## Does reference dependence theory have to be taken

## into account in consumption models?

Thesis: Martijn van der Linden (10667725) Study track: Economics and Finance Supervisor: Stephan Jagau

Date: 30 January 2017

**Abstract: **

The main purpose of this study is to investigate whether reference dependence and loss aversion are significant factors in consumption theory. In the first part, the different consumption theories are discussed. Furthermore, there is shown how reference dependence and loss aversion can be significant in consumption theory. After the literature research two of the consumption models are tested on loss aversion, namely a Keynesian model and a Dynamic State General Equilibrium model. The working method can be described as follows: firstly, the models are tested without reference dependence and loss aversion, then loss aversion is taken into account. In the regressions there is made use of panel data on expenditures and income from the LISS panel from Center Data at the university of Tilburg. The hypothesis was that loss aversion plays a role in consumption theory. However, the Keynesian consumption model did not provide a significant measure for loss aversion. Although, the regression of the general consumption model did also not provide significant result. Conversely, the regression of the Dynamic State General Equilibrium model did provide significant results for loss aversion. However, the Dynamic State General Equilibrium model did make use of many assumptions. Moreover, heteroskedacity and multicollinearity have played a role in the regressions.

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### inhoud.

1. Introduction 2. Literature research

2.1 Macro-economic consumption models 2.2 Reference dependence theory

2.3 Dynamic Stochastic General Equilibrium model 3. Data analysis

3.1 Keynesian consumption model 3.2 Loss aversion in Keynesian model

3.3 Theoretical evidence reference dependence in a two period model 3.4 Dynamic Stochastic General equilibrium without reference dependence 3.5 Dynamic Stochastic General equilibrium with reference dependence 4. Conclusion and discussion

**1. Introduction **

In the past different models have tried to predict the level of future consumption. In the Macroeconomics book of Mankiw (2013) are five different types of models that describe and try to predict consumption. The last paragraph of the consumption chapter from the book of Mankiw (2013) is about consumption theory in behaviour economics. In the book of Mankiw (2013) the following is written: “More recently, economists have started to return to psychology. They have suggested that consumption decisions are not made by the ultrarational Homo economicus but by real human beings whose behaviour can be far from rational. This new subfield infusing psychology into economics is called behavioural

economics.” Becker (1962) agreed and wrote in his paper: “The utility approach to

households decisions has been extensively criticized ever since its conception, although both formulation and criticism have changed drastically over time. Present day, critics either deny that households maximized any function or that the maximized is consistent and transitive. In effect, they deny that households act “rationally” since rational behavior is now taken to signify maximization of a consistent and transitive function.”

Moreover, Kahneman and Tversky contributed to the field of behaviour economics with the reference depended and loss aversion theory (Tversky & Kahneman, 1991).

The question that is posed in this paper is if reference dependence and loss aversion are significant factors in consumption theory.

The hypothesis is that in the different consumption models reference dependence levels and loss aversion play a significant role. Due to the loss aversion the marginal

propensity of consumption is expected to differ between the state where income rises and the state where income lowers.

This paper looks at different consumption models in combination with the reference-point theory from Kahneman and Tversky (1991). There are already papers that try to compare consumption with reference point theory. For instance, Bowman (1999) did look at a two period saving model by making use of a reference level. Whereas Foellmi, Rosenblatt-Wisch & Schenk Hoppé (2011) did make use of a modified Ramsey model. Instead of the above stated models Campbell and Mankiw (1990) did make use of a direct relation of

income on the consumption level. Shea (1995b) extended this model by distinguishing between an income growth and decline to capture loss aversion. This study confronts the question whether empirical consumption data provides significant evidence for a model with reference dependence theory.

To find out which model or models predict best, I will look at the patterns of past consumptions and see if the data fits the different consumption models. The emphasis of this paper is about the reference level dependence of economic agents. Especially in the case of consumption compared to income. To look whether the case of loss aversion applies, two different models will be tested. Firstly, the relatively basic Keynesian consumption function is examined, then a more complex function, a Dynamic State General Equilibrium model, is investigated. The working method can by described in short by initially testing the general models and then taking reference dependence into account.

