there was an overall increase in consumption for
certain products, prompting concerns about unintended consequences resulting
from the brief implementation of the tax.

Keywords: Fat tax, consumer responses, difference-in-differences, health
policy.

JEL classification: D12, I18, H31, C21.

We express our gratitude for the financial support provided by the Independent
Research Fund Denmark, grant 6109-00075B. Additionally, we acknowledge the
valuable feedback received from Phillip Heiler, Toru Kitagawa, Michael
Lechner, Volha Lazuka, Jeff Smith, and the participants of the 2021 DGPE
workshop, as well as the participants of the “Applied Econometrics of Program
Evaluation” course. Special thanks are extended to Joachim Dahl Steensbjerre
for his exceptional research assistance.

##  1 Introduction

Cardiovascular diseases are the world’s primary cause of mortality, and their
prevalence due to modifiable risk factors like unhealthy diets is rising (Roth
et al., , 2020). Since reducing saturated fat intake has been linked to a
lower risk of cardiovascular diseases (Hooper et al., , 2020), it is no
surprise that the World Health Organization strongly recommended to keep
saturated fat content below 10% of the total energy intake (World Health
Organization, , 2023). In Denmark, the dietary intake of saturated fats
equaled 15% in 2010, surpassing the recommended levels and exhibiting
relatively higher values compared to its European counterparts (Eilander et
al., , 2015). Specifically, meat was found to account for 19% of the total
saturated fat intake, while dairy products contributed with 30%, and fat-based
products such as butter and margarine contributed with 32%.

The excessive intake of saturated fat was the main reason for introducing a
tax on saturated fat, the so-called “fat tax”, which was in place in Denmark
between October 2011 and January 2013. It was a national initiative, applying
to foods with saturated fat content exceeding 2.3%, including fats like
margarine and butter, meats, and dairy products, but excluding drinking milk
and milk-based yogurts. Despite its significance, there is limited empirical
evidence on the effectiveness of the Danish fat tax to shape consumer
responses, leaving policymakers with little guidance.

The economic rationale behind the implementation of food taxes, which aim at
improving the healthiness of diets, is to address the externalities associated
with the consumption of unhealthy foods. The effectiveness of a tax hence
depends on consumers actually changing behavior in accordance with the tax
(Cawley et al., , 2019). Assessing the efficacy of food taxes remains a
complex task, influenced by a range of factors that shape consumer behavior
and producer responses. Moreover, the overall impact on public health is
contingent on consumer decisions regarding available substitutes and the
healthiness of these alternatives. A few studies have estimated the effect of
fat taxes using food price elasticities to simulate the effect of a fat tax on
consumer behavior (Chouinard et al., , 2007; Allais et al., , 2010; Nordström
and Thunström, , 2009), but their findings lack a causal interpretation
(Powell et al., , 2013). Furthermore, these analyses assume that the tax is
fully passed on to the consumers, which might not match reality. Theoretical
studies on the consumer responses to food taxes (Lusk and Schroeter, , 2012;
Yaniv et al., , 2009; Gortmaker et al., , 2011) stress the need for more
robust empirical evidence using real-world data. A limited number of studies
evaluated the Danish fat tax using real-world data (Jensen and Smed, , 2013;
Jensen et al., , 2016; Bødker et al., 2015a, ; Smed et al., , 2016), resulting
in inconclusive findings. In a recent review, Lhachimi et al.,  (2020) point
out that two of these studies (Jensen and Smed, , 2013; Jensen et al., , 2016)
lack an analysis of the effects of the tax on household expenditure. More
importantly, all of these studies lack a control group that is not exposed to
the tax and therefore lack a causal interpretation of the effect of the tax on
consumer behavior. This forms a notable gap that is addressed in this study.

Our study design is unique in that we have access to a Northern-German
households panel, which we use to construct a control group from a geographic
area that is culturally close to Denmark in terms of food consumption
behaviors, but is not affected by the tax. This allows us to estimate the
causal effect of the tax on consumption and expenditure behaviors for
different food groups employing the difference-in-differences (DID) estimator
proposed by Callaway and Sant’Anna,  (2021). We use Callaway and Sant’Anna,
(2021) as our estimator for three reasons: it allows us to control for
observed household characteristics in a flexible way; it is doubly robust, and
it provides conservative confidence intervals.

We contribute to the existing literature in several ways. First, having access
to a well-defined control group adds a causal perspective to the limited
literature evaluating the impact of the fat tax on consumption of foods high
in saturated fat. Second, we can estimate the causal effect of the tax on
expenditure behaviors and the prices actually paid by the consumer. Third, our
unique data allows us to study how the effect of the tax evolves over time. In
particular, we offer new insights into the aftermath of the abolishment of the
tax in January 2013, shedding light on potential habit formation and
unintended effects on prices in the post-tax period. Moreover, we are able to
estimate the causal effect of the tax on prices for each product group and
measure how the tax was actually passed over to consumers. Finally, we
estimate effect heterogeneity with respect to income levels to see whether
low-income households were more affected by the tax than higher-income
households. This is crucial to gain insight into the regressivity of the tax.

Our identification strategy relies on the assumption that purchases in Denmark
and Germany would have followed the same trends had the tax not been
introduced. Even though this assumption is essentially untestable, we study
its plausibility through various pre-trend tests. A second crucial assumption
is that there are no anticipation effects. The tax was announced in March 2011
before it was implemented in October 2011. We do not find any empirical
evidence of hoarding behaviors in the two quarters prior to the tax
implementation. However, to completely exclude the presence of potential
anticipation effects, such as hoarding, observations six months before the
introduction of the tax are excluded. Furthermore, to strengthen the validity
of our results, we perform robustness checks with respect to cross-border
shopping by excluding Danish households living close to the border with
Germany from the analysis. We further show that our results do not rely on
controlling for observed covariates, as they remain virtually unchanged when
we use an unconditional DID estimator.

Our main findings suggest that the tax was effective in reducing the
consumption of only three of the products we studied: cheese, liver sausage,
and salami. This reduction in consumption is only present during the tax
period, and we do not find any persistent effects on these products after the
tax was abolished. For butter, cream, margarine, and sour cream, we find a
significant increase in expenditure, which does not translate into a reduction
in consumption. Interestingly, these are the only products for which we find a
significant increase in price during the tax period. This price increase
persists in the post-tax period for butter and sour cream. For butter,
margarine, and sour cream, we observe an overall increase in consumption in
the post-tax period. Overall, our findings suggest that the tax has largely
failed to induce a long-run reduction in consumption for most products. For
butter, cream, margarine and sour cream, the tax actually induced an increase
in consumption, at least in the two years following the tax’s abolishment that
we are able to observe in our data.

Examining effect heterogeneity between high and low-income households reveals
a noteworthy reduction in both consumption and expenditure on cheese and liver
sausage, but this reduction is significant only for the latter product group.
Furthermore, a significant decrease in bacon consumption is identified
exclusively among low-income households. Notably, both high and low-income
households exhibited a comparable increase in expenditure on butter and
margarine. Finally, the post tax increase, which we find for butter, cream,
margarine and sour cream, is largely driven by high-income households.

The remainder of this paper is organized as follows: First, we discuss the
institutional background of the Danish fat tax in Section 2. Subsequently, we
offer an overview of the data, including details of our identification
strategy and its underlying assumptions in Section 3. The results are
presented in Section 4, with a focus on each product category individually,
along with potential price mechanisms. Section 5 addresses concerns related to
our identification strategy, while Section 6 explores potential heterogeneity
in tax responses. The paper concludes in Section 7.

##  2 Background on the Danish fat tax

In October 2011, Denmark introduced a tax targeting saturated fat, with the
aim of improving dietary health and with the expectation of raising a tax
revenue of 1 billion DKK (156.5 million USD333A conversion rate of 6.39 DKK
per USD is used throughout the paper.) (Bødker et al., 2015a, ; Smed, , 2012).
The tax amounted to 16 DKK (2.51 USD) per kilo of saturated fat on foods that
exceeded a threshold limit of 2.3% saturated fat. This amounts to 20 DKK (3.13
USD) per kilo including the 25% value added tax. The threshold was set such
that drinking milk and milk-based yogurts were excluded from the tax. The tax
predominantly affected products such as meat, dairy, oil, margarine, butter,
and butter blends as these products contain considerable amounts of saturated
fat. Producers had the option to use standardized coefficients for meat
products instead of the actual fat content in the products. These coefficients
were animal-specific (that is, there was one coefficient for pork products,
one for beef, etc.), and based on the average content of saturated fat in the
various types of meat consumed in Denmark (Smed, , 2012). Generally these
coefficients were used instead of specific rates for different meat cuts since
the latter option had higher administration costs. The administration of the
fat tax was burdensome and estimated to have a retail and whole-sale cost of
200 million DKK (approximately 31 million USD) according to a report by the
Danish Chamber of Commerce and the Confederation of Danish Industry (Bødker et
al., 2015b, ).

The Danish Tax Committee anticipated an increase in consumer prices up to 7%
for meats, up to 33% for dairy, up to 35% for animal fat, up to 16% for
cooking oils, up to 24% for margarine and up to 20% for blended butter
products (Bødker et al., 2015a, ). Konkurrence- og Forbrugerstyrelsen,  (2014)
analyzed the price increase of 27 taxed products and found that only for six
of these products the consumer prices increased by more than can be explained
by increases in the general food price index. They observed an overshifting of
the tax, i.e. retailers increased the price on meat by more than what could be
justified by the tax, increasing their profit margin by 1% to 5%. This finding
is supported by Jensen et al.,  (2016) who found a price increase of 13% to
16% for high-fat minced beef and cream products. These estimated increases
were higher than the a priori expected tax-induced price increases. The same
study found small negative effect on prices for lower-fat products (Jensen et
al., , 2016).

In an agreement in November 2012, the government decided that the fat tax
should be repealed with effect from January 2013. The main reasons stated were
increased consumer prices, large administration cost, and the endangerment of
Danish jobs (Konkurrence- og Forbrugerstyrelsen, , 2014).444For more
information on the Danish tax on saturated fat see Smed,  (2012) and Ecorys,
Euromonitor and IDEA, DTI,  (2014). For more information on the repeal of the
Danish tax on saturated fat see Vallgårda et al.,  (2015).

##  3 Data, identification strategy, estimation, and inference

###  3.1 Data

To estimate the impact of the Danish fat tax on consumption behavior, we
leverage household panel data from GfK Consumer Scan, which encompasses
households located in Denmark as well as households in Northern Germany,
specifically Schleswig-Holstein and Hamburg.555For more information on the
Danish data set, see Smed,  (2008). It is worth noting that these Danish
household data are also used in the analysis of Jensen and Smed,  (2013) and
Smed et al.,  (2016), yet they lacked the Northern-German households as a
control group and the length of the data periods considered differ.

