A Consumption Function for Malta: Formulation and Analysis · 2015-09-23 · 2.1: Notable Theories...

A Consumption Function for Malta:

Formulation and Analysis

Luke Sultana

A dissertation submitted in partial fulfilment of the

requirements of the Degree of Bachelor of Commerce

(Honours) in Economics at the University of Malta

May 2012

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ii

Declaration of Authenticity

I confirm that this dissertation is all my own work and does not include any work

completed by anyone other than myself, except where due reference has been

made.

Luke Sultana

May 2012

iii

Acknowledgments

I would like to thank my tutor, Mr Carl Camilleri, for all of his advice and guidance

throughout the months of writing this dissertation. I would also like to thank my

family and Erica for all the support that they have given me during my studies.

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Abstract This dissertation sets out to give deeper insight into modelling household

consumption in Malta. This is attempted by constructing and analysing two

conflicting specifications of consumption modelling. These are the random walk

model and the ECM. The conflict between the models stems from the fact that a

pure random walk entails that any consumption changes are caused by random

shocks, and maybe an element of drift. Thus, consumption cannot be forecasted

under this model. The ECM on the other hand, is based on various explanatory

variables which could be utilised in a forecast.

The dissertation shall construct the two specifications and analyse their economic

and econometric features. The study will then go on to build a forecasted series of

consumption, based on the ECM, and test the strength of the forecast. If the

forecast is viable, consumption can be forecasted and the random walk hypothesis

is dropped.

One result of the study is that consumption in Malta can be modelled as a pure

random walk. This model was proven to be econometrically weaker than the ECM

by diagnostic tests. Other than this, the forecasted series proved to be significant

and so the random walk model is seen to be less relevant. The study also sheds

light on the importance of consumer perceptions in modelling consumption. This is

due to the fact that consumer confidence and price expectations were found to be

the main short run drivers of Maltese consumption.

v

Table of Contents

List of Tables .......................................................................................................... vii

List of Figures .........................................................................................................viii

Abbreviations ........................................................................................................... ix

Chapter 1: Introduction ............................................................................................. 2

1.1: Background and Research Focus .................................................................. 2

1.2: Structure ........................................................................................................ 2

Chapter 2: Literature Review .................................................................................... 5

2.1: Notable Theories on the Consumption Function ............................................. 5

2.1.1: About this section..................................................................................... 5

2.1.2: The Absolute Income Hypothesis ............................................................. 5

2.1.3: The Relative Income Hypothesis .............................................................. 9

2.1.4: The Life-Cycle Hypothesis ..................................................................... 11

2.1.5: The Permanent Income Hypothesis ....................................................... 13

2.2: Econometric Models ..................................................................................... 17

2.2.1: About this Section .................................................................................. 17

2.2.2: The Random Walk Model ....................................................................... 17

2.2.3: The Error Correction Model .................................................................... 20

Chapter 3: Data Collection and Analysis ................................................................. 25

3.1: About this Chapter ........................................................................................ 25

3.2: Consumption (Cons) .................................................................................... 25

3.3: Disposable Income (Yd) ............................................................................... 28

3.4: Wealth (W) ................................................................................................... 34

3.5: Interest Rates (HHLR) .................................................................................. 39

3.6: Consumer Confidence (CC) ......................................................................... 41

3.7: Price Expectations (PE)................................................................................ 45

Chapter 4: Methodology and Results ...................................................................... 49

4.1: About this Chapter ........................................................................................ 49

4.2: Stationarity ................................................................................................... 49

4.3: Random Walk Model - Model 1 .................................................................... 50

4.3.1: Construction and Specification ............................................................... 50

4.3.2: Economic Analysis ................................................................................. 52

4.3.3: Diagnostic Tests .................................................................................... 52

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4.4: Error Correction Model - Model 2 ................................................................. 54

4.4.1: Construction and Specification ............................................................... 54

4.4.2: Economic Analysis ................................................................................. 59

4.4.3: Diagnostic Tests .................................................................................... 61

4.5: Random Walk or Error Correction? .............................................................. 62

4.6: Limitations .................................................................................................... 66

Chapter 5: Conclusion ............................................................................................ 69

5.1: Concluding Remarks .................................................................................... 69

5.2: Suggestions for Further Research ................................................................ 70

Bibliography ............................................................................................................ 71

Appendix 1: Chapter 3 Regression Results & Data ................................................. 75

Appendix 2: Chapter 4 Tests & Results .................................................................. 80

vii

List of Tables

Table 4.a: Equation 4.1 regression results (random walk with drift) ........................ 51

Table 4.b: Equation 4.2 regression results (model 1) .............................................. 51

Table 4.c: Equation 4.3 regression results (function with disposable income) ......... 56

Table 4.d: Equation 4.4 regression results (function with employee compensation) 56

Table 4.e: Unit root test on equation 4.3 residual .................................................... 57

Table 4.f: Equation 4.5 regression results ............................................................... 58

Table 4.g: Equation 4.6 regression results (model 2) .............................................. 59

Table 4.h: Equation 4.7 regression results (forecasting test) ................................... 64

Table 4.i: Comparison between model 1 and model 2 summary ............................. 65

viii

List of Figures

Figure 3.1: Real household consumption, annual series ......................................... 26

Figure 3.2: Real household consumption, quarterly series ...................................... 27

Figure 3.3: Household disposable income, annual series estimation 1 ................... 29

Figure 3.4: Household disposable income, annual series estimate 2 ...................... 31

Figure 3.5: Household disposable income, quarterly series .................................... 32

Figure 3.6: Real employee compensation, quarterly series ..................................... 33

Figure 3.7: Housing wealth, quarterly series ........................................................... 36

Figure 3.8: Financial wealth, quarterly series .......................................................... 38

Figure 3.9: Net household wealth, quarterly series ................................................. 39

Figure 3.10: Household lending rate, quarterly series ............................................. 41

Figure 3.11: Consumer confidence, quarterly series ............................................... 44

Figure 3.12: Inverted consumer confidence, quarterly series .................................. 45

Figure 3.13: Price expectations, quarterly series..................................................... 47

Figure 4.1: Actual consumption and forecasted consumption ................................. 63

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Abbreviations

APC Average Propensity to Consume

ADF Augmented Dickey-Fuller

BG Breusch-Godfrey

CBM Central Bank of Malta

DF Dickey Fuller

ECB European Central Bank

ECM Error Correction Model

GDP Gross Domestic Product

MEPA Malta Environment & Planning Authority

MFEI Ministry of Finance, Economy and Investment

MPC Marginal Propensity to Consume

NSO National Statistics Office

OLS Ordinary Least Squares

PP Philips-Perron

SILC Survey of Income and Living Conditions

UK United Kingdom

US United States

VIF Variance Inflation Factors

1

Chapter 1: Introduction

2

Chapter 1: Introduction

1.1: Background and Research Focus

Consumption is a fundamental aspect of every economy, a phenomenon which has

merited an immense amount of research. Economists continuously attempt to

explain how consumption works, how individuals and households make

consumption decisions. This is done through various branches of economics,

theoretically and empirically. Over the years various theories and empirical models

regarding the consumption function have been developed. Theories developed over

the years range from the work of Keynes (1935) to that of Duesenberry (1945),

Modigliani (early 1950s), Friedman (1957) and more. Models are utilised to

empirically explain how consumption works, thus shedding empirical light on these

theories.

This study will present an econometric approach into explaining how household

consumption behaves in Malta. The research focus of this dissertation is to develop

a robust model of consumption for Malta by constructing a random walk and an

ECM. The study will then look into the validity of both models into explaining how

household consumption behaves.

1.2: Structure

The dissertation is made up of five chapters, the introduction, literature review, data

collection and analysis, methodology and results, and conclusion. The literature

review, chapter 2, will consist of an analysis of the theoretical and practical aspects

3

of the main theories of the consumption function and the econometric models

involved. Chapter 3 shall then discuss and analyse the data collected for the study.

Chapter 4 will then go through the methodology and results of the study. Finally, in

chapter 5, the dissertation will be concluded with a quick overview of the study and

suggestions for further research.

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Chapter 2: Literature Review

5

Chapter 2: Literature Review

2.1: Notable Theories on the Consumption Function

2.1.1: About this section

The analysis shall review four major theories that can be said to have shaped

consumption literature over the years. These theories highlight some of the major

determinants of consumption such as disposable income, habit persistence, wealth,

interest rates and time preference. Thus, this section shall deal with both the

theoretical explanation and practical tests of the theories concerned. Later on, in the

data collection chapter, other variables which affect consumption and are not part of

the main literature outlined here shall be further elaborated on.

2.1.2: The Absolute Income Hypothesis

Prior to the 1930s, consumption was observed as a residual of savings. This meant

that interest rates. Thus as a result interest rates were the key determinants of

consumption. Keynes was convinced that consumption had other determinants.

Keynes thus developed the Keynesian consumption function, also known as the

absolute income hypothesis.

The fundamental principle behind this theory is that the main determinant of

consumption expenditure is disposable income. Keynes deemed other determinants

as secondary and did not give them much importance. Keynes also writes that a

positive relationship between disposable income and consumption is expected.

6

We can illustrate the function in algebraic form as follows.

Equation 2.1

Where C denotes consumption expenditure and Yd denotes disposable income. Also

the constant ‘a’ shows the level of autonomous consumption and ‘b’ depicts the

nature and magnitude of the relationship between consumption and disposable

income, the marginal propensity to consume (MPC).