This paper will firstly explain the theory of the macro/micro-economic models (2.1). Then reference dependence (2.2) will be briefly discussed. Moreover, the Dynamic State General Equilibrium model of consumption will be discussed (2.3). After the theoretical part the data will be evaluated and the regressions will be done (3). Ultimately, the results will be discussed and there will be made a conclusion and some discussions (4).

2. **Literature research/ explanation of the theory and models**

**2.1. ** **Macro-economic consumption models**

The most basic model about consumption is the Keynesian consumption function which is often written as:

̅ ̅

In this model C stands for Consumption, Y for disposable income, ̅ is a constant and c is the marginal propensity to consume. (Mankiw, 2013) Following this model the total consumption is dependent on a constant level of consumption and a coefficient c which determines the rate of income that is consumed. Moreover, this model predicts (when income is above ̅ ) that when income rises, consumption rises with the marginal propensity to consume times the change in income:

A criticism regarding the model of Keyns is that economic agents do not only look at current consumption but also make a prediction about future income. Based on this prediction economic agents make rational choices about consumption in different period to maximize their utility. Their consumption level is constrained by their income; they face a budget constraint. (Mankiw, 2013).

When using a two period consumption model where households maximize their utility

function with respect to their budget constraint. The situation can be graphically described by:

The point where utility is maximized is where the slope of the utility function is tangent with the budget constraint. To receive this point one can take the derivatives of the different functions and equate both derivatives.

The graph above shows that if an economic agent spent all of his income that he earns in period 1, Y1, he can consequently consume his income that he earns in period 2, Y2. When an economic agents following this type of income spending he ends up in point y with the

corresponding utility curve U(Y1, Y2). But the graphic shows that it is more convenient for the economic agent to save a part of his consumption in period 1, receive interest of the amount of saving times the interest rate. Thereby, he is able to consume C2 in the second period with yields to a higher utility curve. Namely, point C* and the corresponding utility curve U(C1*, C2*).

In addition, Franco Modigliani made use of the fisher equation, in particular the assumption that there is life time income, to extend the knowledge about the consumption puzzle. Modigliani emphasized that income varies systematically over people’s lives and that saving allows consumers to move income from those times in life when income is high to

those times when it is low. He created the life time income hypothesis (Mankiw, 2013). According to him people want to smooth their consumption over time.

The life cycle income hypothesis of Modigliani (1986) states that consumption depends on both income and wealth according to the formula: where the parameter is the marginal propensity to consume out of wealth, and the parameter is the marginal propensity to consume out of labour income. Economic agents build up their wealth till their retirement. After retirement labour income is supposed to drop to zero and the build-up wealth will be consumed. In the paper of Modigliani (1986) myopia is a short subject of matter. Myopia means in this case that economic agents are time-inconsistent. They make their forecast about lifetime income, with this income they want to smooth their consumption over time. However, they diverse from this optimal path, because they want to consume today rather than in the future. The empirical results were not yet provided. Referring to the introduction where is written that economic behaviour is nowadays more developed. Interesting questions arise about myopia and other irrational behaviour. The irrationality factor where this paper focuses mainly on is Reference level dependence. The theory about reference dependence and loss aversion will be explained in the next chapter.