GfK maintains a representative panel with respect to geographic location,
education, and age. When a household leaves the panel, it is replaced by a
similar household with respect to the aforementioned characteristics.
Participants in the panel are equipped with a hand scanning device, enabling
them to document detailed information on their weekly grocery shopping. The
diary keeper reports the volume of foods purchased for the household, the
expenditure, date and time of the purchase, among other details. While surveys
and self-reported data are often susceptible to recall bias, this is less
likely to be a concern when using scanning devices. A scanning device can ease
registration of purchase information, which subsequently might be experienced
as less burdensome to the households than registering food consumption
manually. Moreover, our data provides an advantage over store scanner data by
incorporating purchases made abroad. However, we acknowledge that our data do
not account for food acquired outside of stores, such as in restaurants. The
purchase diaries are submitted to GfK weekly and thoroughly checked for
correct completion and consistency. As highlighted by Smed,  (2008), a
comparison of the budget-shares of foods from the GfK consumer panel with
budget-shares revealed from data of Statistics Denmark shows no major biases
for the distribution of expenses between basic food categories, even though
the home-scan panel generally under-report in terms of absolute values.

In our analysis, we consider a wide variety of product categories targeted to
a different degree by the tax, encompassing bacon, butter and butter blends
(referred to as butter), hard cheeses (referred to as cheese), cream, liver
sausage and paté (referred to as liver sausage), margarine, salami, and sour
cream. The product categories were first and foremost chosen based on their
substantial contribution to the saturated fat intake in Denmark. We aggregate
different products into products categories in a way that ensures both
comparability between Germany and Denmark as well as an adequate number of
observations.

Our main analysis uses data covering the period from January 2009 until
December 2014. The data are aggregated to a quarterly household panel,
encompassing 11 quarters before the tax introduction and 13 quarters after the
tax introduction. Furthermore, we create product-specific panels where
households that never purchase from the considered product category are
excluded. If the number of zero purchases for a given product changes
systematically over time differentially between Denmark and Northern Germany,
our results could be affected by sample selection bias. However, Figure 9
below shows similar pre-trends in the average number of observations with zero
outcome between Denmark and Northern Germany. In general, for all product, we
do not find any systematic change in the difference in the number of zeros
even in the post-treatment period. The fact that we use quarterly data reduces
the number of excluded households and the potential of sample selection bias.

Figure 1: Bacon.

Figure 2: Butter.

Figure 3: Cheese.

Figure 4: Cream.

Figure 5: Liver sausage.

Figure 6: Margarine.

Figure 7: Salami.

Figure 8: Sour cream.

Figure 9: The figures show the de-trended quarterly average number of
observations with zero value in the outcome variable for Danish and Northern-
German households, respectively.

Figures 12 and 13 in Appendix A.1 illustrate the data preparation steps and
the number of available observations for each step. Our final analysis
incorporates between 2,056 and 2,526 unique Danish households, depending on
the product category, and 553 to 1,616 German households.

The data further contain background information on the participating
households, which is based on an annual questionnaire filled in by the diary
keeper. This includes information on the geographic region of residence, the
age of the head of the household, the number of children below age 15, the
household size, income level, gender of the diary keeper, and education level.
The data set with German households contains similar information as the Danish
data. We harmonize the variables that are reported differently in the two data
set, such as income and education.666The education level is based on the
International Standard Classification of Education (ISCED). To harmonize the
income variable, which is reported in different brackets in the two data sets,
we create quintiles based on the midpoints of the income ranges in the data
set that contains all products for Germany and Denmark. We create five
different levels, representing very low income, low income, medium income,
high income and very high income. For our analysis, we use the most recently
observed pre-tax characteristics for a household. That is, if a household’s
income is observed in both the years 2009 and 2010, we use the income level
observed in 2010. Pre-treatment characteristics of the households in our study
are summarized in Table LABEL:tab:sum_stat in Appendix A.2.777Smed et al.,
(2016) use the same data and compare the descriptive statistics to official
numbers from Statistics Denmark. They observe that the panel contains
relatively more households in the capital and households with a lower level of
educational attainment. There are some notable differences between the
Northern-German and Danish households. For instance, the age of the head of
the household has a tendency to be higher in Germany compared to Denmark.
Additionally, there is a noticeable gender distribution distinction among
diary keepers, with 78% being female in Denmark as opposed to only 59% in
Germany. Moreover, households in Germany tend to be larger compared to those
in Denmark. Since the household characteristics listed in the table are
included as control variables in our difference-in-differences strategy, we
address the concern that differences in consumption trends between Germany and
Denmark might be caused by imbalances in sample composition.

To investigate consumers’ response to the introduction of the fat tax, we
define three distinct outcomes of interest. Firstly, we define three variables
to investigate consumption and expenditure behavior: (1) the average quarterly
household consumption, measured by the average weight or volume in gr or ml
purchased per quarter per household, (2) the average number of packages
purchased per household, and (3) the average quarterly total expenditure per
household in Euro cents. Note that we use product purchases as a proxy for
consumption, recognizing that a purchase does not necessarily indicate
consumption. To investigate the price changes caused by the tax, we construct
a variable for the average quarterly price paid per 100 units (gr or ml
depending on the product) in Euro cents, allowing us to investigate whether
the tax was passed on to consumers by retailers and producers.888Danish
expenditure is converted from DKK to Euro cents using the rate 7.4405.
Additionally, since quarters have different number of days we re-weight our
outcomes such that each quarter consist of the same amount of days. Finally,
we partial out the effect of seasoanl trends from all outcomes. To achieve
this we simply run two separate linear regressions, one for each country, for
each outcome on quarterly dummies and we use the residuals of these
regressions as outcomes.999The pre-tax and tax average quantities of our
outcomes of interest are presented in Table 7 in Appendix A.3. Outliers are
removed using Tukey’s fences with the constant $k=3$.

###  3.2 Identification strategy, estimation, and inference

The key strength of our study lies in the ability to observe a proper control
group, enabling us to identify a causal effect of the Danish fat tax on
consumption behavior. We observe comprehensive information on Northern-German
households from Schleswig-Holstein and Hamburg. A suitable control group not
only removes time trends, but also unobserved demand shocks (Cawley et al., ,
2019). A notable advantage of a geographically close control group is the
cultural proximity between the treated and control sample, increasing the
likelihood that they are subject to similar external shocks. Our
identification strategy relies on the DID framework. The main idea is to
compare Danish households to their German counterparts, both before and after
the introduction of the fat tax, in terms of our outcome variable and for the
different product categories. DID identifies the average treatment effect on
the treated (ATT), that is, the effect of the fat tax on the Danish consumers.

Another noteworthy advantage of our study stems from the availability of
longitudinal data, which allows us to study how consumption behavior varies
with the length of exposure to the tax and how the effects evolve over time,
effectively embracing an event-type study approach. We adopt the estimator for
event-study designs proposed by Callaway and Sant’Anna,  (2021), which extends
the doubly robust estimator of Sant’Anna and Zhao,  (2020) to the setting with
multiple time periods.101010Note that Callaway and Sant’Anna,  (2021)
additionally consider the setting with variation in treatment timing
(staggered adoption), where individuals belong to a certain group depending on
the timing of their treatment. However, in our context, the number of groups
equals one as the tax was simultaneously introduced and repealed for all
individuals. As we have already mentioned in the introduction, the main
advantage of this approach over other estimators, such as the common two-way
fixed effects estimator (see, for instance, Roth et al.,  (2023) for a recent
review of the DID literature), is that it allows to control for observed
covariates in a flexible way.

The quarterly panel we use ranges from 2009 to 2014, encompassing 20 quarters.
Denote a particular quarter with $q$ where $q\in\\{2009-Q1,\allowbreak
2009-Q2,\allowbreak 2009-Q3,\allowbreak...,\allowbreak 2014-Q4\\}$. Denote
with $Y_{iq}$ the outcome of interest for household $i$ in quarter $q$. As
described in Section 3.1, three different outcomes concerning consumption
behavior (weight, packages, and expenditure) are studied. In addition we also
estimate the effect of the tax on average prices paid per 100 units (gr or ml
depending on the product). The tax, our treatment, was introduced at the
beginning of the fourth quarter of 2011, meaning that the third quarter of
2011 ($2011\text{-}Q3$) was the last pre-treatment quarter, and it was
abolished at the beginning of the first quarter of 2013; thus,
$2012\text{-}Q4$ is the last period where the tax was still in place. Let
$D_{i}=1$ if unit $i$ is a Danish household, and $D_{i}=0$ otherwise. Define
$Y_{pre}$ as the reference period, e.g., $2011\text{-}Q3$. It is important to
note that the reference period varies depending on the causal effect of
interest, and the precise reference period used will be explicitly stated on a
case-by-case basis. Ignoring for the moment pre-treatment covariates, when all
the treated units are treated at the same time, as in our case, the $ATT(q)$
are identical to the ATTs in the two-period DID approach and are identified
by:

$ATT(q)=E(Y_{q}-Y_{pre}|D=1)-E(Y_{q}-Y_{pre}|D=0).$ (1)

When controlling for pre-treatment covariates, denoted by $X$, the ATT in each
quarter is identified by the following expression:

$ATT(q)=E\left[\left(\frac{D}{E(D)}-\frac{\frac{p(X)(1-D)}{1-p(X)}}{E\left[\frac{p(X)(1-D)}{1-p(X)}\right]}\right)(Y_{q}-Y_{pre}-m_{q}(X))\right],$
(2)

where the propensity score $p(X)$ denotes the probability of being subject to
the tax, conditional on the pre-tax households characteristics $X$, and
$m_{q}(X)=E(Y_{q}-Y_{pre}|X,D=0)$ denotes the population outcome regression
for the Northern-German households in quarter $q$.

Equations (1) and (2) provide the ATT for each individual quarter. A
straightforward approach to establish the overall average causal effect for a
specific period is to aggregate the time average treatment effects, $ATT(q)$,
of that period. For example, we can aggregate the $ATT(q)$ in the tax period
as follows:

$\displaystyle ATT=\frac{1}{5}\sum_{q\in\\{2011-Q4,...,2012-Q4\\}}ATT(q).$ (3)

Simply put, this is the mean over the $ATT(q)$ for the period that the tax was
in effect.

Estimation proceeds in two steps. In the first step, the propensity score
$p(x)$ and outcome model $m_{q}(X)$ are estimated using logistic and linear
regressions, respectively. In the second step, the fitted values of the two
models are plugged into the sample analogue of Equation (2). The doubly robust
DID estimator attains the semiparametric efficiency bound when both nuisance
models are correctly specified. A strength of using Callaway and Sant’Anna,
(2021) is that they provide simultaneous confidence bands which account for
multiple-testing and are obtained by a multiplier-type bootstrap procedure.

Some assumptions that are standard in literature need to be satisfied for
Equations (1) to (3) to be valid. The first assumption rules out anticipation
effects. This implies that Danish households did not adjust their consumption
behavior in anticipation of the tax, e.g. by hoarding. As the tax was adopted
approximately half a year before its implementation, we cannot exclude the
presence of hoarding. We rigorously study the presence of anticipation effects
of the fat tax in Section 4.1.