The hypothesis also states that the average propensity to consume (APC) is

inversely related to disposable income. This is so because those in lower incomes

will need to consume all or most of their income, and vice versa. The theory also

depicts consumption to be volatile rather than smooth. This is because consumption

is affected by any change in disposable income, whether transitory or permanent.

Early studies related to empirical research on the subject proved the absolute

income hypothesis to be a sound theory. The studies showed a very distinct

correlation between disposable income and consumption. The early studies also

concurred with Keynes’ proposed behaviour of the APC and MPC.

Friedman (1957) notes that although the first studies often showed support for the

Keynesian consumption function, over the course of time Keynes' theory was put in

doubt. Kuznets (1942) had found that in the USA over a period of time where real

7

income increased, the APC stayed the same. This contradicts the principles of the

hypothesis.

Friedman (1957) via data gathered from cross-sectional surveys between 1888 and

1950 came to the conclusion that there is seemingly no stable relation between

consumption and disposable income. Much like Kuznets’ study, Friedman also

found a stable APC during this time period.

However some tests do in fact show support for the absolute income hypothesis. In

fact, Arioglu and Tuan (2011) write that the absolute income hypothesis can hold in

certain circumstances. However this seems to be solely examined when the

hypothesis is tested under cross-sectional or short term data.

On the other hand, studies utilising long term data, such as that of Mankiw (1992),

indicate the consumption function in the long run is incorrectly specified and the

absolute income hypothesis does not hold. The contradiction between the short run

and long run Keynesian consumption function has been named the “consumption

puzzle”.

Other than in empirical studies, the absolute income hypothesis was also attacked

on the theoretical front. Ohlin (1937) argued that disposable income should not be

treated as the primary determinant of consumption as other factors may be more

powerful. Ohlin then states that the expectations of consumers should be a stronger

8

determinant of consumption. Years later, Friedman and Modigiliani provided similar

criticisms to the theoretical foundations of the absolute income hypothesis.

The theoretical and empirical criticisms of the absolute income hypothesis can also

be strengthened by looking at studies relating to Malta. Cassar and Cordina (2001)

apply an empirical test of the absolute income hypothesis on data for Malta using

data from 1970 to 1988. Results from the study indicate a consumption function with

a linear pattern taking the following form.

Equation 2.2

Therefore the results show a consumption function with a MPC of 0.87, and a

constant APC. This gives evidence against the validity of the absolute income

hypothesis in Malta as consumption in the long run seems to move proportionately

with income. In fact, Cassar and Cordina (2001) further state that the absolute

income hypothesis has little relevance in practice.

Because of the theoretical and empirical failures of the absolute income hypothesis

other theories were developed over time to solve the issues left by the hypothesis.

In fact the criticisms the hypothesis faced eventually gave rise to other theories

relating to consumption behaviour. These shall be subsequently discussed.

9

2.1.3: The Relative Income Hypothesis

The relative income hypothesis was put together by James Duesenberry in 1949, in

his book: Income, Saving, and the Theory of Consumer Behaviour. Duesenberry

sought to create an all variable inclusive consumption function by introducing

psychological and social factors into the study.

The relative income hypothesis is based on an assumption that disposable income

is not completely reversible. This would entail that when a household is used to a

certain level of consumption, the household would find it difficult to drop to a lower

level of consumption. This effect is called habit persistence, and Duesenberry

argues that this gives rise to the short run consumption function.

The theory also notes that households will want to maintain consumption along the

societal average. Thus households with lower income will have a higher APC so as

to reach the average and households with higher income will have a lower APC, as

they are above the average. Therefore, as long as the distribution of income is

stable, the APC will remain stable in the long run.

The first empirical study on the subject is a sample survey conducted by

Duesenberry himself. This sample survey supported his hypothesis in showing

consumer’s interest in the level of income of their peers.

Mason (2000) writes that the markets were increasingly showing support for the

hypothesis. Mason also notes that in post-world war two, as discretionary income

10

started to rise there was also a rise in people’s interest to keep up with the average

consumption.

Kosicki (1987) tests the hypothesis by a regression analysis showing the

significance of revealed income rank when determining the savings rate. His

conclusion is that while the hypothesis is an old idea, empirical evidence indicates

that it is very important.

The relative income hypothesis has also had criticism. Cassar and Cordina (2001),

when looking into alternative income based theories (relative income hypothesis and

permanent income hypothesis), note that these theories allow the APC to remain

constant in the long run while noting other influences in the short run. However they

conclude that the hypotheses have certain issues as they lack an explanation into

why the APC might rise with income. This leads them to state that the alternative

income based theories do not provide any further insight into Maltese consumption

that the linear consumption function does. Cassar and Cordina write that the

hypotheses are also troubled as they describe the behaviour of households without

linking it to any macroeconomic time series, do not offer and explanation into why

households shift sensitivity of consumption to income over time, and they do not

explain why consumption should be proportional to income in the long run.

One can conclude that the relative income hypothesis has both merits and flaws in

explaining consumer behaviour. In the end the theory has not been in the limelight

11

of economic theory as it was very quickly replaced by other studies that were more

economically oriented, such as that of Modigliani and Friedman.

2.1.4: The Life-Cycle Hypothesis

The life-cycle hypothesis was established in a series of papers written in the early

1950s by Franco Modigliani along with Albert Ando and Richard Brumberg. One of

the main goals of this theory is to solve the consumption puzzle. This hypothesis

gave a novel idea of consumption, the idea that consumption could be organised

over a consumer’s lifetime.

One important concept for the life-cycle hypothesis is that income will vary over an

individual’s life and consumption is constant throughout. Over one’s lifetime, the

individual will initially borrow until one starts producing an income. As the individual

earns income they will finance current consumption as well as pay what was

borrowed earlier on and save for one’s retirement. At retirement one will finance

consumption through past savings.

Thus consumption throughout time can be considered as a constant, as individuals

will opt for a smooth consumption trend. The key determinant of consumption is

considered to be lifetime wealth. Modigliani notes that the short run consumption

function can be modelled as follows.

Equation 2.3

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Where YL is labour income and W is wealth. Thus is the MPC out of labour

income and is the MPC out of wealth.

Although initial tests, on the USA, by Modigliani showed support for the hypothesis,

the theory could not be properly tested in other economies due to lack of statistical

information in many countries. During the 1960s empirical tests of the hypothesis

were then conducted on a number of economies, all with positive results.

Mork and Smith (1989) test the life-cycle hypothesis using Norwegian household

panel data. Their conclusions state that the hypothesis was accepted and fit the

data. However, Mork and Smith also acknowledge that more time was needed as

full confirmation of the hypothesis will require better understanding of the level of

consumption over time.

Butelmann and Gallego (2001) use household panel data for Chile in order to test

the life-cycle hypothesis. Their findings conclude that although at first the hypothesis

does not seem to hold, it gathers potential when demographic corrections are

included and pensions are excluded from the analysis.

To see the relevance of the theory within a Maltese context one can refer to Cassar

and Cordina (2001) who note that the life-cycle hypothesis is becoming increasingly

important with time. This can be merited to the fact that observations show that as

the population ages, the APC increases. Cassar and Cordina (2001) continue to

13

state that this factor will be very relevant to the Maltese scenario, maybe even more

so in the future.

This brings us to the flaws of the hypothesis. As it is, the life-cycle model may be a

bit too simplistic to fully depict consumption behaviour. The hypothesis excludes

certain important features of the economy and individual behaviour. These include

borrowing constraints, income uncertainty, and myopia.

The life-cycle hypothesis at its time offered a new insight into consumption

behaviour. It offered explanations for the behaviour of short and long run APCs and

also endured some empirical tests. However one must realise that the hypothesis is

flawed as well. This is due to the fact that, without additional variables, the

hypothesis might be too simplistic in its analysis.

2.1.5: The Permanent Income Hypothesis

The permanent income hypothesis was first brought forward in “A Theory of the

Consumption Function”, written by Milton Friedman in 1957. The theory,

complementing that of Modigliani, argues that consumption is not based solely on

current income, but on an individual’s permanent income. What mainly distinguishes

this theory from that of Modigiliani is that Friedman emphasises that people

experience random shocks in income, which can be transitory or permanent over

the years, while the life cycle hypothesis states that income follows a stable

identified pattern over the years.

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The hypothesis is structured around three relationships identified by Friedman. One

must note that in the theory that follows when a variable is permanent, it will

continuously shock the system into the future and when it is transitory, it will only

shock the system once or temporarily.

The first relation is between current, permanent and transitory income. Thus the

following equation is derived.

Equation 2.4

Where is total income, is permanent income, and is transitory income. Thus

permanent income is the average income, while transitory income is simply a

deviation from the mean level of income.

The second relationship identifies the link between current, permanent and

transitory consumption. This gives the following equation.

Equation 2.5

Where is total consumption, is permanent consumption, and is transitory

consumption. Again one finds that current consumption is based on permanent

consumption and the deviation brought by transitory consumption.

15

The final relationship identified by Friedman’s hypothesis is the link found between

permanent consumption and permanent income. This relation can be written as

follows.

Equation 2.6

Where i is the interest rate at which consumers are able to borrow and lend, w is the

ratio of nonhuman wealth to income, and u is the consumer’s preference for

consumption over savings.

Summing these together one can reach the following consumption function where

consumption is affected by the level and variations in permanent income.

Equation 2.7

Here, is considered to be a constant and not change over time.