Moreover, Milton Friedman believed that there exists permanent income and besides a Transitory income exist, that is an error term. Following this, he suggested that current income t can be explained by the formula (Mankiw, 2013):

Friedman concluded that consumption can be explained by the formula (Mankiw,2013):

after all, Robert Hall (1979) stated that that the life cycle permanent income

hypothesis is widely accepted as the proper application of the theory of the consumer to the problem of dividing consumption between the present and the future. The life cycle random walk theory with trend is according to him widely accepted and used. Combining this with the rational expectation theory he concluded that consumption follows a random walk. (Mankiw, 2013). Following the random walk model from Hall (1978) consumption cannot be forecasted because the change in consumption is caused by an error term in formula:

(Campbell & Mankiw,1989)

### .

through housing and financial assets, on consumption by using a linear regression model. The model they use is as follows:

Foellmi et al. (2011) make use of a different model, they applied utility theory in the model. They made use of Dynamic Stochastic General Equilibrium model, in specific a Ramsey model with Euler equation. The theory behind the utility maximisation will be briefly shown below.

The utility function that Foellmi et al. (2011) used is a Constant Relative Risk Aversion (CRRA) function. This represents an economic agent with constant relative risk aversion. This utility function is concave and thus has an optimal point with the budget constraint. Constant relative risk function with respect to consumption can be shown by the formula:

( )

When one wants to measure the point where the utility function is tangent to the budget restriction one has to take both derivatives and equalise them. The derivative of the CRRA function is:

( )

When log linearizing this utility function, the function – ( ) arises.

The loss aversion factor can take different values, when the value is one the utility function is the linear version in consumption. Romer (1996) shows that how lower the risk aversion is how more willing economic agents are to shift consumption over time. This does not depend on the formerly briefly discussed loss aversion. In Foellmi et al. (2011) the loss aversion parameter is set to be 0.

Another feature of the CRRA function is that is decreasing if and

increasing if ; dividing by thus ensures that the marginal utility of consumption is always positive. (Romer, 1996)

On the other side of the optimization problem is the budget constraint. Consumption is constrained by the total money available. In the paper of Bowman (1999) consumption is

constrained by income. This will give the constraint of:

Income can be gained out of different categories, for example out of labour or out of capital. In this paper there will be likewise to Barnett and Allison (2005) assumed that there is no capital accumulation. So, in period 1 income either be consumed or stored in a savings account by the bank. On the money that is stored in the save account interest is gained. Then, the amount that can be consumed in period 2 is the labour income generated in period 2 and the savings multiplied by the interest rate. Another factor that has to be taken into account is the inflation, because when there is inflation, one can consume less in period two with respect to period one with the same.

**2.2. ** **Reference dependence theory **

Kahneman and Tversky (1991) start their paper with the assumption that the standard models of decision making assume that preferences do not depend on current assets. In their paper they are going to test if decisions depend on current assets. They test this with three different characteristics, namely: reference dependence, loss aversion and diminishing sensitivity. Loss aversion and reference dependence are as already written in the introduction the focus points of this paper.

The basic intuition that Kahneman and Tversky (1991) are concerning is that in a situation where the new outcomes are below the reference level a greater utility loss is

occurred than a similarly outcome but above the reference level. In the case of consumption, I assume that the reference level will be the current level of consumption, so a reduce in total consumption will lead to a greater loss in utility than a likewise rise in consumption.

when looking at a two period consumption model, there will be 2 dimensions. As already written a concave utility function will be used. For the explanation of reference theory and loss aversion the same graphs as Kahneman and Tversky(1991) will be provided. Instead of dimension one and two, the x and y as can be respectively seen as period one and period two. Firstly, the case of loss aversion will be shown, secondly reference dependence is covered.

aversion entails that a decision maker who is indifferent between x and y from t will prefer x over y from x, and y over x from y (Kahneman & Tversky, 1991). For the two periods of the consumption model one does not want to give up consumption in period one when he is in point x, the economic agent also does not want to give up consumption in period two when his initial point was y. The second that is concluded by Kahneman and Tversky (1991) is that the marginal utility when looking from point r is Ur whereas coming from point s Us will be the representative marginal utility.

Suppose that both are (from point t) indifferent between position x (high consumption first period, moderate consumption second period) and position y (high consumption second period, moderate consumption first period). Imagine now that both individuals move to new positions, which become their respective reference points; one individual moves to r (high consumption period one, low consumption period two), and the other moves to s (high second period consumption, low first period consumption). Loss aversion implies that the person who moved to r now prefers x, whereas the person who moved to s now prefers y, because they are reluctant to give up either consumption in period one or consumption in period two

(Kahneman and Tversky, 1991).