The second assumption is the parallel trends assumption. This assumption
states that in the absence of the Danish fat tax, the outcome trends in
Denmark would have followed the same trends as the ones observed in Northern-
Germany during the tax period. If the composition of the treatment and control
groups are different in terms of household characteristics, then this might
cause the German and Danish trends to diverge in case of heterogeneous
treatment effects, leading to a violation of the unconditional parallel trends
assumption (see Roth et al.,  (2023)). To address this concern, we relax the
parallel trends assumption slightly and allow for the presence of covariate-
specific trends by conditioning on pre-tax household characteristics. When
controlling for observed covariates we also need to impose the standard
overlap assumption, i.e., it must hold that for all $X$ that $p(X)<0$. This
assumption ensures that for each Danish household, we can find German
households with similar characteristics. We investigate the plausibility of
the parallel trends and overlap assumptions in Section 4.1.

It is crucial to note that tests for the parallel trends assumption offer
insights into pre-tax trend similarities. However, the parallel trends
assumption is essentially untestable as the post treatment trends that Denmark
would have experienced had the tax not been introduced cannot be observed.
This means that this assumption could be perfectly plausible in the pre-tax
period, while violated in the post-tax period, and vice-versa. Nonetheless,
observing similar pre-tax trends provides evidence in favor of the parallel
trends assumption.

In Section 5 we run further robustness checks. First, we exclude Danish
households living close to the German border, since the introduction of a tax
can lead to increased border trade to avoid the tax. Second, we investigate
how much our results rely on controlling for household characteristics by
estimating the effects unconditionally.

##  4 Results

In this section, we report the main results.111111We tailored the R package of
Callaway and Sant’Anna,  (2021) to our setting and express our gratitude to
the original authors for making their code publicly available.

###  4.1 Plausibility of identifying assumptions

We first examine the plausibility of the no anticipation assumption which is
crucial for DID. As mentioned in Section 3.2, this assumption posits that
households did not change their behavior in anticipation of the tax
implementation. To explore this, we estimate the effect of the tax in the two
quarters preceding its introduction, namely the second and third quarters of
2011. The tax was announced on March 17, 2011, and introduced in October,
2011. The results reported in Table 1 do not show any statistically
significant anticipation effect. Nevertheless, we take a conservative stand
and, to avoid any potential bias due to anticipation effects, we exclude the
second and third quarter of 2011 from the analysis. We find qualitatively
similar results including these two quarters.121212The results are available
from the authors upon request.

Table 1: The causal effect of the Danish fat tax in the two quarters preceding
the tax, using the first quarter of 2011 as reference period.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Quarterly average weight consumed in
gr/ml $ATT_{2011-Q2}$ -13.910 82.603 -142.069 -45.696 38.916 -54.424 54.246
106.351 (se) (47.829) (107.047) (160.676) (94.261) (60.690) (124.059) (47.474)
(51.176) $ATT_{2011-Q3}$ 26.963 95.758 -99.659 -37.812 45.896 202.126 76.975
72.012 (se) (42.933) (100.254) (143.327) (87.195) (63.777) (135.263) (49.936)
(48.075) Panel B: Quarterly average expenditure in Euro cents $ATT_{2011-Q2}$
-19.721 14.544 -48.137 -13.068 32.325 -44.864 71.076 28.082 (se) (39.060)
(49.050) (130.123) (28.545) (38.540) (28.308) (48.302) (14.516)
$ATT_{2011-Q3}$ 8.636 51.837 -12.612 -4.428 12.671 39.789 99.147 20.986 (se)
(36.968) (47.847) (133.483) (28.970) (40.789) (30.300) (47.703) (13.646) Panel
C: Quarterly average amount (in packages) consumed $ATT_{2011-Q2}$ 0.009 0.243
-0.145 -0.309 0.087 -0.095 0.317 0.263 (se) (0.231) (0.419) (0.497) (0.366)
(0.255) (0.269) (0.296) (0.207) $ATT_{2011-Q3}$ 0.182 0.196 -0.278 -0.200
0.059 0.405 0.522 0.197 (se) (0.188) (0.427) (0.484) (0.320) (0.270) (0.283)
(0.279) (0.185) Significance level: * $p<0.1$ ** $p<0.05$ *** $p<0.01$.
Standard errors are clustered at household level. The results are obtained
controlling for the age of the head of the household, the number of children
under 15 years, the gender of diary keeper, the educational level (ISCED), the
income level, and the household size.

A second aforementioned crucial assumption for the credibility of our
estimates is the parallel trends assumption. An advantage of having multiple
pre-tax time periods is the opportunity to gain some insight into the
plausibility of this assumption. We assess the plausibility in two different
ways. First, Table 2 contains the p-values of a Wald test for parallel trends,
where the assumption of parallel trends in the pre-tax period is tested under
the null hypothesis that they are parallel. Notably, the p-values derived from
this approach do not raise concerns, as we fail to reject the null hypothesis
of parallel trends, with the exception of butter in the expenditure outcome.
Second, the results of pseudo treatment effects for the pre-tax periods are
shown in Appendix C. Reassuringly, the uniform confidence intervals in all
pre-tax periods contain zero, offering further evidence in support of the
parallel trends assumption for all product categories and all outcomes.
Altogether, inspection of the pre-tax trends lends strong support of the
plausibility of parallel trends between Danish and Northern-German households
in the tax period.

Finally, we address the overlap assumption, which is commonly tested by
ensuring sufficient overlap in the treated and control units’ propensity score
distributions. Histograms displaying the fitted propensity scores for the
Danish and Northern-German households can be found in Appendix B. The
histograms show good overlap.

In conclusion, we do not find any substantial empirical evidence against the
plausibility of the assumptions underlying our DID identification strategy.

###  4.2 The causal effect of the fat tax on consumer responses during the tax
period

The results depicted in Panel A of Table 2 reveal a statistically significant
decrease in the consumption of cheese, liver sausage, and salami during the
tax period. Specifically, there is an average reduction of approximately 13%
for cheese, 11% for liver sausage, and 12% for salami compared to the pre-tax
quarter. While we do not observe significant changes in expenditure for cheese
and salami, there was a noteworthy 13.75% (about 0.8 Euro) reduction in
expenditure for liver sausage, as illustrated in Table 2, Panel B. Conversely,
we observe a substantial increase in expenditure for butter (2.34 Euro,
25.2%), cream (0.7 Euro, 14.49%), margarine (0.8 Euro, 15.42%), and sour cream
(0.27 Euro, 16%) despite the absence of any discernible impact on the
consumption of these products.

Table 2: The causal effect of the Danish fat tax on the average quarterly
consumption and expenditure during the tax period (October 2011 to December
2012).

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Quarterly average weight consumed in
gr/ml Danish fat tax (ATT) $-56.891$ 73.292 $-351.109^{*}$ 27.663
$-120.925^{*}$ 114.433 $-66.774^{**}$ 27.768 (se) (35.788) (78.927) (127.263)
(65.761) (47.718) (101.072) (36.823) (36.351) % change -10.07% 4.81% -13.05%
2.01% -11.07% 6.24% -12.10% 4.85% obs. 29,645 40,929 32,129 39,274 31,246
38,687 31,243 36,121 p-val. pre-trend 0.273 0.384 0.344 0.455 0.846 0.772
0.963 0.208 Panel B: Quarterly average expenditure in Euro cents Danish fat
tax (ATT) -25.075 $234.879^{***}$ $-240.166$ $70.823^{**}$ $-81.437^{*}$
$84.643^{***}$ $-50.452$ $27.131^{*}$ (se) (26.216) (37.992) (105.520)
(19.589) (28.147) (22.041) (38.160) (10.413) % change -6.85% 25.20% -10.42%
14.49% -13.75% 15.42% -8.81% 16.03% obs. 29,645 40,929 32,129 39,274 31,246
38,687 31,243 36,121 p-val. pre-trend 0.653 0.000 0.505 0.748 0.929 0.603
0.921 0.075 Panel C: Quarterly average amount (in packages) consumed Danish
fat tax (ATT) -0.010 0.361 -0.304 -0.202 $-0.463$ $0.404$ -0.009 0.059 (se)
(0.160) (0.314) (0.398) (0.272) (0.199) (0.198) (0.233) (0.145) % change
-0.51% 6.01% -7.09% -6.19% -14.40% 10.39% -0.33% 4.77% obs. 29,645 40,929
32,129 39,274 31,246 38,687 31,243 36,121 p-val. pre-trend 0.987 0.557 0.249
0.954 0.984 0.795 0.977 0.512 Significance level: * $p<0.1$ ** $p<0.05$ ***
$p<0.01$. Standard errors clustered at unit level. % change compares the
estimated tax average to the pre-tax sample mean for Danish households. The
estimates are obtained using the doubly robust DID approach, controlling for
age of head of household, number of children under 15, gender, ISCED, income
level, and household size.

Notably, there is no observed statistically significant impact on the quantity
of packages purchased across all products. Nevertheless, the observed decrease
in consumption of cheese, liver sausage, and salami hints at a potential
adjustment by producers who may have responded to the imposed tax by reducing
the package size of these three items. In contrast, our results suggest that
the package sizes for butter, cream, margarine, and sour cream remained
unaltered, as there was no significant impact on either the number of packages
purchased or the weight consumed. At the same time, we observe a significant
rise in expenditure, possibly driven by elevated prices and a low elasticity
of demand for these particular products.

In summary, our findings indicate that the tax successfully achieved the
intended reduction in the consumption of cheese, liver sausage, and salami
during the tax period. However, it did not yield the desired effect on the
consumption of the other products under examination. Notably, the tax led to
increased consumer expenditure on butter, cream, margarine, and sour cream
without significantly affecting the consumption of these particular products.

###  4.3 The causal effect of the fat tax on consumer responses after its
abolishment

Table 3: The causal effect of the Danish fat tax on the average quarterly
consumption and expenditure during the two years after abolishment of the tax
(January 2013 to December 2014), using the final tax period (October 2012 to
December 2012) as reference period.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Quarterly average weight consumed in
gr/ml Danish fat tax (ATT) $124.442^{**}$ 5.298 $557.856^{***}$ -35.433
$195.790^{***}$ 72.082 $131.118^{**}$ 78.072 (se) (42.177) (86.445) (115.098)
(89.103) (50.680) (98.307) (40.289) (40.092) % change 23.43% 0.33% 22.52%
-2.54% 19.36% 4.20% 25.39% 13.17% obs. 22,354 28,507 23,735 27,544 23,315
27,085 23,312 25,831 p-val. pre-trend 0.310 0.000 0.296 0.335 0.334 0.018
0.414 0.564 Panel B: Quarterly average expenditure in Euro cents Danish fat
tax (ATT) 57.635 $-171.538^{***}$ $415.404^{***}$ -24.235 $122.264^{**}$
$-67.918^{**}$ $136.449^{***}$ 7.812 (se) (29.636) (42.352) (92.873) (26.516)
(33.875) (22.868) (38.423) (11.110) % change 15.85% -16.77% 19.19% -4.51%
22.67% -13.20% 25.21% 4.28% obs. 22,354 28,507 23,735 27,544 23,315 27,085
23,312 25,831 p-val. pre-trend 0.456 0.000 0.358 0.833 0.051 0.013 0.252 0.093
Panel C: Quarterly average amount (in packages) consumed Danish fat tax (ATT)
$0.430^{**}$ -0.017 $0.938^{*}$ 0.145 $0.782^{**}$ 0.144 $0.654^{**}$ 0.341
(se) (0.158) (0.340) (0.393) (0.327) (0.255) (0.187) (0.234) (0.175) % change
21.53% -0.26% 21.14% 4.47% 26.19% 3.87% 23.69% 26.58% obs. 22,354 28,507
23,735 27,544 23,315 27,085 23,312 25,831 p-val. pre-trend 0.128 0.000 0.914
0.956 0.577 0.002 0.881 0.495 Significance level: * $p<0.1$ ** $p<0.05$ ***
$p<0.01$. Standard errors clustered at unit level. % change compares the
estimated tax average to the pre-tax sample mean for Danish households. The
estimates are obtained using the doubly robust DID approach, controlling for
age of head of household, number of children under 15, gender, ISCED, income
level, and household size.