Friedman, in his writings, tests the robustness of his theory with both cross-sectional

and time series studies. Friedman’s studies were all conducted using data from the

US. Evidence from these studies outline the flaws of previous consumption

functions, namely the absolute income hypothesis, and support Friedman’s model.

Over the years many have provided studies and tests to whether the permanent

income hypothesis is feasible. One of the most prominent is Holms (1970). Holms

16

argued that the hypothesis as it is was not econometrically feasible unless the

distribution function of transitory income is given by a first order Markov process.

Thus, Holms states that the original hypothesis is just a theoretical one. Mayer

(1973) concludes the permanent income hypothesis as it is quite limited, mainly is

asserting that APC is equal to MPC. Wirjanto (1991) also highlights that the

permanent income hypothesis was not robust enough to give a comprehensive

model of Canadian consumption. Some however, have agreed with Friedman’s

hypothesis. Dejuan et al. (2003) in a study on US states say that the hypothesis at a

state level is consistent.

In linking the permanent income hypothesis to Maltese studies, one can again refer

to Cassar and Cordina (2001). Their conclusion on the permanent income

hypothesis the same one they give on alternative income hypotheses (as already

described under the relative income hypothesis theory). In short, they state that

these hypotheses provide no more insight on the behaviour of Maltese household

consumption than the linear consumption function would.

The permanent income hypothesis was a great milestone in the study of the

consumption function. Although it had criticisms the model itself sheds a new view

on consumption, that of a very forward looking consumer. Also the theory goes

beyond one’s income and shows the implications of wealth, myopia and interest

rates.

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2.2: Econometric Models

2.2.1: About this Section

Within this section a discussion is initiated regarding the theory behind the two main

econometric models that are to be used in the modelling exercise. The models

concerned are the random walk model and the ECM. Given this, this section shall

take a look at the fundamental theory and literature behind these models as well as

the reasoning behind the use of these models for household consumption.

2.2.2: The Random Walk Model

The term ‘random walk’ was first coined by Karl Pearson in 1905, as he identified

the issue of the random walk and its uses. The random walk model is defined as a

process which starts at a point and then goes through a number of successive

random steps, or shocks. We can distinguish between two variations of the random

walk model in econometrics. The first is the random walk without drift and the

second is a random walk with drift.

A random walk without drift means that the model utilised has no constant or

intercept in the specification. Thus a dependent variable is said to be a random

walk given the following specification.

Equation 2.8

18

Where is a white noise error term with mean 0 and variance . Thus the value of

Y at time t is that of Y at t-1 with the inclusion of a random shock. The movement of

Y can thus be generalised as follows.

∑

Equation 2.9

Thus Y is dependent on the random shocks that it experiences across time. One

can therefore state that both the mean and variance will depend on time and so the

model will be non-stationary.

On the other hand, a random walk model with drift will utilise a constant

term/intercept in the model. We can thus specify the model as follows.

Equation 2.10

Where is the drift parameter in the equation. Due to the drift parameter, Y will be

seen to move upward or downward over time, depending on whether is positive or

negative. This can be shown algebraically.

Equation 2.11

From this one can note that as before, the mean and variance of the random walk

model shall have a time trend, resulting in a non-stationary series.

19

The use of random walk models in order to study consumption was pioneered by

Robert Hall in 1978 and due to its strong theoretical foundations the random walk

model of consumption has been utilised and tested extensively over the years. Hall

based his model on the assumption of having forward looking consumers with

rational expectations, thus the random walk model is built on the life cycle-

permanent income framework.

Hall initially examines how households/individuals optimise utility over time, his

results show that the conditional expectation of marginal utility in the future is solely

based on today’s consumption. This concludes that marginal utility follows a random

walk with a trend. So as long that marginal utility and consumption adhere to a linear

relationship, one can state that the stochastic properties of consumption will follow

those of a random walk, with a trend. This implies that Hall’s specification of the

random walk model is that of a random walk with drift. Given this one can generalise

the random walk model of consumption as follows.

Equation 2.12

Where C represents consumption at its relevant time, is a constant parameter

representing the trend in consumption, and is a white noise error term

representing shocks to consumption. This can also be represented as a log-linear

random walk model.

20

Equation 2.13

Hall firstly tests the model by seeing if lags beyond that of one have any effect on

consumption, and secondly by seeing if consumption has any relation to any other

economic factor that is observed in an earlier period. Results of the tests conducted

by Hall shows that the pure model where only consumption lagged by one period

has predictive power is rejected. A modified version of the hypothesis is then

brought forward. The modified model accepts the fact that consumption needs time

to adjust to changes in permanent income.

Other economists over the years have also sought to test the relevance of the

random walk hypothesis within consumption. Molana (1991) notes that overall

evidence on the random walk model in its pure form indicate rejection of the random

walk hypothesis. Molana also notes that the random walk model of consumption is

flawed given its simple life-cycle approach which indicates that the model assumes

no borrowing constraints. This position in further strengthened by Jaeger(1992) as

his findings indicate that the primary reason for deviation from the random walk

hypothesis is due to liquidity constraints.

2.2.3: The Error Correction Model

What is most appealing about the use of error correction models in economic

modelling is the fact that such models find a necessary compromise between the

essential statistical requirements of time series data, stationarity, and economic

theory. This is so as the ECM, as stated by Nwachukwu & Egwaikhide (2007),

21

presents a combination of short run dynamics and long run equilibrium under one

econometric system. Take the following equation as an example of an ECM

specification.

Equation 2.14

Where represents a constant/intercept term and is a white noise error term.

The use of error correction within the field of economics is older than one would

think. In fact Philips (1954 1957) was the first to introduce the concept of error

correction while conducting a study on feedback control mechanisms for

stabilisation policy.

The next development in the use of the ECM is the work of Sargan. Sargan (1964)

studies the econometric methodology of estimating structural equations with

autocorrelated error. Thus Sargan utilises an ECM with wage and price equations in

order to reach his results.

Alogoskoufis & Smith (1991) state that the great rise in importance given to the use

of error correction models can be attributed to the works of Davidson, Hendry, Srba

and Yeo (1978). This study, coincidentally being a study on consumption, introduced

the ECM as a representation of time series data regarding consumption expenditure

and income.

22

One of the most significant developments in the study of the ECM is the work done

by Engel and Granger (1981&1987). The relevant studies identified the relationship

between cointegration and error correction models and later on produced estimation

procedures, tests, and empirical examples.

It is also important to analyse the validity of the ECM for modelling consumption.

The consensus is that an ECM would be the best fit variables that are integrated at

order level 1. If data would be at integration order level two, then the resulting model

would lose a substantial amount of room for analysis of the relevant variable. A

model with variables of integration order level of zero on the other hand is already

stationary and does not need to be processed to take account of changes. Thus

given the tendency for consumption and the explanatory variables associated with it

to be I(1) variables, an ECM should be effective.

Davis (1984) conducts a study in order to test different specifications of the

consumption function on UK data. Davis took five different consumption functions,

each function was either an ECM or a partial adjustment model, and tested them

against each other. The comparison was based on the performance of the

specification in estimation and test statistics, stability, non-nested testing,

forecasting, and simulations. Davis concludes that error correction models fit the

data better and are theoretically superior.

Molana (1990) conducts a comparative test between the random walk and the ECM

of estimating consumption. The main focus of the comparison is to analyse the

23

model’s relation to a steady state. Molana notes that while error correction models

have little theoretical justification, the model aims to yield a pre-determined steady

state. Results of the study show that both tests are likely to fail in this regard,

however noting that the ECM for consumption achieves good results.

Slacalek (2004) compares a random walk, an ECM without consumer confidence

and an ECM with consumer confidence in order to find which model will have the

most robust forecasting ability. Results prove that the error correction models are

superior for forecasting; also the ECM with consumer confidence was the best

model to utilise overall.

Saad (2011) tests the ECM of consumption using data on Lebanon from 1957 to

2007. The model performs well in the study and produces a robust model of

consumption. In the study it is found that the consumption expenditure in Lebanon

is mainly dependent on current income, wealth, and expected inflation.

One can conclude that while studies have shown that error correction models may

have issues with its theoretical underpinnings, these models are perhaps the most

viable specifications for consumption available. This is due to its positive

econometric significance as well as forecasting ability.

24

Chapter 3: Data Collection and Analysis

25

Chapter 3: Data Collection and Analysis

3.1: About this Chapter

This part of the study shall deal with documenting the data collection procedure as

well as briefly analysing the time trend of the data collected. For the purpose of this

study data is collected at quarterly intervals from the first quarter of 2000 to the third

quarter of 2011. A cut-off date of March 13th 2012 is applied, any data developments

after this date shall not be considered. Throughout the chapter some OLS

regressions had to be conducted so as to estimate some missing observations in

the data, a detailed result of each regression can be found in Appendix 1.1. Also

note that one can find the final data for all the variables in Appendix 1.2.

3.2: Consumption (Cons)

Household consumption data was collected, from NSO, in real terms for both annual

and quarterly formats for the period between 2000 and 2011. The following graph

represents annual data for household consumption expenditure.

26

Figure 3.1: Real household consumption, annual series

Source: NSO

At the end of 2011 household consumption expenditure stood at about 3,118 million

euro, up by a total of 19.12% since 2000. One can observe an upwards trend in

Maltese household consumption. Despite the general upward trend during the time

period observed, one can also note some periods where consumption remained

unchanged or even slowed down. Between 2000 and 2002 one can observe a

period where real consumption in Malta remained relatively unchanged. Negative

growth in real consumption was observed with the global economic crisis. The data

also indicates that the global economic recession impacted Maltese household

consumption in 2009.