Kahneman and Tversky (1991) provide in their paper experimental validation for reference dependence and loss aversion.

**2.3. ** **Dynamic State General Equilibrium model **

A Dynamic State General Equilibrium model in macro-economics contains of different parts. The households, The firms and the government. In the section about the macro-economic consumption models (2.1) the first type of dynamic models were introduced. The book of Mankiw (2011) showed that people make assumptions about their lifetime income. With this lifetime income economic agents choose their consumption level for each period. But the lifetime income depends on many factors, for example on interest rates. When interest rates are high one is more likely to save his money instead of spend it on consumption

Mankiw (2011). In the first graph of section 2.1 the budget restriction line gets a different slope when the interest rate change. The interest rate depends on the monetary policy of the government. According to the basic Dynamic State General Equilibrium model from Barnett & Allison (2005) the interest rate depends on inflation and shocks. They believe that firms maximise present discounted value of expected profit from now until infinite future, subject to demand curve, nominal price rigidity and labour supply curve. The part about a Dynamic State General Equilibrium model where this paper mainly focusses on, is the consumption part. According to Barnett & Allison (2005) maximise present discounted value of expected utility from now until infinite future, subject to budget constraint. The function in the formula is discussed and regressed in in the data analyses in paragraph 3.4

**3. ** **Data analysis **

This paper examines if reference point dependence influences the level of

consumption of economic agents. This will be done by implementing a couple of models from micro/macro-economics that are discussed in the literature research. Campbell and Mankiw (1991) did their study with panel data from different countries. Likewise, Bowman (1999) used the same panel data. In this paper there will be, in line with the latter, made use of panel data. As well as the working paper of “de Nederlandse Bank” (2014) I will use data on expenditures and income from the longitude study from the LISS panel from Center Data at the university of Tilburg.

**3.1. Keynesian consumption function **

The first model that is tested is a Keynesian consumption function, which already explained in the literature review, contains of a constant consumption level of ̅ and the marginal consumption rate c times current income. When assuming that every household

consumes above ̅ a change in consumption can be directly measured by a change in consumption (Mankiw, 2011).

This is the first model that is tested with the data from the LISS panel about income and consumption. Shea (1995b) did test the dependence of a change in income on consumption by regressing the following model:

Similarly, as Shea (1995b) and Campbell & Mankiw (1990) the regression will be done with data of consumption and income. In this paper the data from Dutch economic agents from the LISS panel is used.

I derived the percentage change in income and consumption by using the following formula.

For income the same is done but with respect to the income levels.

The output of the regression of and the scatterplots are the following:

The year 2009 versus 2008: Number of

observations

Coefficient of the regression

p-value Standard error 95%

Confidence- interval

163 0.050 0.590 0.092 -0.133 – 0.232

The year 2012 versus 2009: Number of observations Coefficient of the regression

p-value Standard error 95%

Confidence- interval

97 0.168 0.138 0.11 -0.055 – 0.392

Neither the coefficients of the regressions are significant, nor the coefficient of income shock compared to consumption in the regression of Christellis et al (1999) are. By contrast,

Campbell and Mankiw (1990) present significant estimates of the elasticity of consumption with respect to predictable income ranging from 0.351 to 0.713. With the regressor of the ordinary least squares version being 0.328.

Shea(1995b) extended the model by distinguishing between a positive income growth and a decline in income. Consequently, he was possible to capture loss aversion.

**3.2. ** **Loss aversion in a Keynesian consumption model **

To look whether my data provides empirical evidence for loss aversion in a Keynesian consumption model, a regression likewise as the method of Shea (1995b) is applied. There is made a distinction between two cases, on the one hand, the case where there is a rise in income, corresponding to a positive in the model: . On the other hand the case where there is an income decline, . Shea (1995) expected and found that and income decline has less effect on consumption than respectively an income rise. If this is the case in my data sets, will be discussed after the result are presented. The results are presented below.