Table 4: The causal effect of the Danish fat tax on the average quarterly
consumption and expenditure during the two years after abolishment of the tax
(January 2013 to December 2014), using the pre-tax period (January 2011 to
March 2011) as reference period.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Quarterly average weight consumed in
gr/ml Danish fat tax (ATT) 0.586 $256.953^{**}$ 31.182 117.048 1.505
$325.944^{**}$ 5.839 $90.648^{*}$ (se) (35.004) (72.408) (129.746) (71.148)
(46.676) (92.464) (37.856) (35.617) % change 0.10% 16.05% 1.15% 8.31% 0.14%
18.05% 1.05% 15.41% obs. 33,510 45,295 36,043 43,648 35,160 42,954 35,175
40,299 p-val. pre-trend 0.182 0.362 0.268 0.369 0.859 0.853 0.959 0.138 Panel
B: Quarterly average expenditure in Euro cents Danish fat tax (ATT) 0.024
$162.860^{***}$ 12.967 $57.764^{**}$ -33.561 39.009 21.002 $37.947^{**}$ (se)
(26.678) (38.977) (105.804) (19.152) (30.410) (21.705) (38.239) (10.451) %
change 0.01% 16.92% 0.56% 11.39% -5.73% 7.66% 3.59% 21.65% obs. 33,510 45,295
36,043 43,648 35,160 42,954 35,175 40,299 p-val. pre-trend 0.516 0.000 0.235
0.668 0.950 0.734 0.905 0.050 Panel C: Quarterly average amount (in packages)
consumed Danish fat tax (ATT) 0.175 $1.348^{***}$ 0.586 0.058 -0.001
$0.916^{***}$ $0.597^{*}$ 0.285 (se) (0.150) (0.294) (0.368) (0.254) (0.196)
(0.210) (0.222) (0.145) % change 8.53% 20.86% 12.83% 1.74% -0.04% 23.65%
21.17% 22.28% obs. 33,510 45,295 36,043 43,648 35,160 42,954 35,175 40,299
p-val. pre-trend 0.982 0.472 0.282 0.939 0.991 0.797 0.989 0.481 Significance
level: * $p<0.1$ ** $p<0.05$ *** $p<0.01$. Standard errors clustered at unit
level. % change compares the estimated tax average to the pre-tax sample mean
for Danish households. The estimates are obtained using the doubly robust DID
approach, controlling for age of head of household, number of children under
15, gender, ISCED, income level, and household size.

The fat tax was abolished in January 2013. We study the two years after the
abolishment to gain insight into potential habit formation induced by the tax.
We present the effects of the abolishment of the fat tax on consumption in
comparison to the final quarter of the tax period in Table 3 and in comparison
to the pre-tax period in Table 4.

For cheese, liver sausage, and salami, we find that consumption increased
after the tax was abolished, as shown in Panel A of Table 3. This increase
brought the consumption of these products back to pre-tax levels, as indicated
in Panel A of Table 4. Regarding salami, we observe that the abolishment of
the tax resulted in a consistent reduction in packaging size, with a 23.69%
increase in the average number of packages purchased. However, this change had
no significant effect on the average consumption in terms of weight. Overall,
despite the short-term reduction in consumption observed during the tax
period, these effects seemed to have disappeared after the tax was abolished.
This is in line with Allais et al.,  (2010), who found that long-term effects
can take seven years to establish, as mentioned in the literature review.

Panel A of Table 4 shows that butter, margarine and sour cream experienced a
substantial increase in consumption after the abolishment of the tax in
comparison to the pre-tax period as well as an overall increase in expenditure
and average number of packages purchased (see Panel B and C).

In summary, the tax failed in creating any long-term reductions in consumption
of the targeted products, and its abolishment induced a short-term increase in
consumption for some of these products.

###  4.4 Price mechanism

Since the tax was imposed on producers, it remains unclear to what extent
consumers experienced price increases for the taxed products. In this section,
we aim to estimate the causal effect of the tax on the prices paid for each
product. One limitation of this approach is that we can only observe prices
for products that have been purchased, not the overall price level. However,
the results presented in Table 5 provide us with insights into whether
consumers encountered higher prices for the products they chose to purchase.

Table 5 shows that prices for butter, cream, margarine, and sour cream
significantly increased in response to the tax by 23.44%, 10.58% , 11.35%, and
12.31%, respectively. These price increases are lower than those anticipated
by the Danish Tax Committee, who anticipated increases in consumer prices up
to 35% for animal fat, 33% for dairy, and 24% for margarine. The price
increases to a large extent explain our previous finding that consumer
expenditure on these products increased by 16%, 22%, and 10%, respectively.
The rise in prices corresponded with a notable expenditure increase for both
butter and margarine products. Evidently, consumers were willing to pay higher
prices for these particular products. The price increase persisted also after
the tax was abolished for butter and sour cream, while we find an overall
decrease for margarine. We do not find a significant increase in price for
other products during the tax period. Interestingly, we observe a substantial
decrease in liver sausage prices of about 18%.

Table 5: The causal effect of the Danish fat tax on the quarterly average
price paid per 100 units.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Tax period versus pre-tax quarter Danish
fat tax (ATT) -1.918 $14.935^{***}$ $3.610$ $3.968^{***}$ -3.076 $3.566^{***}$
1.976 $3.863^{***}$ (se) (2.916) (0.558) (1.660) (0.408) (2.478) (0.509)
(3.292) (0.586) % change -2.81% 23.44% 3.92% 10.58% -4.95% 11.35% 1.65% 12.31%
obs. 16,863 32,189 27,511 27,735 22,726 28,682 20,925 19,590 p-val. pre-trend
0.554 0.000 0.683 0.009 0.718 0.441 0.833 0.000 Panel B: Post-tax period
versus last taxed quarter Danish fat tax (ATT) -3.444 $-10.671^{***}$ -2.434
$-1.701^{***}$ -3.917 $-4.054^{***}$ -3.465 $-1.898^{***}$ (se) (2.894)
(0.676) (1.996) (0.474) (2.716) (0.569) (3.595) (0.530) % change -4.82%
-15.79% -2.58% -4.18% -6.27% -13.03% -2.92% -5.83% obs. 12,568 22,942 19,930
19,452 16,170 19,230 15,208 13,678 p-val. pre-trend 0.787 0.000 0.489 0.000
0.538 0.032 0.533 0.000 Panel C: Post-tax period versus pre-tax quarter Danish
fat tax (ATT) -6.734 $2.039^{**}$ 0.086 -0.093 $-11.091^{***}$ $-1.483^{**}$
-5.631 $2.585^{***}$ (se) (2.889) (0.583) (1.644) (0.371) (2.414) (0.484)
(3.351) (0.572) % change -9.67% 3.22% 0.09% -0.24% -17.95% -5.01% -4.73% 8.15%
obs. 19,235 36,058 31,104 30,979 25,609 31,466 23,729 21,739 p-val. pre-trend
0.723 0.000 0.757 0.009 0.615 0.557 0.820 0.000 Significance level: * $p<0.1$
** $p<0.05$ *** $p<0.01$. Standard errors clustered at unit level. % change
compares the estimated tax average to the pre-tax sample mean for Danish
households. The estimates are obtained using the doubly robust DID approach,
controlling for age of head of household, number of children under 15, gender,
ISCED, income level, and household size.

Overall, we do not find a significant increase in prices for products where we
observed a short run decrease in consumption. Since we use prices of products
purchased by households, the effect on prices might actually be downward
biased, because households might decide not to buy when confronted with
excessively high prices.

##  5 Robustness checks

In this section, we conduct several robustness checks to assess the
reliability of the main findings presented in the previous section, addressing
the potential concerns with respect to our identification strategy stated in
Section 3.2. First, the issue of potential cross-border shopping merits
attention, as it might obscure the effect of the tax. To investigate potential
cross-border shopping effects, we exclude Southern-Danish households from
South/West Jutland and Funen, focusing on Danish households that are less
likely to engage in cross-border shopping and hence fully subject to the tax.
Interestingly, the results in Table 11 in Appendix D.1 exhibit similar
patterns as our main results, indicating that changes in consumption behavior
were similar for Danish households that were able to cross-border shop
compared to Danish households that did not have this opportunity. Note that in
our main results, the unintended effect of cross-border shopping is
incorporated as we do include purchases made abroad.

Second, we consider concerns surrounding disparities in Danish and Northern-
German household characteristics and assess whether differences in household
characteristics between Danish and Northern-German households produced the
effects of our main results in Section 4. To gauge the influence of the
covariates, we contrast the treatment effects obtained under the conditional
parallel trends assumption with those derived under the unconditional parallel
trends assumption. If doubly robust DID estimates based on the conditional
parallel trends assumption resemble the estimates based on the unconditional
parallel trends assumption, this would indicate that covariates contain
limited information on consumer behavior trends and are unlikely to drive the
results in Section 4. For brevity, we only included the results for the weight
outcome, but similar observations apply to the other two main outcomes.
Interested readers may obtain the complete set of results upon request.
Reassuringly, Figure 39 in Appendix D.2 display extremely similar trends
compared to the figures in Appendix C. This suggests that covariates have
minimal influence on the trends. Upon comparing the results, it becomes
evident that, unsurprisingly, incorporating covariates enhances precision.

##  6 Heterogeneity analysis by income levels

Criticisms of the tax being regressive suggest that low-income households may
be disproportionately affected compared to wealthier ones. Groceries
constitute a larger proportion of the income of poorer households, making them
disproportionately affected by the tax if they do not adjust their consumption
behavior (Allais et al., , 2010; Zhen et al., , 2011). High-income households,
on the other hand, might respond more to health incentives rather than
monetary ones. Understanding how the tax affects different income groups is
vital for targeted policy improvements, and extrapolating the tax’s
applicability to other countries.

(a) Average quarterly weight consumed (gr/ml).

(b) Average quarterly expenditure in Euro cents.

(c) Average quarterly number of packages.

Figure 10: Doubly robust DID estimates of the causal effect of the Danish fat
tax during the tax period (October 2011 to December 2012) for low, medium and
high-income households. Low-income households are defined as households with
very low income or low income. High-income households are defined as
households with very high income or high income. 95% confidence intervals in
red.

(a) Average quarterly weight consumed (gr/ml).

(b) Average quarterly expenditure in Euro cents.

(c) Average quarterly number of packages.