€2,600m

€2,700m

€2,800m

€2,900m

€3,000m

€3,100m

€3,200m

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Real Household Consumption

27

Quarterly data for household consumption was gathered and subsequently

seasonally adjusted with the use of the Tramo-Seats method1 within the program

Demetra+ 2 . The following graph represents quarterly data for household

consumption in Malta, seasonal adjusted, for the years 2000 to 2011.

Figure 3.2: Real household consumption, quarterly series

Source: NSO & author’s calculations

Upon analysing the quarterly data one would find the same trend identified before,

an overall upward trend with slowdowns in certain periods. A closer look at the data

1 Tramo/Seats is a method to seasonally adjust data by removing the deterministic attribute

of the series and then sets the series through decomposition. 2 Demetra+ is a computer program developed by Eurostat to conduct seasonal adjustment

€600m

€640m

€680m

€720m

€760m

€800m

€840m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Real Household Consumption

28

also highlights that the downturn for consumption due to the economic recession

specifically hit the variable in the final quarter of 2008.

3.3: Disposable Income (Yd)

Another important aspect of this study’s consumption function is the use of a

variable to represent disposable income. The relationship between disposable

income and consumption is seen as crucial for many theories, as already noted in

the literature review. A priori one would expect to find a positive relationship

between consumption and disposable income.

Given that no complete data set for disposable income for Maltese households

exists, one was built by partly using a method put forward by Debono (2010) and

also by the development of an OLS equation to estimate some missing years.3

One can find an annual measure of disposable income in Malta published within the

‘Economic Survey’ conducted by the MFEI. The source of the data is the NSO.

However, the issue with utilising this data is that it is only available till 2005. Another

source of disposable income data comes from the NSO’s ‘Survey on Income and

Living Conditions’ (SILC). The data provided in this study is at yearly intervals

between 2005 and 2009.

3 No complete annual or quarterly series for Maltese household disposable income is

available for the years between 2000 and 2011.

29

Debono (2010) constructs a yearly measure of disposable income by using annual

data from the Economic Survey for the years 2000 to 2005, then takes the annual

growth rate of consumption from the SILC and applies it to the Economic Survey

data. This method was applied and an annual series for household disposable

income was constructed for the years 2000 to 2009. However, further assumptions

had to be made to estimate 2010 and 2011.

Two methods were explored for estimating the missing data. The first being to

estimate the missing years by assuming that the rate of change in disposable

income for 2009 to 2011 was the same as the average for previous years. This gave

the following graph.

Figure 3.3: Household disposable income, annual series estimation 1


€2,400m

€2,600m

€2,800m

€3,000m

€3,200m

€3,400m

€3,600m

€3,800m

€4,000m

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Household Disposable Income

30

This estimation is dubious as the resulting data indicates that the economic crisis

had no effect on disposable income. Hence, another estimation procedure is

attempted.

The missing yearly data was constructed by using an OLS regression for 2000 to

2009 between disposable income, real compensation per employee (CE) gathered

from Eurostat and real GDP gathered from NSO. The regression was thus used to

calculate the remaining two years by plugging in explanatory variable data. The

regression took the following form:

Equation 3.1

This equation holds limited use in economic analysis, however the equation proved

to be a sufficient forecasting tool as both explanatory variables have significant t-

statistics and the equation has an adjusted of 0.9715. The following graph

represents the measure for disposable income in Malta between 2000 and 2011.

31

Figure 3.4: Household disposable income, annual series estimate 2


With this one can observe a similar pattern as seen in the consumption data. There

seems to be an upward trend in household disposable income in Malta, albeit some

negative growth rates along the way. The most obvious decline in disposable

income stems from the recent economic recession.

The data constructed still needed processing at this point due to the need for

quarterly intervals. As done by Debono (2010) annual data was disaggregated into

quarterly intervals by using the Boots, Feibes, and Lisman temporal disaggregation

method4. This method was done by using ‘Ecotrim’5. After disaggregation the data

4 The Boots, Feibes, and Lisman method is a disaggregation and smoothing method

developed to conduct interpolation estimates for disaggregation.

€2,400m

€2,600m

€2,800m

€3,000m

€3,200m

€3,400m

€3,600m

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

Household Disposable Income

32

was set into real terms by using a GDP deflator 6 and seasonally adjusted via

Demetra+. Thus the following graph represents quarterly data for real seasonally

adjusted disposable income in Malta between 2000 and 2011.

Figure 3.5: Household disposable income, quarterly series


Given the number of assumptions put into place in order to develop a measure for

disposable income, it seems wise to create another measure/proxy so that the most

viable can be utilised. As a proxy for disposable income compensation per

employee is used. The variable in nominal form is available from Eurostat as a

5 Ecotrim is a temporal disaggregation program developed by Eurostat

6 A GDP deflator was constructed by dividing nominal GDP by real GDP, using NSO data.

€600m

€620m

€640m

€660m

€680m

€700m

€720m

€740m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Real Household Disposable Income

33

quarterly series. The measure was then put into real terms by utilising the GDP

deflator and adjusted for seasonality via Demetra+. The following graph is derived.

Figure 3.6: Real employee compensation, quarterly series

Source: Eurostat & author’s calculations

Upon analysing employee compensation one can find an upward trend throughout

the years as with disposable income. The effect of the recession on employee

compensation is evident, as of 2009 real employee compensation has exhibited a

downward trend. One can also note that even after seasonal adjustment, employee

compensation is quite volatile.

€3,400m

€3,450m

€3,500m

€3,550m

€3,600m

€3,650m

€3,700m

€3,750m

€3,800m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Real Employee Compensation

34

3.4: Wealth (W)

By many consumption function theories, such as the permanent income hypothesis,

wealth is seen as a factor which is very influential on consumption. This stems from

the notion that the wealthier an individual is, the more the individual will consume.

Thus, a priori, one would expect a positive relationship between household

consumption and household wealth.

A quarterly time series for net household wealth had to be constructed.7 For the

purpose of calculating net household wealth a method similar to that underlined by

Debono (2010) is utilised. Total household wealth is assumed to be the sum of

housing wealth and financial wealth for the purpose of this study.

Total housing wealth was calculated by constructing a time series of housing stock

in Malta and then applying the average advertised prices on the stock. Four different

types of properties were considered. These were apartments, terraced houses,

maisonettes, and others. The term others includes: bungalows, farmhouses, semi-

detached, and villas.

Given that housing stocks are only available for the years when a census was

conducted, the other years had to be estimated. As done by Debono (2010) housing

stock for each type of property for 1995, 2000, and 2005 were gathered from census

data and the years in between were calculated using development permits.

Assuming that development permits issued will take a year to be constructed,

7 No series for net household wealth is currently available for Malta.

35

housing stock for a given year was assumed to be the housing stock of the year

before and the number of development permits approved the year before. This

calculation gave an annual time series for housing stock for each type of property

listed. The annual time series was disaggregated into quarterly data by using the

Boots, Feise, and Lisman disaggregation method in Ecotrim.

Prices for housing types had to be calculated as well. The CBM provides an index of

property prices with 2000 as the base year. This index is found in quarterly intervals

between 2000 and 2011 and already split into the before mentioned property types.

Debono (2010) gives a value of average property price of the different types of

property for 2000. Thus the property prices for all quarters between 2000 and 2011

quarter three were calculated by applying the property price index on the average

2000 prices, as it is the base year.

The total value of the different types of property was hence calculated by multiplying

the stock by the price. Total housing wealth was the result of summing the total

value of the different types of property. The following graph represents housing

wealth from 2000 to quarter three of 2011.

36

Figure 3.7: Housing wealth, quarterly series

Source: NSO & CBM & MEPA & Debono (2010) & author’s calculations

The second aspect of household wealth in Malta is financial wealth. A measure of

household financial wealth was gathered from Eurostat data. No total household

financial wealth series was available, thus household financial wealth was calculated

by summing up the following household holdings: currency, deposits, long and short

term securities other than shares, shares and other equity other than portfolio

investment, mutual fund holdings, holdings in life insurance, and prepayments of

insurance premiums and reserves for outstanding claims.

It is important to note that some assumptions were made. Firstly, it was assumed

that the rate of change of two aggregates (long term securities other than shares,

€15,000m

€20,000m

€25,000m

€30,000m

€35,000m

€40,000m

€45,000m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Housing Wealth

37

and shares and other equity other than portfolio investment) for the period between

2003 quarter four and 2004 quarter four was equal to the average rate of change

overall. With this assumption in place a series for financial wealth between 2003

quarter four and 2011 quarter three was constructed. Data prior to the last quarter of

2003 was not available for all aggregates. An OLS regression using deposits (DEP)

as the explanatory variable and financial wealth (FW) as the dependent variable was

created. Note that the figure for deposits is the only available aggregate that spans

for the entire period under consideration.

The alternative to this is to estimate the missing series by assuming the rate of

change during the missing period to be equal to that of the average change for the

rest of the periods. However, a regression based on one of the components of

financial wealth is better suited to reflect reality. The following regression for

financial wealth (FW) was obtained.

Equation 3.2

Note that the intercept was left out as the regression without the intercept provided

stronger results. While the regression does not provide sufficient detail for economic

analysis, it proves to be viable for forecasting due to an and an adjusted of

0.82, and a significant t-statistic on the explanatory variable. With this a complete

quarterly time series for financial wealth was derived, this is displayed in the

following graph.