The regression of the formula : for both cases: case Number of observations Coefficient of the regression p-value Standard error 95% Confidence- interval 367 -0.040 0.68 0.098 -0.233 – 0.152 352 -0.376 0.222 0.307 -0.980 – 0.228

Both regressions did not provide coefficient significantly different from zero, zero is in the 95% confidence interval of both regressions. Thus, the empirical evidence for loss aversion is rather limited.

**3.3. ** **Theoretical evidence reference dependence in a two period consumption model **
In the following paragraphs there will be examined if loss aversion does

controversially to the latter method is significant in dynamic consumption models. Another way to look at consumption is by using a two period model. The two period model is the simplest version of the Dynamic State General Equilibrium model, because two periods are

taken into account, instead of the lifetime periods. For instance, Bowman (1999) did make use of a two period model. In one of his models he assumes that there is certainty about income, as discussed before we will assume this in this paper.

His model for consumption under certainty in a two period model is divided in two parts. The first part is the Utility function and the second part is the constraint function:

( ) ( ) ( ) { ( ) ( )}

r stands in this model for the reference level in period t. ct is the consumption in period t the constraint is described as follows:

Like Bowman (1999) and other habit studies I will let r1 , the first period reference point, as exogenous determined. The second period reference point can be derived by:

( )

where represents the speed at which the reference point changes in response to recent consumption. If 0, then first-period consumption has no effect on the consumer's second period reference level, consequently that utility is time-separable; if 1, then the second-period reference level adjusts fully to first-period consumption.

The theorem of Bowman (1999) when income is certain is stated below.

*“Theorem : If A and either B or C hold, then (1) c1(Y) and c2(Y) are continuous and *
*non-decreasing, with c1(Y) = c2(Y) = r1 when Y = r1 and (c1(Y) r1)(c2(Y) r2) ** 0. (2) If Y = r1 *
*then (c1(Y) r1)(c2(Y) r2)= 0 whenever the constraint ct ** 0 is non- binding. If in addition *
*> 0, then c2(Y) = r2.” *

With A, B and C as assumptions about loss aversion and reference points from Bowman (1999). In short, assumption A implies that more is better and a loss has a greater marginal utility than a likewise gain. Assumption B1 is about the marginal utility of a loss being more than twice as unpleasant as a gain of one unit is pleasant. Assumption B2 says that a person derives more satisfaction from a fixed consumption level the lower his reference point is. This is equivalent to the condition that ( ) ( ) for all y and .

Assumption C is an alternative to assumption b1 and b2. It assumes that when consumption level c is closer to the reference point. C: U(r,c) is decreasing in r when r > c, and increasing in r when r < c.

The first part proves that an economic agent will not consume above his reference point in period one or two if that forces him to consume under his reference point in the other period. This is in line with the theory about consumption and reference dependence theory explained in the literature research. It also shows that both first and second period

consumption are normal goods. Besides, it clarifies that one will never consume below his reference level when lifetime income does not force him to.

**3.4. ** **Dynamic Stochastic General equilibrium without reference dependence **

Furthermore, Foellmi, Rosenblatt-Wisch and Reiner Schenk-Hoppe (2011) did make use
**of a Ramsey model to capture loss aversion at consumption growth paths. **

When there are two periods the households can choose their level of consumption for t=0 and t=1, we assume that there is certainty about income and prices.

The utility model for a loss averse agent is according to Foellmi et al. (2011) the following:
( _{ } ) ( ) ( _{ })

if a =1 the pure prospect theory holds because only the second term will give an answer. The second term is the term where the consumption at t=0 is compared to the consumption at t=1. The factor v is calculated as follows:

( ) { _{ } _{ } _{ } if the consumption level lowers there is a penalty for
the loss of consumption. This is due to the loss aversion; the penalty is the coefficient .