Figure 11: Doubly robust DID estimates of the causal effect of the Danish fat
tax during the post-tax period (January 2013 to December 2014) compared to the
pre-tax quarter (January 2011 to March 2011) for low, medium and high-income
households. Low-income households are defined as households with very low
income or low income. High-income households are defined as households with
very high income or high income. 95% confidence intervals in red.

In order to investigate potential heterogeneity in the effects of the Danish
fat tax, we estimate the effect in two different subsets of the data. First,
we estimate the effects of the tax on our three consumption outcomes in the
subsample of households who have a low or very low income (refer to Section
3.1 to see how we define income categories). Second, we estimate the same
effects but for households who have high or very-high income. The results are
presented in Figure 10. Interestingly, Panel (a) of Figure 10 shows a
significant reduction in bacon consumption for low-income households, for whom
we also observe a significant decrease in consumption of cheese and liver
sausage. The effects are not statistically significant for these products, for
neither medium-income nor high-income households. Moreover, we find that low-
income and medium-income households also reduced their expenditure on cheese
and liver sausage, as shown in Panel (b) of Figure 10.

Similar to the main analysis, we observe an uptick in expenditure for both
butter and margarine. Notably, the increase is fairly similar between
households with high and low incomes, but not statistically significant for
medium-income households. This means that low-income households were
disproportionately affected by the tax.

The results in Figure 11 show that, after the abolishment of the tax, the
increase in butter, cream, margarine, and sour cream consumption is largely
driven by high-income households, with relatively weaker effects on low-income
households. Interestingly, we find a decrease in the consumption of bacon only
for low-income households. However, the effect is marginally
significant.131313For the interested reader, Figure 40 in Appendix E provides
the heterogeneity results for the abolishment effects when comparing the post-
tax period to the last taxed quarter.

##  7 Conclusion

The present study has been the first to estimate the causal effect of the
Danish tax targeting saturated fats on consumer behavior and expenditure,
employing a valid and culturally-close geographic control group consisting of
Northern-German households, located in Schleswig-Holstein and Hamburg. Our
analysis is based on Callaway and Sant’Anna, ’s (2021) doubly robust DID
estimators that allow to flexibly include observed covariates and provide
confidence intervals that account for multiple hypothesis testing. The
longitudinal nature of our data allowed us to gain valuable insights into the
evolution of causal effects over time. To ensure the validity of our findings,
we studied the plausibility of the identifying assumptions, most crucially the
parallel trends and no anticipation assumption, and performed robustness
checks with respect to cross-border shopping.

Distinguishing itself as the first to investigate expenditure patterns, tax
abolishment effects, and sustained habit formation post-tax, our research
contributes a comprehensive analysis of the policy’s implications. Findings on
the purchased weight, the number of packages purchased, and the expenditure
paint an interesting picture of the effect of the tax on consumer behavior.
Perhaps the most relevant finding is that the tax achieved a reduction in
consumption of bacon, cheese, and liver sausage, and salami ranging between
11% and 13%. For bacon, cheese, and liver sausage, the effect of the tax was
mainly driven by low-income consumers. This indicates that the tax aligned
with its goal of reducing the intake of saturated fats from these products in
the population that might benefit most from a reduction. It is important to
emphasize, however, that it is unclear whether these products are substituted
by healthier alternatives, offering an important avenue for future research.
After the tax was repealed, these effects are no longer statistically
significant.

The second most significant finding to emerge from this study is the unchanged
consumption of margarine, butter, sour cream, and cream, while expenditure on
these products increased between 14% and 25%. Interestingly, the increase in
expenditure for these products is similar for low and higher-income
households, which implies the tax’s regressivity with respect to these
products. There are various reasons for this observation, and to improve the
design of fat taxes in future, more research is needed to understand why low-
income consumers do not substitute away from these products. Exploring the
mechanisms behind observed consumer responses is a promising avenue for future
research. For instance, gaining information on final consumer characteristics,
rather than household characteristics, could provide deeper insights.

Previous studies exclusively focused on the tax’s implementation phase,
neglecting post-tax dynamics. Our study, however, sheds light on intriguing
post-tax patterns. Notably, the removal of the tax led to varied effects
across different product categories. An important finding showed elevated
quantities consumed of products high in saturated fat content, even surpassing
pre-tax levels in some cases. This raises concerns that the process of
implementing and abolishing the tax might have exacerbated unfavorable
consumer behavior. For instance, we did observe persisting elevated
consumption patterns for butter, margarine, and sour cream in the two years
post-tax, indicating that there might be some tax-induced habit formation with
respect to this product, especially for high-income households. In future
research, it could be interesting to further investigate the longer-term
impact (i.e., the impact beyond the year 2014) of the tax’s abolishment.

Our examination of price dynamics has revealed that not all price changes are
passed on to the consumers and reflected in the store prices. Among certain
product categories (butter, cream, margarine, and sour cream), we noted price
increases, while other products displayed no significant price alterations.
The abolishment of the tax again resulted in divergent price changes. While
prices decreased for some products, such as margarine and liver sausage,
others, like butter and sour cream, exhibited persistent elevated prices.

Understanding these effects and the underlying mechanisms is imperative for
policymakers. A food tax can be used as a tool to improve public health by
influencing consumers’ behavior while increasing revenue from tax. Taken
together, our findings do not support strong recommendations to impose a broad
tax on saturated fat, as the patterns in consumer responses vary heavily
across products. To optimize the design of a tax on saturated fats, more
research is required to understand the mechanisms driving consumer choices and
whether substitutions towards healthier alternatives are made. Equally
important is the consideration of the policy’s impact on low-income
households, as our results clearly show that they are disproportionately
affected by the tax.

At present, several questions persist regarding the impact of the fat tax.
While our analysis considered specific aggregated food categories, an
intriguing avenue for future research involves studying substitution dynamics
within these product categories. Unfortunately, the study’s scope was
constrained by the lack of detailed data on the fat percentages of products
within these categories. Access to data on fat percentages could also enable a
direct comparison between observed price changes and anticipated adjustments
if the tax were entirely shifted to consumers, providing a more thorough
analysis of the tax’s pricing dynamics. Furthermore, more research is required
to determine the implications of the tax on health outcomes. An extended
investigation into health-related consequences, such as potential effects on
BMI, would offer a more comprehensive understanding of the tax’s potential
long-term health implications. Finally, understanding the impact of health
messaging induced by the fat tax and how the public debate shaped attitudes
toward products high in saturated fat is a crucial aspect that warrants
further study.

## References

  * Allais et al., (2010) Allais, O., Bertail, P., and Nichèle, V. (2010).  The Effects of a Fat Tax on French Households’ Purchases: A Nutritional Approach.  American Journal of Agricultural Economics, 92(1):228–245.
  * (2) Bødker, M., Pisinger, C., Toft, U., and Jørgensen, T. (2015a).  The Danish Fat Tax - Effects on Consumption Patterns and Risk of Ischaemic Heart Disease.  Preventive Medicine, 77:200–203.
  * (3) Bødker, M., Pisinger, C., Toft, U., and Jørgensen, T. (2015b).  The Rise and Fall of the World’s First Fat Tax.  Health Policy, 119(6):737–742.
  * Callaway and Sant’Anna, (2021) Callaway, B. and Sant’Anna, P. H. (2021).  did: Difference in Differences.  R package version 2.1.2.
  * Callaway and Sant’Anna, (2021) Callaway, B. and Sant’Anna, P. H. (2021).  Difference-in-Differences with Multiple Time Periods.  Journal of Econometrics, 225(2):200–230.
  * Cawley et al., (2019) Cawley, J., Thow, A. M., Wen, K., and Frisvold, D. (2019).  The Economics of Taxes on Sugar-Sweetened Beverages: A Review of the Effects on Prices, Sales, Cross-Border Shopping, and Consumption.  Annual Review of Nutrition, 39:317–338.
  * Chouinard et al., (2007) Chouinard, H. H., Davis, D. E., LaFrance, J. T., and Perloff, J. M. (2007).  Fat Taxes: Big Money for Small Change.  In Forum for Health Economics & Policy, volume 10. De Gruyter.
  * Ecorys, Euromonitor and IDEA, DTI, (2014) Ecorys, Euromonitor and IDEA, DTI (2014).  Food Taxes and Their Impact on Competitiveness in the Agri-Food Sector: Annexes to the Main Report.  Available online: www.ec.europa.eu/DocsRoom/documents/6150/attachments/1/translations/en/renditions/pdf (accessed on November 5, 2021).
  * Eilander et al., (2015) Eilander, A., Harika, R. K., and Zock, P. L. (2015).  Intake and Sources of Dietary Fatty Acids in Europe: Are Current Population Intakes of Fats Aligned with Dietary Recommendations?  European Journal of Lipid Science and Technology, 117(9):1370–1377.
  * Gortmaker et al., (2011) Gortmaker, S. L., Swinburn, B. A., Levy, D., Carter, R., Mabry, P. L., Finegood, D. T., Huang, T., Marsh, T., and Moodie, M. L. (2011).  Changing the Future of Obesity: Science, Policy, and Action.  The Lancet, 378(9793):838–847.
  * Hooper et al., (2020) Hooper, L., Martin, N., Jimoh, O. F., Kirk, C., Foster, E., and Abdelhamid, A. S. (2020).  Reduction in Saturated Fat Intake for Cardiovascular Disease.  Cochrane Database of Systematic Reviews, 2020(8).
  * Jensen and Smed, (2013) Jensen, J. D. and Smed, S. (2013).  The Danish Tax on Saturated Fat–Short Run Effects on Consumption, Substitution Patterns and Consumer Prices of Fats.  Food Policy, 42:18–31.
  * Jensen et al., (2016) Jensen, J. D., Smed, S., Aarup, L., and Nielsen, E. (2016).  Effects of the Danish Saturated Fat Tax on the Demand for Meat and Dairy Products.  Public Health Nutrition, 19(17):3085–3094.
  * Konkurrence- og Forbrugerstyrelsen, (2014) Konkurrence- og Forbrugerstyrelsen (2014).  Fedtafgiftens Afskaffelse. Betydning for Forbrugerpriserne? Available online: https://www.kfst.dk/media/2799/20140626-fedtafgiftens-afskaffelse-betydning-for-forbrugerpriserne.pdf (accessed on October 1, 2021).
  * Lhachimi et al., (2020) Lhachimi, S. K., Pega, F., Heise, T. L., Fenton, C., Gartlehner, G., Griebler, U., Sommer, I., Bombana, M., and Katikireddi, S. V. (2020).  Taxation of the Fat Content of Foods for Reducing their Consumption and Preventing Obesity or Other Adverse Health Outcomes.  Cochrane Database of Systematic Reviews, 2020(9).
  * Lusk and Schroeter, (2012) Lusk, J. L. and Schroeter, C. (2012).  When Do Fat Taxes Increase Consumer Welfare?  Health Economics, 21(11):1367–1374.
  * Nordström and Thunström, (2009) Nordström, J. and Thunström, L. (2009).  The Impact of Tax Reforms Designed to Encourage Healthier Grain Consumption.  Journal of Health Economics, 28(3):622–634.
  * Powell et al., (2013) Powell, L. M., Chriqui, J. F., Khan, T., Wada, R., and Chaloupka, F. J. (2013).  Assessing the Potential Effectiveness of Food and Beverage Taxes and Subsidies for Improving Public Health: A Systematic Review of Prices, Demand and Body Weight Outcomes.  Obesity Reviews, 14(2):110–128.
  * Roth et al., (2020) Roth, G. A., Mensah, G. A., Johnson, C. O., Addolorato, G., Ammirati, E., Baddour, L. M., Barengo, N. C., Beaton, A. Z., Benjamin, E. J., Benziger, C. P., et al. (2020).  Global Burden of Cardiovascular Diseases and Risk Factors, 1990-2019: Update from the GBD 2019 Study.  Journal of the American College of Cardiology, 76(25):2982–3021.
  * Roth et al., (2023) Roth, J., Sant’Anna, P. H., Bilinski, A., and Poe, J. (2023).  What’s Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature.  Journal of Econometrics, 235(2):2218–2244.
  * Sant’Anna and Zhao, (2020) Sant’Anna, P. H. and Zhao, J. (2020).  Doubly Robust Difference-in-Differences Estimators.  Journal of Econometrics, 219(1):101–122.
  * Smed, (2008) Smed, S. (2008).  Empirical Studies on Health, Information, and Consumer Behavior.  Copenhagen: University of Copenhagen, Department of Economics.
  * Smed, (2012) Smed, S. (2012).  Financial Penalties on Foods: The Fat Tax in Denmark.  Nutrition Bulletin, 37(2):142–147.
  * Smed et al., (2016) Smed, S., Scarborough, P., Rayner, M., and Jensen, J. (2016).  The Effects of the Danish Saturated Fat Tax on Food and Nutrient Intake and Modelled Health Outcomes: An Econometric and Comparative Risk Assessment Evaluation.  European Journal of Clinical Nutrition, 70(6):681–686.
  * Vallgårda et al., (2015) Vallgårda, S., Holm, L., and Jensen, J. D. (2015).  The Danish Tax on Saturated Fat: Why It Did Not Survive.  European Journal of Clinical Nutrition, 69(2):223–226.
  * World Health Organization, (2023) World Health Organization (2023).  Saturated Fatty Acid and Trans-Fatty Intake for Adults and Children: WHO Guideline.  WHO: Geneva, Switzerland. Available online: https://www.who.int/publications/i/item/9789240073630 (accessed on July 27, 2023).
  * Yaniv et al., (2009) Yaniv, G., Rosin, O., and Tobol, Y. (2009).  Junk-Food, Home Cooking, Physical Activity and Obesity: The Effect of the Fat Tax and the Thin Subsidy.  Journal of Public Economics, 93(5-6):823–830.
  * Zhen et al., (2011) Zhen, C., Wohlgenant, M. K., Karns, S., and Kaufman, P. (2011).  Habit Formation and Demand for Sugar-Sweetened Beverages.  American Journal of Agricultural Economics, 93(1):175–193.