38

Figure 3.8: Financial wealth, quarterly series

Source: Eurostat & author’s calculations

By adding up household housing and financial wealth, a figure for total household

wealth was reached. From this, total household net wealth was calculated by

subtracting the amount of quarterly household loans outstanding from the total

amount of wealth. Household net wealth is shown in the following graph.

€8,000m

€9,000m

€10,000m

€11,000m

€12,000m

€13,000m

€14,000m

€15,000m

€16,000m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Financial Wealth

39

Figure 3.9: Net household wealth, quarterly series

Source: Author’s calculations

One can easily identify an upward trend in household net wealth over the past

eleven years. The upward trend, although persistent, did slow down in 2008. A

closer look at previous graphs will indicate that the slowdown can be attributed to

housing wealth in specific. One can also that financial wealth follows a steadier

upward trend with, more or less, a constant gradient throughout.

3.5: Interest Rates (HHLR)

Interest rates are seen as a factor which will either increase or decrease one’s

incentive to consume or save between different periods. Given this, a priori one

would expect to find a negative relationship between interest rates and

€25,000m

€30,000m

€35,000m

€40,000m

€45,000m

€50,000m

€55,000m

€60,000m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Wealth

40

consumption. This is due to the fact that high interest rates would incentivise a

household to save or disincentive a household to not take out loans, and vice versa.

However, high interest rates may result in the perception that interest rates may rise

again in the future, thus increasing consumption in the present. Due to this

ambiguity outlined by Cassar and Cordina (2001), one does not expect to find a

strong relationship between interest rates and household consumption.

Data regarding interest rates for consumers was found readily available in monthly

format from the CBM. In order to assess the impact of interest rates on consumption

the household lending rate will be considered in this study. This rate is the average

lending rate which households have to pay on loans for asset purchase, consumer

credit and other lending. Monthly data retrieved from the CBM was aggregated into

quarterly data by taking the average of the relevant months in each quarter. Thus

the following graph is derived for the household lending rate in Malta.

41

Figure 3.10: Household lending rate, quarterly series

Source: CBM & author’s calculations

The graph highlights a generally downward trend in the household lending rate in

Malta. Also, one can observe that the biggest decline happened at the end of 2008.

This can be attributed to ECB rate cutting at the time so as to induce consumption

during the economic crisis of the time.

3.6: Consumer Confidence (CC)

Consumer confidence is often treated as an essential variable in any consumption

function; a priori one would expect a positive relationship between consumer

confidence and consumption. A measure of consumer confidence was gathered

3.6%

4.0%

4.4%

4.8%

5.2%

5.6%

6.0%

6.4%

6.8%

7.2%

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Household Lending Rate

42

from Eurostat data. The measure is based on consumer confidence surveys

conducted by EMCS Ltd. for Eurostat. The survey data contains questions on

employment prospects, the opinion on the state of the economy, prospects on

consumption and savings, and prospects of future income. The consumer

confidence indicator can range between -100 to +100, the former being all

respondents answer the most negative and the latter being all respondents answer

the most positive possible.

The data from Eurostat is available in a monthly interval format and is seasonally

adjusted. Given the monthly format, averages were taken so that a quarterly series

can be established. At this point one must note that data from Eurostat for Malta is

only available from the last quarter of 2002 onwards. Thus an estimation procedure

had to be implemented for previous quarters. Two different estimation procedures

based on two different assumptions were conducted to select the most applicable.

The first estimation procedure is done by constructing an OLS regression between

consumer confidence (CCM), real GDP, real employee compensation (ECOMP) and

the unemployment rate (U). The basis of this is that the indicator is based on survey

questions regarding prospects for the economy, wage, and employment. The

resulting regression gave poor results with low t-statistics and an adjusted of

0.19. As with all regressions in this chapter, the full results can be found in Appendix

1.1.

43

The second procedure is based on the assumption that the relationship between

consumer confidence in Malta and consumer confidence in the euro area observes

is applicable to the missing periods. Thus an OLS regression was constructed. It

was found that the most efficient regression is one with; the consumer confidence

for Malta (CCM) as the dependent variable, the consumer confidence for the euro

area lagged for four quarters (CCEA) as the explanatory variable and an intercept

term. This regression proved to be more effective than the previous one. The

following regression is obtained.

Equation 3.3

The equation gave and of 0.41 and an adjusted of 0.39 and both the intercept

and the explanatory proved to be significant. With this the following time series for

consumer confidence in Malta is produced.

44

Figure 3.11: Consumer confidence, quarterly series

Source: EMCS Ltd. & author’s calculations

As one can see consumer confidence in Malta has over the years always been on

the negative side of the range. The reason for this is difficult to interpret. One might

say that this is attributed to a pessimistic culture in Maltese consumers regardless of

the true situation. This is supported by the results of the first estimation procedure

where it was found that the relation between the perceived situation and the real

situation is quite ambiguous.

Given that the ECM to come shall be attempted in log form, the indicator was

multiplied by -1 so that an inverse indicator can be given. This simply means that

100 now represents completely negative responses and a priori one would expect to

-40

-35

-30

-25

-20

-15

-10

-5

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Consumer Confidence

45

find a negative relationship between the indicator and consumption. Thus from this

point on consumer confidence (CCM) shall refer to the inverse of the consumer

confidence indicator for Malta. The following graph is derived.

Figure 3.12: Inverted consumer confidence, quarterly series


3.7: Price Expectations (PE)

The concept of price expectations is another variable that should affect consumption

behaviour. Economic theory states that with consumers thinking prices are going to

rise they will consume more now, and if consumers think prices are going to fall they

will hold off consumption. Thus a priori, one would expect a positive relationship

between consumption and price expectations.

5

10

15

20

25

30

35

40

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Consumer Confidence

46

In order to model price expectations a time series from Eurostat was utilised. As with

consumer confidence, the survey data is collected by EMCS Ltd. and published by

Eurostat. This measure is based on a survey question which asks individuals to give

their opinion on whether they think prices will rise of fall over the next twelve months

as opposed to the previous twelve months. Thus, the quantification of this measure

is between -100 to 100 where -100 is where all respondents answered prices will fall

significantly and 100 being all respondents answered prices will rise significantly.

The data was only available at monthly intervals from the last quarter of 2002 to the

last quarter of 2011. Quarterly estimates were obtained by taking averages of the

relevant months. Data prior to the last quarter of 2002 had to be estimated. An OLS

regression with a constant term and the rate of inflation (INF) as explanatory

variables, and price expectations (PE) as the dependent variable was constructed.

The rate of inflation, based on aggregated 12 month moving average data, proved to

be insignificant. Thus an OLS regression using price expectations (PE) as the

dependent variable, a constant term, and the price of crude oil per barrel (OIL) as

the explanatory variable was attempted. This gave positive results. The following

regression was formulated.

Equation 3.4

The price of crude oil per barrel proved to be significant with a t-statistic of about

9.76. The equation’s and adjusted were calculated to be 0.74 and 0.73

47

respectively. With the equation a quarterly time series for price expectations for

Maltese consumers was constructed. The series gave the following graph.

Figure 3.13: Price expectations, quarterly series


Since the series is always positive, 2000 to 2011 Maltese consumers always

expected prices to rise in the next twelve months over the previous months. One

can also observe that the series generates an upward trend, so as time goes by

consumers keep anticipating prices to rise faster. However the series is based on

perceptions and can be seen as quite volatile, thus meriting caution in interpretation.

0

10

20

30

40

50

60

70

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

Price Expectations

48

Chapter 4: Methodology and Results

49

Chapter 4: Methodology and Results

4.1: About this Chapter

This chapter shall discuss the methodology and results of the econometric models

constructed. The analysis shall start off by examining the property of stationarity for

each variable under study. After this, the discussion will go on to estimate and

examine each model constructed. For each model an economic and econometric

analysis shall be made on the results obtained. A comparison between the models

will also be made. With this, the conclusions regarding consumption modelling in

Malta are reached. The chapter will close with a discussion on the limitations of the

study.

4.2: Stationarity

This study shall apply the Phillips-Perron (P.P.) test to test for stationarity. The P.P.

test identifies stationarity in a variable by testing for a unit root. The null hypothesis

of the test is that the variable has a unit root, and is thus non-stationary. The P.P.

test has been chosen over other tests, such as the Dickey-Fuller (DF) or the

augmented Dickey-Fuller (ADF), as it is not as tied down by assumptions of no

autocorrelation. The P.P. statistics are only modifications of the ADF t-statistics that

have fewer restrictions on the error process.

Each variable is first tested for a unit root at level and then at first difference. By

viewing the graphical representations for each variable, found in chapter 3, one can

50

establish that all variables involve a time trend. Given this, the P.P. tests are

conducted by assuming a trend and intercept.

The results from the unit root tests, at a 5% confidence level, indicate that all

variables considered are non-stationary (have a unit root) at levels but are stationary

(no unit root) at first difference. Thus all variables are I(1) variables. Results from the

P.P. tests are summarised in Appendices 2.1 and 2.2.

4.3: Random Walk Model - Model 1

4.3.1: Construction and Specification

The first model of consumption to be considered shall be based on Hall’s log-linear

discrete time version of the random walk consumption function. Thus the following

specification shall be tested.

Equation 4.1

As already explained in the literature review, here we have a log-linear random walk

model where consumption is thought to be influenced by consumption in the

previous period, a constant parameter representing the growth of consumption ( )

and a random shock ( ). The specification was modelled via eviews and the

following regression results were obtained. Note that full results for all tests and

procedures for the section on the random walk model can be found in Appendix 2.3.