The Ramsey model according to Foellmi et al. (2011) in Euler equation in total is:

The difference is that in a classical Ramsey model without reference dependence there are no different coefficients for the time series, it focusses on one steady state. Though, the model of Foellmi et al. (2011) uses such a Ramsey model and time frames that consumption and capital will come to the steady state point.

The utility function that will be used in this paper as well as in the paper of Foellmi et al. (2011) is the CRRA utility function, this function is used because it reflects an economic agent with risk aversion and a concave utility function.

( )

The derivative of this formula is:

( )

Firstly, I will derive the regression function for a normal Ramsey model. In the case of the article from Foellmi et al. (2011) this will correspond to the situation where a=0.

As explained in the literature research one can either save or consume its money. The money that is saved in period one can be consumed in the next period with the interest that is gained. But the money that is saved can be less worth in the second period due to inflation. Barnett & Ellison (2005) illustrate that the dynamic IS curve that follows from this consumption

function is:

_{ } _{[ }

]

is the discount factor, the risk aversion factor, Ct the consumption in period t and Ct+1 the consumption in the following period. It is the interest rate that agents receive when they store their money on a savings account. is the inflation rate. When taking logarithms of the dynamic function to get the log-linear function:

( ) ( ) ( ) ( ) ( ( )

Since I have assumed certainty about the income and inflation the expected values of _{ }
and _{ } are the true values. Thus, the model that is going to be regressed is:

( ) ( ) ( _{ }) ( ) ( _{ })
Consequently, the regression function in stata takes the form of:

̂ ( )

*For the regression of 2010 versus 2009 the inflation rate was 0.82% according to the Centraal *
*Bureau voor de Statistiek. The real interest rate for 2009 was 1.577% using the data from the *
*World Bank. I will use the same amount for risk aversion coefficient ( ) as Foellmi et al. *
(2011). The value that they used is 0.5.

So, firstly the model will be tested without the loss aversion coefficient, it is just a standard
dynamic stochastic general equilibrium model that is tested. The regression of ̂ _{ }

_{( } _{ }

) leads to the following outcome table: Number of

observations

Coefficient of the regression =

p-value Standard error 95%

Confidence- interval

2,545 -0.58*** 0.000 0.017 -0.61 - -0.55

* significance at 10% level. ** significance at 5%. *** significance at 1% level

The scatterplot with fitted line will be provided underneath.

Where on the x-axis the consumption level of consumption in 2010 is displayed and on the y-axis the consumption in 2009. According to Allison and Barnet (2005) the slope of the dynamic IS curve is equal to the negative risk aversion parameter. Whether this is true, according to our regression, will be tested. According to the confidence levels, the regression coefficient is significantly different from 0.5. Calling our regression parameter ̂ The t

statistics are:

̂ — _{ } , degrees of freedom= 2544

parameter is significantly different from 0.5 on a 1 % significance level.

**3.5. ** **Dynamic Stochastic General equilibrium with reference dependence. **

Not only the regression of a standard DSGE model is regressed in this paper but also a model including a penalty factor. The model of Foellmi et al. (2011) showed that when an economic agents lowered his consumption level he gets a penalty. In Bowman (1999), as well as Foellmi et al. (2011) the total function is in the form of:

( _{ } ) ( ) ( _{ })

The case where reference dependence was not used corresponds to a=0. Now there will be looked at a weighted reference dependence model where a= 0.5.

The model that is going to be regressed is the same as for the case without reference dependence and loss aversion but the penalty factor is taken into account, so that will lead to the linear function of:

( ) ( ) ( ) ( ) ( ) Consequently, the regression function in stata takes the form of:

̂ ( )

This formula is only applicable when an agent his consumption in period t+1 is lower than period t, because that is the case where a penalty is occurred.