##  Appendix A Data processing steps and descriptives

###  A.1 Data processing steps

Figure 12: Data flow chart with the number of observations per step for
constructing the Danish data set covering January 2009 to December 2014. For
each product category, a quarterly panel is created which includes households
that purchase some product from that category at least once between January
2009 and December 2014.

some text such that figure appears at top of page

Figure 13: Data flow chart with the number of observations per step for
constructing the Northern-German data set covering January 2009 to December
2014. For each product category, a quarterly panel is created which includes
households that purchase some product from that category at least once between
January 2009 and December 2014.

###  A.2 Summary statistics of pre-tax household characteristics

Table 6: Summary statistics of pre-tax socio-economic household characteristics for Danish and Northern-German households used in the main analysis in Table 2. Variable | Levels | $\mathbf{n_{\mathrm{Denmark}}}$ | $\mathbf{\%_{\mathrm{Denmark}}}$ | $\mathbf{n_{\mathrm{Germany}}}$ | $\mathbf{\%_{\mathrm{Germany}}}$ | $\mathbf{n_{\mathrm{all}}}$ | $\mathbf{\%_{\mathrm{all}}}$
---|---|---|---|---|---|---|---
Geographic region | Capital region | 575 | 21.3 | 0 | 0.0 | 575 | 12.8
| Zealand | 606 | 22.5 | 0 | 0.0 | 606 | 13.5
| Funen | 276 | 10.2 | 0 | 0.0 | 276 | 6.2
| North Jutland | 382 | 14.2 | 0 | 0.0 | 382 | 8.5
| East Jutland | 456 | 16.9 | 0 | 0.0 | 456 | 10.2
| South/West Jutland | 402 | 14.9 | 0 | 0.0 | 402 | 9.0
| Hamburg | 0 | 0.0 | 661 | 37.0 | 661 | 14.8
| Schleswig-Holstein | 0 | 0.0 | 1,123 | 63.0 | 1,123 | 25.1
Age (head of hh.) | Under 30 | 573 | 21.2 | 202 | 11.3 | 775 | 17.3
| 30-39 | 713 | 26.4 | 362 | 20.3 | 1,075 | 24.0
| 40-49 | 609 | 22.6 | 468 | 26.2 | 1,077 | 24.0
| 50-59 | 512 | 19.0 | 333 | 18.7 | 845 | 18.9
| 60-69 | 136 | 5.0 | 304 | 17.0 | 440 | 9.8
| 70 or over | 154 | 5.7 | 115 | 6.4 | 269 | 6.0
Children under 15 | 1 | 2,131 | 79.0 | 1,300 | 72.9 | 3,431 | 76.6
| 2 | 253 | 9.4 | 280 | 15.7 | 533 | 11.9
| 3 | 224 | 8.3 | 154 | 8.6 | 378 | 8.4
| 4 | 82 | 3.0 | 45 | 2.5 | 127 | 2.8
| 5 | 7 | 0.3 | 4 | 0.2 | 11 | 0.2
| 7 | 0 | 0.0 | 1 | 0.1 | 1 | 0.0
Gender (diary keeper) | Male | 599 | 22.2 | 737 | 41.3 | 1,336 | 29.8
| Female | 2,098 | 77.8 | 1,047 | 58.7 | 3,145 | 70.2
Education | 2 | 543 | 20.1 | 413 | 23.1 | 956 | 21.3
(ISCED level) | 3 | 1,011 | 37.5 | 666 | 37.3 | 1,677 | 37.4
| 5 | 392 | 14.5 | 175 | 9.8 | 567 | 12.6
| 6 | 578 | 21.4 | 211 | 11.8 | 789 | 17.6
| 7 | 173 | 6.4 | 319 | 17.9 | 492 | 11.0
Income (head of hh.) | Very low income | 837 | 31.0 | 608 | 34.1 | 1,445 | 32.2
| Low income | 547 | 20.3 | 344 | 19.3 | 891 | 19.9
| Medium income | 361 | 13.4 | 298 | 16.7 | 659 | 14.7
| High income | 451 | 16.7 | 214 | 12.0 | 665 | 14.8
| Very high income | 501 | 18.6 | 320 | 17.9 | 821 | 18.3
Household size | 1 | 981 | 36.4 | 455 | 25.5 | 1,436 | 32.0
| 2 | 1,045 | 38.8 | 689 | 38.6 | 1,734 | 38.7
| 3 | 274 | 10.2 | 327 | 18.3 | 601 | 13.4
| 4 | 286 | 10.6 | 226 | 12.7 | 512 | 11.4
| 5 | 92 | 3.4 | 62 | 3.5 | 154 | 3.4
| 6 | 18 | 0.7 | 20 | 1.1 | 38 | 0.8
| 7 | 1 | 0.0 | 4 | 0.2 | 5 | 0.1
| 8 | 0 | 0.0 | 1 | 0.1 | 1 | 0.0
Country | Denmark | 2,697 | 100.0 | 0 | 0.0 | 2,697 | 60.2
| Germany | 0 | 0.0 | 1,784 | 100.0 | 1,784 | 39.8
| all | 2,697 | 100.0 | 1,784 | 100.0 | 4,481 | 100.0

###  A.3 Summary statistics for the consumption and price outcomes during the
pre-tax and tax period

Table 7: This table contains the average total quarterly consumption per
household measured by the average weight and the average amount (counted by
number of packages) purchased before and after the tax introduction. It
further contains the average quarterly expenditure in Euro cents per household
and the average price paid per 100 units. The pre-tax period covers January
2009 to September 2011, and the tax period covers October 2011 to December
2012.

Product Outcome Pre-tax DK Tax DK $\Delta_{\text{DK}}$ Pre-tax DE Tax DE
$\Delta_{\text{DE}}$ Bacon Weight 562.67 486.51 -76.16 382.82 371.16 -11.66
Amount 1.89 1.80 -0.09 1.71 1.68 -0.03 Expenditure 359.84 331.98 -27.86 268.52
274.60 6.08 Price 67.74 71 3.26 79.93 85.08 5.15 Butter Weight 1,607.62
1,554.70 -52.92 1,507.32 1,483.01 -24.31 Amount 6.27 6.22 -0.05 6.13 6.00
-0.13 Expenditure 913.97 1,068.94 154.97 595.71 625.36 29.65 Price 59.65 72.36
12.71 41.06 43.41 2.35 Cheese Weight 2,717.23 2,146.68 -570.55 2,678.16
2,569.77 -108.39 Amount 4.24 3.76 -0.48 9.44 9.30 -0.14 Expenditure 2,306.91
1,912.95 -393.96 1,942.41 1,948.03 5.62 Price 90.50 95.79 5.29 74.37 78.13
3.76 Cream Weight 1,465.81 1,548.64 82.83 1,099.53 1,108.92 9.39 Amount 3.47
3.53 0.06 5.10 5.14 0.04 Expenditure 481.91 569.35 87.44 242.29 267.57 25.28
Price 34.95 39.24 4.29 23.03 25.14 2.11 Liver sausage Weight 1,138.17 977.71
-160.46 538.43 549.05 10.62 Amount 3.31 2.84 -0.47 2.87 2.89 0.02 Expenditure
613.31 530.67 -82.64 374.37 402.22 27.85 Price 61.47 63.19 1.72 75.21 79.22
4.01 Margarine Weight 1,842.00 1,693.05 -148.95 1,969.10 1,760.18 -208.92
Amount 3.87 3.63 -0.24 4.12 3.58 -0.54 Expenditure 511.17 570.55 59.38 368.39
350.34 -18.05 Price 29.35 34.78 5.43 19.87 21.29 1.42 Salami Weight 568.87
480.48 -88.39 490.46 477.05 -13.41 Amount 2.69 2.47 -0.22 3.12 3.02 -0.10
Expenditure 598.54 506.25 -92.29 465.39 466.93 1.54 Price 121.07 121.47 0.40
111.13 113.61 2.48 Sour cream Weight 613.76 604.32 -9.44 506.46 524.83 18.37
Amount 1.33 1.30 -0.03 2.47 2.55 0.08 Expenditure 176.17 186.28 10.11 127.57
132.27 4.70 Price 30.57 32.43 1.86 26.01 25.96 -0.05 DK indicates Danish
households and DE indicates Northern-German households. $\Delta$ indicates the
difference.