51

Table 4.a: Equation 4.1 regression results (random walk with drift)

Variable Coefficient Std. Error t-Statistic Prob.

0.418638 0.332372 1.259545 0.2146

0.936892 0.050593 18.51818 0.0000

R-squared 0.888579

Adjusted R-squared

0.885988

Even at first glance one can identify some issues in the application of Hall’s random

walk model to Maltese data. Mainly, one finds that the drift parameter is insignificant.

This identifies the need to alter Hall’s model for Maltese data. The drift parameter is

eliminated and the regression is rerun without it. The following equation and results

are obtained; this model shall hereafter be referred to as model 1.

Equation 4.2

Table 4.b: Equation 4.2 regression results (model 1)


1.000559 0.000515 1942.497 0.0000

R-squared 0.886005

Adjusted R-squared

0.886005

For a pure random walk model, the coefficient of past consumption needs to be

equal to 1.This factor is what causes the model to be non-stationary. Given that

stationarity tests have already shown consumption to be I(1), the coefficient is likely

52

to be statistically equal to 1. A formal procedure is yet applied to test whether the

coefficient of is equal to 1.This is done through a Wald test. Results from

the Wald test indicate that the coefficient of is 1, meaning the model

derived is rightly a pure log-linear random walk model. The results of the Wald test

can be found in Appendix 2.3.

4.3.2: Economic Analysis

It is established that model 1 follows a pure random walk. The economic implication

of such a model is that consumption in Malta is only influenced by random shocks.

This would entail that consumption in Malta cannot be forecasted as any changes in

consumption from time t-1 to time t is only attributed to a random shock. Later on, a

forecasting test shall be conducted to test if Maltese consumption does in fact follow

a pure random walk as depicted by the model.

4.3.3: Diagnostic Tests

The t-statistic of is highly significant and the goodness of fit of the model

is also quite positive. In fact, the and adjusted indicate that the equation

explains about 89% of all movements in . However, the high goodness of fit

is most likely brought about by spurious regression, a result of the fact that

consumption is non-stationary at levels.

Further diagnostic tests are conducted to evaluate the model in greater detail.

Multicollinearity in this model is not an issue due to the fact that only one

53

explanatory variable is observed. The model is also tested for heteroscedasticity;

this is done through the White Test. The results from the White test indicate that the

null hypothesis of no heteroscedasticity is accepted.

The regression is tested for autocorrelation through the Breusch-Godfrey (BG) test.

The BG test is performed by taking three lags, chosen due to data being in quarterly

intervals. The null hypothesis in this test is that there is no serial correlation of any

order. This hypothesis is rejected as the F and test statistics prove to be

significant, hence indicating the presence of serial correlation.

Another important factor for the model is normality. A normality test is conducted via

the Jarque-Bera statistic on a histogram normality test. The null hypothesis is that

the errors of the constructed regression are normally distributed. The Jarque-Bera

statistic was found to be insignificant, meaning that the residuals are normally

distributed.

The Ramsey RESET test is used to diagnose the specification of the regression.

The Ramsey RESET test is done with the inclusion of one fitted term. The null

hypothesis is that the original model is correct, and given that the F statistic derived

is insignificant, the null hypothesis is not rejected. This indicates that the model is

correctly specified.

The final test applied is used to determine the model’s stability over different time

regimes. The Chow breakpoint test was utilised to indicate whether or not there was

54

any significant structural change in the model. The breakpoint test was conducted

on the first quarter of 2009. This was done to check whether the economic crisis had

any structural effect on the consumption function. The test resulted in not rejecting

the null hypothesis that no breaks where present. Thus, under this model, the

economic crisis did not have any structural effects on the consumption function.

4.4: Error Correction Model - Model 2

4.4.1: Construction and Specification

The second model to be considered in this study shall take the form of an ECM,

brought about through the Engle-Granger two-step procedure. This approach entails

that even though variables are non-stationary, a non-spurious long run and short run

model can be found through cointegration. Initially two long run equations shall be

estimated, each with a different measure for current income. One will utilise the

author’s disposable income measure and the other will utilise employee

compensation. The more efficient of the two will be developed into an ECM. The

rationale behind this is to ensure that disposable income is well represented, as both

measures are built on quite a few assumptions.

One must note that the Engle-Granger approach is best suited for models with only

two explanatory variables, as a model with more explanatory variables can have

more than one cointegrating relationship. Thus it is assumed that there is only one

cointegrating relationship present. Note that full results for all procedures run in the

ECM section can be found in Appendix 2.4.

55

4.4.1.1: Long Run Equation

All the variables to be utilised have already been tested for integration order and all

proved to be I(1) variables. This was the first part of the Engle-Granger Approach.

Given this, the next step is to compute the long run OLS equations for the two

models. The specifications for the initial two functions are presented in log form and

given as follows. Note that equation 4.3 represents to specification with disposable

income, and equation 4.4 represents the specification with employee compensation.

Equation 4.3

Equation 4.4

Here and represent the regression residual that is white noise error, as shall be

determined by a unit root test. Both equations specify that the dependent variable

( ) will be determined by changes in the constant, household income (

, ), household net wealth ( ), the household lending rate ( ),

consumer confidence lagged by one period ( ), and price expectations

( ). A priori, one would expect a positive relationship between consumption and

income, wealth, and price expectations. A negative relationship between

consumption and the household lending rate and the consumer confidence measure

is expected as well. It is important to restate that represents an inverse

measure for consumer confidence and that is why a negative relationship is

56

expected. Also note that the measure is lagged by one period, this is because a

higher significance for the lagged measure was found during testing. Both

regressions are computed, giving the following results.

Table 4.c: Equation 4.3 regression results (long run OLS for function with

disposable income)


4.018807 0.362541 11.08513 0

0.170792 0.0583 2.929521 0.0056

0.141766 0.023318 6.079801 0

-0.0821 0.025263 -3.24976 0.0024

-0.03779 0.007527 -5.02124 0

0.05755 0.008644 6.657524 0

R-squared 0.940967

Adjusted R-squared 0.933399

Table 4.d: Equation 4.4 regression results (long run OLS for function with

employee compensation)


0.656749 1.627832 0.40345 0.6888

0.576885 0.224065 2.574628 0.0139

0.112542 0.031107 3.617876 0.0008

-0.06322 0.025094 -2.51917 0.016

-0.03451 0.007787 -4.43103 0.0001

0.061602 0.009038 6.816257 0

R-squared 0.93844


57

Regression results indicate little difference between the two equations. In fact, the

only differences found are in the significance of the intercept and the coefficient of

the current income measure. Goodness of fit between the two functions, as well as

the coefficients and significance of other variables are just about identical. Since the

functions are quite similar, observing both functions in further detail should not

produce any unique results, thus the study shall go on to only consider the function

utilising disposable income. This variable is chosen due to its higher significance,

albeit the difference is minimal.

4.4.1.2: Cointegration and ECM Specification

To have a cointegrating relationship, a necessity for computing the ECM, the

residual of the long run OLS regression ( ) has to be stationary in levels. The

residual is tested for stationarity by applying the P.P. test. Given that the series

exhibits no trend and fluctuates around 0, the P.P. tests conducted do not make use

of a trend or intercept. Table 4.e below gives a summary of the results obtained, the

full results are found in Appendix 2.4.

Table 4.e: Unit root test on equation 4.3 residual

P.P. Test on Levels

Residual Adj. t-Stat Observed Adj. t-Stat 5% Critical

Value Unit Root

-7.134490 -1.948495 No

The residual is stationary at level as it does not contain a unit root, therefore one

can conclude that a cointegrating relationship exists in the function. Thus the

58

function can be expressed in error correction form. The following equation is the

error correction specification of the long run equation.

Equation 4.5

Where represents the white noise error term derived from the equation. The

results of the above regression are summarised in table 4.f.

Table 4.f: Equation 4.5 regression results


0.004646 0.003122 1.488221 0.1452

0.116207 0.079922 1.454008 0.1544

-0.12248 0.107445 -1.13993 0.2616

-0.03599 0.048304 -0.74505 0.4609

-0.0243 0.008196 -2.96525 0.0053

0.045347 0.009956 4.554911 0.0001

-0.81607 0.154283 -5.28944 0

R-squared 0.590755


Given that disposable income, wealth, and the household lending rate were found to

be insignificant in the ECM, the model was modified to not include these variables.

The ECM equation was modified as follows. One can note that the following model,

given by equation 4.6, shall be referred to as model 2 from this point on.

59

Equation 4.6

The following table represents the regression results for model 2.

Table 4.g: Equation 4.6 regression results (model 2)


0.003159 0.00252 1.253415 0.2173

-0.02033 0.007669 -2.65018 0.0115

0.043975 0.009866 4.45719 0.0001

-0.79151 0.155846 -5.07883 0

R-squared 0.529342


4.4.2: Economic Analysis

At this point it is important to analyse the model developed from an economic point

of view. One can start this by analysing the long run regression results. All

statements made in this section are describing Maltese household consumption

based on the model result for the time period under consideration.