The regression is done for the economic agents that have a negative change in consumption. The regression leads to the following outcome table:

Number of observations is 1,378 Coefficients for the regression p- value Standard error 95% confidence interval R-squared Consumption = -0.91 0.000 0.00709 -0.928 - - 0898 0.907 Penalty= -0.0043 0.000 0.0043 -0.0045 - -0.004

Without penalty factor: the regression for a decline in income is provided in the table underneath. Without penalty -0.588 0.000 0.128 0.613 -0.563 0.604

factor =

To conclude whether the model with the penalty factor explains significantly better than the model without the penalty factor, the F-test has to be done. The F-test is can be used if comparing the significance of two models to each other. The restricted model without the penalty is compared to the so called unrestricted model; here the model with the penalty factor in it.

The f- statistic formula is:

( ) ( ) ( ) ( )

( )

( ) ( ) according to the F- test the improvement of the model with the penalty factor is highly significant. The critical value for this f-test is 6.63, 4483.1 >> 6.63, thus at a significance level of one percent the model with penalty factor fits better than the model without.

However, there is an assumption that needs to be made to do the f- statistics. The errors need
to be homoskedastic. In the econometrics book of Stock and Watson (2012), there is stated
that the formula of the F-statistic only applies if the errors are homoskedastic. Morevover,
they write that there cannot be counted on homoskedacity with economic data and especially
the assumption is questionable with social sciences. To test this homoskedacity assumption a
Breusch-Pagan test is done. The Breusch-Pagan test for the regression of ̂ _{ }

_{( } _{ }

) did not show significant results for heteroskedacity. However, with the penalty factor taken into the regression, the Breusch-Pagan test did give a significant chi square of 101.2, the corresponding p-value was 0.00.

Furthermore, multicollinearity can play a role in this set up. In Stock and Watson (2012) imperfect multicollinearity is defined by the situation where two or more of the regressors are highly correlated in the sense that there is a linear function of the regressor that is highly correlated with another regressor. I think that this can be the case in this set up because a R-square of 0.9 is really high. The problem is probably caused because the first part of the regression depends on the level of consumption and the second part depends on the change of consumption from period t0 to t1. These two regressors can have a linear function that is highly correlated between the consumption level and the change in the level of consumption.

The results are in line with the results of Foellmi et al (2011) in the since that an economic agent does not want to lower his consumption, but instead of using consumption

data from a study panel they did a numerical simulation. They showed that over time consumption converges to a steady state. Furthermore, they showed that economic agents reject to lower consumption in the future. It is also in line with the theoretical support of Bowman (1999)

**4. Conclusion/discussion **

First of all, the question asked in the title cannot be clearly answered. According to different studies, Bowman (1999) Foellmi et al. (2011) Campbell & Makniw (1989) Shea (1995) provided theoretical evidence for reference dependence models. The latter two also provided empirical evidence with data.

In this paper a direct model of how a change in income effects a change in consumption did, in general, not provide any significant results. Neither did the regression where the distinction between an income increase and an income decline was made. However, the dynamic stochastic general equilibrium model did provide significant results. Although, for testing the Dynamic State General Equilibrium model in this paper many assumptions where necessary. Moreover, there can be posed some questions about the validity of the results, multicollinearity can for example play a role in the models, because the models have many different exogenous set values, like the interest rate. Another obstacle is the homoscedasticity of the errors between the model without the penalty factor for the loss of consumption and the model with. Purely based on the regression outcomes one can say in general that an DSGE model predicts better than a Keynesian model. Moreover, the DSGE model that I used explained better after taking loss aversion into account. When the data of more successive years is available one can take more periods into account. Hereby, the results of the test get more value. Another advantage of data of more successive years is that one can make more use of dynamic models. However, to completely run tests on DSGE models, one needs to have extensive knowledge about mathematics and macro-economics. Besides, the data for a DSGE model in macro-economics consists of different parts. The household section with consumption and capital, the firm section with and the monetary part with interest rate and inflation. To have high value estimator all the data need to be carefully selected.

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