##  Appendix B Fitted propensity scores for overlap verification

Figure 14: Bacon.

Figure 15: Butter.

Figure 16: Cheese.

Figure 17: Cream.

Figure 18: Liver sausage.

Figure 19: Margarine.

Figure 20: Salami.

Figure 21: Sour cream.

Figure 22: Fitted propensity scores for the Danish and Northern-German
households obtained with a logistic regression controlling for the age of the
head of the household, the number of children under 15, gender, educational
attainment (ISCED), income level, and household size. The overlap assumption
requires a positive probability of being treated at every covariate value,
which seems to be valid for the cases depicted here.

##  Appendix C Evolution of tax effects over time

###  C.1 Bacon

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 23: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (1) of Tables 8 to 10.

###  C.2 Butter

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 24: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (2) of Tables 8 to 10.

###  C.3 Cheese

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 25: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (3) of Tables 8 to 10.

###  C.4 Cream

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 26: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (4) of Tables 8 to 10.

###  C.5 Liver sausage

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 27: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (5) of Tables 8 to 10.

###  C.6 Margarine

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 28: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (6) of Tables 8 to 10.

###  C.7 Salami

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 29: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (7) of Tables 8 to 10.

###  C.8 Sour cream

(a) Average quarterly weight consumed (gr/ml) per household.

(b) Average quarterly expenditure in Euro cents per household.

(c) Average quarterly number of packages per household.

Figure 30: Time average treatment effects, $ATT(q)$. The two vertical dashed
lines indicate the introduction and abolishment of the Danish fat tax,
respectively. Red estimates and simultaneous 95% confidence intervals for pre-
tax periods, and blue estimates and simultaneous 95% confidence intervals for
tax and post-tax periods, clustered at the household level. Under conditional
parallel trends, red estimates should be close to zero. Estimates are based on
the doubly robust Equation (2). Point estimates and standard errors are
reported in Column (8) of Tables 8 to 10.

Table 8: Dynamic treatment effects, $ATT(q)$, for quarterly average weight
consumed in gr/ml.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream $ATT_{2009-Q2}$ -69.13 -62.88 46.73 82.69 18.71
-155.22 -40.79 108.83 (se) (49.88) (108.28) (176.68) (99.88) (65.42) (132.20)
(59.06) (54.68) $ATT_{2009-Q3}$ 54.29 84.87 183.78 -61.67 30.27 42.89 44.76
-20.94 (se) (52.08) (107.77) (167.77) (98.53) (64.20) (130.56) (48.70) (53.75)
$ATT_{2009-Q4}$ -22.12 -26.10 -205.94 141.64 -45.28 54.04 -39.73 -18.69 (se)
(51.48) (95.67) (174.33) (98.05) (66.10) (127.49) (48.99) (47.99)
$ATT_{2010-Q1}$ 60.76 -16.14 207.32 -13.82 19.83 39.28 25.31 52.41 (se)
(55.35) (102.61) (163.09) (91.72) (65.27) (120.48) (48.77) (46.31)
$ATT_{2010-Q2}$ -51.84 -39.90 -53.03 -120.96 -38.56 66.58 -11.71 -21.71 (se)
(49.27) (93.27) (159.11) (87.73) (62.45) (125.17) (45.25) (43.43)
$ATT_{2010-Q3}$ -79.11 75.50 -183.07 31.91 -2.71 -157.30 -32.46 -5.21 (se)
(47.49) (98.59) (162.64) (93.02) (59.56) (119.92) (50.48) (44.93)
$ATT_{2010-Q4}$ 98.44 -91.26 -102.94 79.42 45.10 115.30 50.27 -64.08 (se)
(51.84) (109.75) (159.96) (98.80) (58.94) (129.49) (51.06) (45.00)
$ATT_{2011-Q1}$ -51.77 -154.55 53.94 -146.26 -93.69 -131.65 -23.13 7.46 (se)
(49.12) (111.97) (164.07) (89.22) (65.03) (141.44) (47.87) (52.78)
$ATT_{2011-Q4}$ -38.20 $-268.51^{*}$ -166.35 9.60 -69.14 -187.42 -50.96 -6.96
(se) (47.50) (104.34) (168.12) (87.73) (62.90) (133.87) (51.35) (48.24)
$ATT_{2012-Q1}$ -37.38 173.17 -374.49 -71.29 -118.45 176.18 -78.86 39.55 (se)
(43.02) (99.00) (163.40) (87.94) (62.85) (119.92) (51.04) (47.33)
$ATT_{2012-Q2}$ -10.37 183.92 -305.58 49.40 $-151.23^{*}$ 263.02 -10.87 25.81
(se) (42.52) (104.80) (170.58) (98.59) (59.75) (114.91) (48.00) (51.86)
$ATT_{2012-Q3}$ -67.53 84.42 $-432.40^{*}$ 14.28 -72.74 121.99 -61.36 76.91
(se) (47.41) (97.27) (151.62) (93.62) (60.68) (126.53) (48.25) (53.78)
$ATT_{2012-Q4}$ $-130.98^{*}$ 193.46 $-476.73^{*}$ 136.32 $-193.07^{*}$ 198.39
-131.82 3.52 (se) (50.01) (101.65) (161.99) (105.67) (64.65) (125.44) (53.77)
(56.03) $ATT_{2013-Q1}$ -35.86 203.63 -190.38 14.09 -117.06 138.68 -66.08
29.40 (se) (46.82) (113.12) (172.27) (113.39) (61.08) (127.11) (52.69) (47.13)
$ATT_{2013-Q2}$ -58.44 185.93 -252.18 4.00 -74.42 235.68 -74.10 4.28 (se)
(44.69) (102.01) (175.48) (109.42) (64.31) (128.40) (55.48) (49.50)
$ATT_{2013-Q3}$ -68.15 83.94 -240.44 99.26 -11.90 $321.98^{*}$ -32.42
$141.56^{*}$ (se) (47.15) (107.25) (166.99) (109.50) (65.00) (122.13) (47.74)
(53.04) $ATT_{2013-Q4}$ -4.98 $334.66^{**}$ -84.59 238.34 -107.59
$408.00^{**}$ -69.05 70.68 (se) (53.13) (122.59) (153.75) (108.01) (66.53)
(132.07) (53.49) (52.88) $ATT_{2014-Q1}$ 35.33 171.35 409.49 103.39
$199.76^{*}$ $347.68^{*}$ 66.88 60.76 (se) (50.44) (115.20) (177.38) (92.15)
(68.70) (134.56) (54.76) (50.25) $ATT_{2014-Q2}$ 66.08 $373.91^{**}$
$532.98^{**}$ 235.67 $177.27^{*}$ $382.61^{*}$ 71.63 138.02 (se) (49.66)
(107.07) (175.17) (100.61) (69.07) (126.95v (56.85) (57.16) $ATT_{2014-Q3}$
55.80 239.85 $571.49^{**}$ 114.29 91.23 270.31 108.76 132.13 (se) (49.77)
(106.39) (157.07) (97.36) (66.37) (136.47) (47.13) (54.38) $ATT_{2014-Q4}$
94.84 $406.58^{**}$ 310.35 193.80 90.84 $420.97^{**}$ 61.84 34.57 (se) (54.20)
(115.83) (185.60) (100.97) (68.32) (134.54) (54.52) (49.74)

Table 9: Dynamic treatment effects, $ATT(q)$, for quarterly average
expenditure in Euro cents.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream $ATT_{2009-Q2}$ -31.04 -21.88 -30.48 12.80 -1.18
-46.41 -33.34 33.05 (se) (36.93) (43.08) (146.61) (26.52) (42.08) (32.55)
(55.09) (14.97) $ATT_{2009-Q3}$ 35.68 -11.59 84.82 -23.96 31.27 0.78 28.94
-3.56 (se) (36.72) (40.63) (131.02) (25.57) (38.95) (30.84) (49.14) (13.45)
$ATT_{2009-Q4}$ -9.44 $-107.16^{*}$ -120.58 8.55 -44.16 13.18 -24.89 -9.83
(se) (36.81) (40.67) (124.97) (25.30) (38.11) (28.32) (51.16) (11.70)
$ATT_{2010-Q1}$ 23.51 -0.60 144.59 7.57 20.36 -2.28 21.20 4.65 (se) (35.88)
(45.53) (122.55) (27.11) (43.61) (28.83) (50.98) (12.32) $ATT_{2010-Q2}$
-32.24 -36.30 -59.73 -25.60 -9.85 31.54 -32.31 -4.75 (se) (35.10) (41.60)
(122.78) (27.02) (40.23) (28.84) (45.35) (12.76) $ATT_{2010-Q3}$ -39.12 30.61
-87.50 14.24 11.29 -39.83 -24.43 -2.91 (se) (31.80) (43.56) (134.71) (26.56)
(38.32) (27.40) (47.54) (13.14) $ATT_{2010-Q4}$ 48.00 22.71 -121.89 19.77
16.34 35.52 38.51 -17.71 (se) (37.24) (49.20) (135.13) (25.68) (40.65) (27.97)
(51.33) (12.49) $ATT_{2011-Q1}$ -23.38 $-142.21^{*}$ 1.83 -44.53 -49.93 -28.71
-33.84 1.34 (se) (35.96) (51.37) (142.75) (28.18) (43.26) (31.01) (48.12)
(13.06) $ATT_{2011-Q4}$ -25.36 5.41 -83.51 67.51 -25.99 11.52 -16.28 6.71 (se)
(37.24) (50.84) (136.30) (26.61) (38.77) (30.44) (51.35) (14.04)
$ATT_{2012-Q1}$ -14.43 $217.48^{***}$ -264.10 47.97 -87.25 $99.13^{**}$ -71.69
22.93 (se) (31.82) (48.47) (128.00) (28.60) (39.82) (28.47) (47.25) (13.76)
$ATT_{2012-Q2}$ 12.74 $324.86^{***}$ -248.37 $86.44^{*}$ $-98.86^{*}$
$117.37^{***}$ -2.84 31.84 (se) (29.84) (50.69) (130.35) (29.09) (38.18)
(28.61) (46.73) (13.39) $ATT_{2012-Q3}$ -38.24 $288.38^{***}$ -254.46 65.20
-45.69 $89.35^{**}$ -42.75 $46.27^{**}$ (se) (34.55) (49.14) (127.70) (25.62)
(40.62) (29.98) (50.34) (13.97) $ATT_{2012-Q4}$ -60.10 $338.27^{***}$
$-350.39^{*}$ $87.00^{*}$ $-149.40^{**}$ $105.84^{**}$ -118.69 27.90 (se)
(37.80) (56.32) (136.13) (30.84) (43.71) (28.86) (51.54) (14.39)
$ATT_{2013-Q1}$ -32.24 $163.85^{**}$ -179.63 32.94 $-101.29^{*}$ 28.18 -58.35
26.79 (se) (35.70) (53.27) (142.15) (29.79) (38.01) (29.36) (57.03) (13.87)
$ATT_{2013-Q2}$ -27.56 122.16 -219.92 16.71 -79.78 46.91 -57.49 34.10 (se)
(32.52) (55.70) (134.93) (30.63) (41.05) (28.91) (48.70) (13.90)
$ATT_{2013-Q3}$ -50.83 97.25 -145.88 56.58 -52.54 42.48 -18.54 $57.03^{***}$
(se) (36.92) (55.79) (139.93) (32.66) (36.21) (29.52) (49.46) (14.24)
$ATT_{2013-Q4}$ -19.64 125.40 -210.05 45.55 $-108.22^{*}$ 52.37 -61.48 31.53
(se) (35.77) (58.63) (136.76) (30.07) (42.44) (28.48) (51.21) (14.14)
$ATT_{2014-Q1}$ 27.81 51.14 329.05 69.48 54.22 32.90 87.94 22.87 (se) (37.11)
(57.51) (144.13) (29.96) (42.00) (25.59) (52.09) (15.57) $ATT_{2014-Q2}$ 52.16
$247.94^{***}$ $506.17^{**}$ $117.15^{**}$ 77.91 45.32 102.81 $52.46^{**}$
(se) (37.18) (53.58) (147.39) (31.26) (38.47) (29.46) (51.35) (16.24)
$ATT_{2014-Q3}$ 44.99 $233.53^{***}$ $480.43^{**}$ 63.47 73.67 17.97
$137.29^{*}$ $42.90^{*}$ (se) (34.80) (52.20) (139.03) (30.35) (42.48) (29.35)
(50.23) (15.62) $ATT_{2014-Q4}$ 63.37 $295.09^{***}$ 297.82 61.34 34.85 38.80
84.19 21.29 (se) (39.28) (55.95) (138.15) (31.53) (40.90) (28.42) (51.81)
(13.30)