The long run regression for model 2 found that the log of Maltese household

consumption has a significant relationship with intercept term as well as all variables

tested. The intercept term was found to be 4.02. The anti-log of this figure is

10,471.285. This can be said to be the level of consumption when all other factors

are equal to 0. The long run elasticity of consumption with respect to disposable

income is found to be about 0.17. This essentially means that in the long run if

60

disposable income rises by 1%, consumption rises by 0.17%. This is difficult to back

with a priori expectations as one expects to find a higher MPC. The partial elasticity

of consumption with respect to wealth is found to be 0.14 in the long run. Thus if

household wealth rises by 1% consumption rises by 0.14%. A negative relationship

is found with respect to interest rates in the long run. Although, a priori, the

relationship was not expected to be significant, it is evident that a rise in the

household lending rate by 1% will reduce current consumption by 0.08%. Consumer

confidence is found to be positively related to household consumption. This is

evident as when the inverse of consumer confidence rises by 1%, consumption falls

by 0.03. The final long run relationship found is with price expectations. A positive

relationship is found, as expected, due to the perception of rising prices.

Given all of this, the long run equation for model 2 seems to be in line with a priori

expectations for the variables. That being said, one must go on to analyse the ECM

in order to determine both the short run relationships and the long run movement

towards the steady state.

The results from the ECM indicate that, in the short run, consumer confidence and

price expectations are the only significant determinants of household consumption

from the tested variables. One must note that both of these measures are based on

survey data, hence they represent perceptions. Given this, it would seem that

consumers’ perceptions may be a very important factor to consider in modelling

consumption.

61

In model 2 the coefficient of the lagged long-run residual proves to be significant and

close to -1. This implies that the model holds a steady state and adjusts towards it at

a relatively fast pace. In fact, the rate of adjustment is 0.79. However, given the

nature of consumption one must consider that the steady state is dynamic.

4.4.3: Diagnostic Tests

In order to properly assess the validity of the model an econometric analysis has to

be made on the model’s error correction form, model 2. Full results for all diagnostic

tests conducted on model 2 can be found in Appendix 2.4.

The and adjusted of model 2 are 0.53 and 0.49 respectively. This means that

about 49% of variations in consumption are explained by the model. The goodness

of fit of the model is thus not as high as one would like, albeit the model eliminates

the possibility of spurious regression.

Multicollinearity is tested using variance inflation factors (VIF). The tests indicate

that there is no evidence of multicollinearity in model 2. The model is also tested for

heteroscedasticity through a White test. The specification was found to be

homoscedastic. The BG serial correlation test was conducted to assert whether or

not the model suffers from autocorrelation. As with model 1, three lags were

assumed due to the quarterly data. The null hypothesis of no serial correlation is not

rejected. The model is also found to be normally distributed. This was examined with

the use of the Jarque-Bera statistic in a normality test. The Ramsey RESET test,

with 1 fitted term, indicates that the model is correctly specified.

62

One final test was conducted to check the stability of the model. A Chow Breakpoint

test was conducted on 2009 quarter four. As with model 1, this was done to make

sure that the economic crisis did not have any structural effects on the consumption

function. Results show that the model remained stable and the economic crisis

created no breaks in the function.

4.5: Random Walk or Error Correction?

So one must ask, does household consumption in Malta truly follow a random walk?

And if not, is the ECM specification superior? These questions can be answered

with two approaches. Firstly, one has to identify whether or not consumption in

Malta does follow a random walk. Secondly, the models have to be compared

econometrically in order to identify the superior model.

In order to prove or disprove the random walk model derived, one needs to look at

whether consumption can be forecasted or not. According to model 1, since the

coefficient of the log of past consumption is statistically equal to 1, consumption

cannot be forecasted as movements in the variable are the result of random shocks.

Jaeger (1990) tests a random walk model of consumption by creating a regression

where actual consumption growth is the dependent variable and forecasted

consumption growth is the explanatory variable, no intercept was included. Jaeger

then states that if consumption is truly a random walk, then the coefficient of

forecasted consumption would be insignificant and the of the regression should

be close to zero. This method shall be applied.

63

Model 2 is estimated once again, however, using data up till the end of 2009. This is

done so that a forecast for consumption from 2010 quarter 1 to 2011 quarter 3 can

be produced. The result of the regression can be found in Appendix 2.5.

A dynamic forecasting procedure was conducted. One must note that the forecast is

built on the specification of model 2 that is run up till 2009 quarter 4.This procedure

created a series where household consumption at time t is a forecast based on data

from time t-1. Being a dynamic forecast, only the first forecast is built on actual data

from time t-1. All other forecasts are built on the previous forecasted values and not

actual data. The following graph represents forecasted consumption (consf) and

actual consumption (cons).

Figure 4.1: Actual consumption and forecasted consumption

€600m

€640m

€680m

€720m

€760m

€800m

€840m

2000

:1

2001

:1

2002

:1

2003

:1

2004

:1

2005

:1

2006

:1

2007

:1

2008

:1

2009

:1

2010

:1

2011

:1

CONSF CONS

64

The graph indicates that up till 2009 quarter 4 both series were the same, this is due

to the fact that the forecast was from 2010 onwards. As one can see, the forecasted

series follows the trend of the actual series, however on a higher level. So while the

forecast does follow the actual series, it is still not perfect.

With this, a regression is conducted between the growth rate of actual consumption

( ) and the growth rate of the ECM based forecasted consumption ( ).

Note that the regression is based only on data from 2010 onwards. The equation

specified and a summary of the regression result is as follows. Note that full results

are found in Appendix 2.5.

Equation 4.7

Table 4.h: Equation 4.7 regression results (forecasting test)


0.841639 0.384541 2.188684 0.0712

R-squared 0.443680


Analysing the t-statistic using a t distribution table, one finds that the coefficient is

significant at a 90% level of confidence. This indicates a significant relationship with

the actual growth of household consumption. Other than this, the goodness of fit of

the model is not close to zero. One can thus conclude that, based on the above

65

regression results, household consumption in Malta does not follow a pure random

walk as indicated by model 1.

The discussion now turns to the relative robustness of model 2. Given that the

random walk is not very applicable, does model 2 perform better econometrically?

To answer this, a table which summarises and compares the results of the two

models is drafted.

Table 4.i: Comparison between model 1 and model 2 summary

Model 1 Model 2

Goodness of fit (Adjusted ) 0.886005 0.494042

Stationarity in Model No Yes

Multicollinearity N/A No

Heteroscedasticity No No

Autocorrelation Yes No

Normality Yes Yes

Specification Error No No

Stability (Chow Breakpoint) Yes Yes

Sum of Squared Residual 0.023717 0.009567

With the above summary one can clearly see that model 2 is a better model of

consumption than model 1. While the goodness of fit of model 2 seems lower, one

can argue that model 1 shows a high goodness of fit due to the implication of a time

trend. This brings us to the next issue, stationarity. The fact that model 1 is non-

stationary leads to a clear conclusion that any results obtained from the specification

will not be sound. Other than this model 2 is proven to have no evidence of serial

correlation, giving it another advantage over model 1. The rest of the diagnostic

66

tests prove to be in favour of both models. Finally, it would seem that the sum of

squared residual of model 2 is significantly lower, indicating that the model is

stronger.

With all of this in place, one can make some conclusions about the matter. It is clear

that the random walk model is an inefficient econometric model of household

consumption in Malta. This is made clear due to the fact that consumption can be

forecasted. The second conclusion is that the ECM shows superior econometric

attributes over the random walk model. However, one must keep in mind that model

2 can still be improved. This will be discussed in the next section.

4.6: Limitations

It is important to note the limitations of the study. One can start with the limitations

that can be attributed to the data collection procedure. Given that no measure for

household disposable income and household wealth existed, these had to be

estimated. There is the possibility of bias in the disposable income measure as the

measure resulted in being smaller than consumption for some periods. Also, during

estimation a number of assumptions were put in place that may not be entirely

realistic. For example the assumption of valuing true housing prices using an index

of advertised prices. Also, during data collection some OLS regressions were

conducted to estimate missing data. These regressions, although the best option

available, were not based on any theoretical foundations.

67

Other limitations were encountered in the methodology chapter. The main issue with

this chapter is related to the use of the Engle-Granger procedure to construct the

ECM. Given that the formula had more than two explanatory variables there is the

possibility that more than one cointegrating relationship could exist. Given this, the

Johansen procedure should have been undertaken, however it was assumed that

only one relationship was present.

68

Chapter 5: Conclusion

69

Chapter 5: Conclusion

5.1: Concluding Remarks

This study set out to create a robust model for household consumption in Malta.

This goal was attempted by analysing two conflicting approaches and determining

which model truly depicts how consumption behaves in Malta.

Given the data considered, the dissertation has established that consumption in

Malta does not follow a random walk, making the ECM superior. Firstly, it was found

that consumption can be modelled as a pure random walk without drift. However,

after developing a forecasted series of consumption and testing its significance, the

pure random walk model was found to be not very applicable as the test indicated

that consumption can be forecasted. Other than this, diagnostic tests indicated that

the random walk model is less efficient than the ECM.

Thus, to truly depict consumption behaviour between 2000 and 2011, the ECM

proved to be a lot more feasible. It was found that in the long run, consumption is

influenced by disposable income, wealth, interest rates, consumer confidence and

price expectations. However, only consumer confidence and price expectations

were found to be significant in the short run. This has shed light on the importance

of the households’ perceptions of the economy on consumption behaviour.

As already stated, one cannot ensure these statements perfectly reflect reality. Both

models have been subject to numerous assumptions and estimations. This leads

70

one to state that while the models constructed do depict a possible picture of

consumption behaviour, they are not perfect. With all this taken into consideration

one cannot state that the study resulted in an ideal econometric model of

consumption. However the study does give a deeper understanding of consumption

behaviour and the econometric modelling behind it.