Table 10: Dynamic treatment effects, $ATT(q)$, for quarterly average amount
(in packages) consumed.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream $ATT_{2009-Q2}$ -0.21 -0.28 -0.03 0.08 -0.02 -0.36
-0.33 0.18 (se) (0.26) (0.46) (0.52) (0.40) (0.28) (0.27) (0.31) (0.21)
$ATT_{2009-Q3}$ 0.15 0.37 0.66 -0.11 0.29 0.14 0.21 0.01 (se) (0.23) (0.40)
(0.51) (0.38) (0.27) (0.27) (0.29) (0.19) $ATT_{2009-Q4}$ -0.11 -0.12 -0.30
0.37 -0.23 0.07 -0.08 -0.05 (se) (0.25) (0.38) (0.48) (0.35) (0.27) (0.24)
(0.27) (0.19) $ATT_{2010-Q1}$ 0.16 -0.03 0.79 0.01 0.05 0.07 -0.02 0.23 (se)
(0.27) (0.41) (0.46) (0.35) (0.27) (0.26) (0.28) (0.18) $ATT_{2010-Q2}$ -0.11
-0.09 -0.08 -0.18 0.05 0.14 0.01 -0.04 (se) (0.25) (0.36) (0.48) (0.35) (0.26)
(0.26) (0.28) (0.18) $ATT_{2010-Q3}$ -0.06 0.33 -0.39 0.18 -0.04 -0.27 -0.12
-0.05 (se) (0.22) (0.36) (0.44) (0.34) (0.27) (0.25) (0.24) (0.19)
$ATT_{2010-Q4}$ 0.13 -0.38 -0.19 -0.03 0.13 0.21 0.23 -0.23 (se) (0.20) (0.41)
(0.47) (0.33) (0.29) (0.26) (0.26) (0.19) $ATT_{2011-Q1}$ -0.11 -0.54 0.25
-0.16 -0.10 -0.31 -0.11 0.02 (se) (0.23) (0.42) (0.51) (0.35) (0.29) (0.28)
(0.27) (0.18) $ATT_{2011-Q4}$ 0.07 -1.06 -0.56 -0.23 -0.33 -0.35 -0.02 -0.06
(se) (0.24) (0.44) (0.58) (0.32) (0.27) (0.28) (0.32) (0.19) $ATT_{2012-Q1}$
0.22 0.61 0.10 -0.24 -0.40 0.50 -0.12 0.21 (se) (0.19) (0.39) (0.50) (0.33)
(0.28) (0.26) (0.30) (0.19) $ATT_{2012-Q2}$ 0.07 0.70 -0.07 -0.33 -0.50
$0.74^{*}$ 0.17 0.01 (se) (0.20) (0.38) (0.47) (0.37) (0.27) (0.27) (0.30)
(0.21) $ATT_{2012-Q3}$ -0.12 0.41 -0.44 -0.10 -0.26 0.51 0.03 0.21 (se) (0.19)
(0.41) (0.47) (0.36) (0.27) (0.28) (0.33) (0.20) $ATT_{2012-Q4}$ -0.29
$1.14^{*}$ -0.55 -0.11 $-0.82^{*}$ 0.62 -0.10 -0.08 (se) (0.21) (0.42) (0.50)
(0.37) (0.30) (0.26) (0.30) (0.23) $ATT_{2013-Q1}$ 0.02 1.06 0.79 -0.43 -0.30
0.60 0.15 0.04 (se) (0.22) (0.48) (0.92) (0.44) (0.29) (0.26) (0.30) (0.20)
$ATT_{2013-Q2}$ -0.10 $1.14^{*}$ -0.19 -0.12 -0.20 $0.81^{**}$ 0.22 0.29 (se)
(0.20) (0.39) (0.49) (0.46) (0.29) (0.26) (0.31) (0.19) $ATT_{2013-Q3}$ -0.02
0.67 -0.20 0.23 -0.09 $0.87^{**}$ 0.28 0.46 (se) (0.23) (0.40) (0.54) (0.39)
(0.27) (0.25) (0.31) (0.21) $ATT_{2013-Q4}$ 0.22 $1.61^{**}$ 0.18 0.25 -0.44
$0.98^{**}$ 0.39 0.22 (se) (0.22) (0.50) (0.51) (0.37) (0.28) (0.28) (0.32)
(0.19) $ATT_{2014-Q1}$ 0.06 0.94 0.83 0.25 0.39 $1.03^{**}$ $0.83^{*}$ 0.23
(se) (0.22) (0.43) (0.51) (0.38) (0.32) (0.29) (0.30) (0.20) $ATT_{2014-Q2}$
0.24 $1.49^{**}$ 1.05 0.36 0.63 $1.00^{**}$ 0.77 0.36 (se) (0.21) (0.43)
(0.53) (0.36) (0.28) (0.29) (0.34) (0.21) $ATT_{2014-Q3}$ $0.67^{**}$
$1.46^{**}$ 1.02 0.13 0.32 0.65 $0.95^{**}$ 0.44 (se) (0.21) (0.43) (0.52)
(0.38) (0.30) (0.28) (0.30) (0.21) $ATT_{2014-Q4}$ 0.40 $1.76^{**}$ 0.86 0.19
0.16 $0.98^{**}$ 0.78 0.17 (se) (0.24) (0.47) (0.53) (0.37) (0.32) (0.29)
(0.32) (0.20)

##  Appendix D Robustness checks

###  D.1 Results when excluding Southern-Danish households

Table 11: The causal effect of the Danish fat tax on the average quarterly
consumption and expenditure per household during the tax period (October 2011
to December 2012). Southern-Danish households located in South/West Jutland
and Funen are excluded.

(1) (2) (3) (4) (5) (6) (7) (8) Bacon Butter Cheese Cream Liver sausage
Margarine Salami Sour cream Panel A: Quarterly total weight consumed in gr/ml
Danish fat tax (ATT) -51.848 56.607 $-417.038^{**}$ 6.714 -116.145 118.680
-58.025 18.472 (se) (39.344) (87.142) (122.812) (74.980) (51.767) (98.194)
(37.582) (40.566) % change -9.39% 3.72% -15.42% 0.50% -10.99% 6.93% -11.39%
3.30% obs. 23,844 34,792 26,029 33,376 25,232 32,761 25,186 30,678 nr. of
Danish hh. 1,690 1,892 1,841 1,700 1,813 1,647 1,752 1,520 nr. of
North.-German hh. 553 1,616 698 1,596 627 1,614 660 1,409 Panel B: Quarterly
total expenditure in Euro cents Danish fat tax (ATT) -25.626 $227.535^{***}$
$-294.203^{*}$ $63.645^{*}$ -75.550 $79.356^{**}$ -42.121 22.480 (se) (28.542)
(41.428) (110.695) (22.569) (31.786) (23.360) (37.458) (11.112) % change
-7.13% 24.07% -12.52% 13.16% -13.10% 15.28% -7.78% 13.42% obs. 23,844 34,792
26,029 33,376 25,232 32,761 25,186 30,678 nr. of Danish hh. 1,690 1,892 1,841
1,700 1,813 1,647 1,752 1,520 nr. of North.-German hh. 553 1,616 698 1,596 627
1,614 660 1,409 Panel C: Quarterly total amount (in packages) consumed Danish
fat tax (ATT) -0.058 0.278 -0.370 -0.272 -0.438 0.406 0.005 0.014 (se) (0.164)
(0.334) (0.383) (0.262) (0.205) (0.215) (0.207) (0.148) % change -3.09% 4.64%
-8.43% -8.41% -13.95% 11.19% 0.19% 1.13% obs. 23,844 34,792 26,029 33,376
25,232 32,761 25,186 30,678 nr. of Danish hh. 1690 1,892 1,841 1,700 1,813
1,647 1,752 1,520 nr. of North.-German hh. 553 1,616 698 1,596 627 1,614 660
1,409 Significance level: * $p<0.1$ ** $p<0.05$ *** $p<0.01$. Standard errors
are clustered at the household level. % change compares the estimated tax
average to the pre-tax sample mean for Danish households. The estimates are
obtained using the doubly robust DID approach, controlling for age of head of
household, number of children under 15, gender, ISCED, income level, and
household size.

###  D.2 Results under unconditional parallel trends for the weight outcome

Figure 31: Bacon.

Figure 32: Butter.

Figure 33: Cheese.

Figure 34: Cream.

Figure 35: Liver sausage.

Figure 36: Margarine.

Figure 37: Salami.

Figure 38: Sour cream.

Figure 39: Average quarterly weight consumed in gr/ml for the different
product categories. The figures depict the trends when unconditional parallel
trends is assumed and provide insights into the strength of the influence of
the household characteristics on the differences in trends between Northern-
German and Danish households. The trends are similar to those observed under
conditional parallel trends (see Appendix C), indicating that the household
characteristics are not strongly influencing differences in consumption trends
between Danish and Northern-German households.

##  Appendix E Supplemental material for the heterogeneity analysis

(a) Average quarterly weight consumed (gr/ml).

(b) Average quarterly expenditure in Euro cents.

(c) Average quarterly number of packages.

Figure 40: Doubly robust DID estimates of the causal effect of the Danish fat
tax during the post-tax period (January 2013 to December 2014) compared to the
last taxed quarter (October 2012 to December 2012) for low, medium and high-
income households. Low-income households are defined as households with very
low income or low income. High-income households are defined as households
with very high income or high income. 95% confidence intervals in red.