5.2: Suggestions for Further Research

As the study was being undertaken a few possible topics for further research were

unearthed. For the sake of future possible research to be undertaken, the final

paragraph of this dissertation is dedicated to outlining them. Firstly, research could

be undertaken to see the implication of credit availability on consumption behaviour.

Due to restrictions this was not undertaken in this study; however the possibility of a

link between consumption and credit availability in Malta exists. Another topic for

further research is the effect of the economic crisis on consumption modelling.

Stability tests on the models indicate that the crisis did not have any effects on

consumption modelling, however a deeper study into the matter may prove to be

significant. Lastly, further research could go into applying the Johansen procedure

for modelling consumption in Malta. This should result in a more robust model with

fewer assumptions in place.

71

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Appendix 1: Chapter 3 Regression Results & Data

Appendix 1.1: Variable Estimation Regression Results

1.1.1: Disposable Income

Dependent Variable: YD Method: Least Squares Date: 04/07/12 Time: 10:42 Sample (adjusted): 2000 2008 Included observations: 9 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C(1) -4910.386 810.1209 -6.061301 0.0009

GDP 0.803229 0.111543 7.201053 0.0004 ECOMPSA 0.305430 0.082215 3.715040 0.0099

R-squared 0.986216 Mean dependent var 2864.019

Adjusted R-squared 0.981621 S.D. dependent var 306.0569 S.E. of regression 41.49204 Akaike info criterion 10.55008 Sum squared resid 10329.53 Schwarz criterion 10.61582 Log likelihood -44.47537 Durbin-Watson stat 1.954631

1.1.2: Financial Wealth

Dependent Variable: FW Method: Least Squares Date: 03/27/12 Time: 12:49 Sample: 2003Q4 2011Q3 Included observations: 32

Variable Coefficient Std. Error t-Statistic Prob. DEP 2.133414 0.017684 120.6400 0.0000 R-squared 0.822381 Mean dependent var 13047.20

Adjusted R-squared 0.822381 S.D. dependent var 1458.841 S.E. of regression 614.8271 Akaike info criterion 15.71131 Sum squared resid 11718384 Schwarz criterion 15.75711 Log likelihood -250.3810 Hannan-Quinn criter. 15.72649 Durbin-Watson stat 0.174182

76

1.1.3:Consumer Confidence

Dependent Variable: CCM Method: Least Squares Date: 04/09/12 Time: 12:22 Sample (adjusted): 2002Q4 2011Q2 Included observations: 35 after adjustments

Variable Coefficient Std. Error t-Statistic Prob. C(1) 133.2493 51.79882 2.572438 0.0151

GDP -0.018671 0.029892 -0.624609 0.5368 ECOMP -0.072849 0.032663 -2.230288 0.0331

U -11.79527 4.311790 -2.735586 0.0102 R-squared 0.264352 Mean dependent var -25.59810

Adjusted R-squared 0.193160 S.D. dependent var 9.569597 S.E. of regression 8.595820 Akaike info criterion 7.247640 Sum squared resid 2290.532 Schwarz criterion 7.425394 Log likelihood -122.8337 Durbin-Watson stat 0.336285

Dependent Variable: CCM Method: Least Squares

Date: 03/22/12 Time: 10:56 Sample (adjusted): 2003Q4 2011Q2 Included observations: 31 after adjustments


CCEA(-4) 0.761112 0.168304 4.522237 0.0001 R-squared 0.413556 Mean dependent var -27.67957

Adjusted R-squared 0.393334 S.D. dependent var 7.826875 S.E. of regression 6.096255 Akaike info criterion 6.515567 Sum squared resid 1077.765 Schwarz criterion 6.608083 Log likelihood -98.99129 Hannan-Quinn criter. 6.545725 Durbin-Watson stat 0.545903

77

1.1.4: Price Expectations

Dependent Variable: PE Method: Least Squares Date: 04/09/12 Time: 14:09 Sample (adjusted): 2002Q4 2011Q3 Included observations: 36 after adjustments


INF 1.893645 2.467690 0.767376 0.4482 R-squared 0.017025 Mean dependent var 32.94444

Adjusted R-squared -0.011886 S.D. dependent var 14.36254 S.E. of regression 14.44765 Akaike info criterion 8.232893 Sum squared resid 7096.972 Schwarz criterion 8.320866 Log likelihood -146.1921 Hannan-Quinn criter. 8.263598 Durbin-Watson stat 0.245059

Dependent Variable: PE Method: Least Squares Date: 03/26/12 Time: 10:00 Sample (adjusted): 2002Q4 2011Q3 Included observations: 36 after adjustments


OIL 0.720731 0.073827 9.762496 0.0000 R-squared 0.737058 Mean dependent var 32.94444


78

Appendix 1.2: Data Collected Time Series

Cons

(€millions) Yd

(€millions) Ecomp

(€millions) W

(€millions) HHLR

% CC PE

2000Q1 647.30 603.86 3,424.52 27,381.73 6.88 18.15 16.84

2000Q2 644.34 608.00 3,425.80 27,148.26 6.91 20.51 18.25

2000Q3 648.96 616.26 3,452.71 27,682.58 7.00 19.31 21.72

2000Q4 659.31 628.66 3,463.83 29,404.08 7.00 17.87 22.35

2001Q1 644.40 636.41 3,478.43 28,219.56 6.82 16.04 17.94

2001Q2 660.73 645.50 3,548.24 29,212.18 6.78 14.90 20.30

2001Q3 656.36 630.86 3,499.50 30,400.99 6.67 15.64 18.34

2001Q4 653.32 641.83 3,505.48 31,035.52 6.42 16.35 13.58

2002Q1 663.35 636.55 3,529.56 31,408.67 6.13 16.22 15.19

2002Q2 665.77 622.84 3,476.29 31,756.75 6.05 17.82 17.51

2002Q3 645.13 630.07 3,533.12 33,532.08 5.96 22.18 17.09

2002Q4 640.26 644.68 3,528.81 34,239.17 5.89 6.10 8.85

2003Q1 683.81 629.00 3,549.12 34,073.75 5.74 5.63 8.83

2003Q2 679.66 605.86 3,560.97 35,087.57 5.72 8.13 9.50

2003Q3 665.75 618.32 3,582.91 38,558.66 5.89 18.00 8.43

2003Q4 706.66 636.31 3,610.96 38,044.65 4.65 26.10 18.43

2004Q1 694.48 611.34 3,595.62 40,386.57 4.71 30.47 23.60

2004Q2 691.78 601.44 3,616.99 41,917.60 4.68 24.90 14.07

2004Q3 704.04 602.80 3,605.59 42,827.39 4.69 28.03 21.30

2004Q4 709.92 625.61 3,606.97 43,481.20 4.68 29.17 26.53

2005Q1 702.02 622.03 3,569.47 45,899.17 4.76 28.53 23.27

2005Q2 712.36 598.99 3,573.67 46,315.13 5.02 30.40 29.57

2005Q3 726.60 613.73 3,573.18 47,373.54 4.99 31.27 36.90

2005Q4 707.81 660.53 3,581.19 49,435.33 4.94 31.47 30.77

2006Q1 709.11 666.37 3,675.91 50,398.34 4.92 30.77 30.93

2006Q2 740.36 648.34 3,678.65 51,017.27 5.07 33.00 45.20

2006Q3 752.82 665.78 3,690.34 50,900.46 5.13 30.87 34.13

79

2006Q4 745.82 698.00 3,685.23 51,527.64 5.29 24.53 23.43

2007Q1 727.60 669.97 3,638.81 52,029.94 5.54 25.83 29.23

2007Q2 738.45 646.33 3,639.55 52,635.50 5.64 17.13 33.30

2007Q3 748.12 654.10 3,647.66 52,646.36 5.81 15.47 32.73

2007Q4 752.04 689.59 3,666.08 52,490.32 5.80 11.57 28.57

2008Q1 764.69 674.49 3,683.96 53,164.54 5.60 5.87 28.13

2008Q2 783.55 669.29 3,700.73 53,295.47 5.57 14.80 45.83

2008Q3 798.14 687.99 3,728.39 52,632.81 5.79 18.17 40.00

2008Q4 772.73 723.65 3,732.13 52,540.64 4.97 31.23 43.13

2009Q1 764.63 710.25 3,773.20 51,605.61 3.93 31.97 32.93

2009Q2 760.43 707.71 3,745.51 52,373.75 3.92 35.03 37.50

2009Q3 779.39 703.41 3,706.67 52,837.17 3.92 33.13 32.70

2009Q4 771.29 711.83 3,701.85 53,032.85 3.91 31.73 36.97

2010Q1 764.16 645.01 3,629.12 53,530.16 3.90 34.20 44.17

2010Q2 742.35 624.73 3,621.53 52,583.97 3.81 31.67 40.30

2010Q3 743.13 609.96 3,624.30 54,237.18 4.06 30.93 46.77

2010Q4 775.38 633.07 3,582.63 53,228.69 4.04 32.23 54.37

2011Q1 800.00 605.24 3,573.30 53,722.44 4.08 38.40 61.90

2011Q2 777.39 607.16 3,563.90 53,806.01 4.02 39.20 62.00

2011Q3 768.24 610.78 3,537.32 55,282.64 3.99 36.87 61.17

80

Appendix 2: Chapter 4 Tests & Results

Appendix 2.1: Philips-Perron Tests on Levels

P.P. Tests on Levels: Trend and Intercept

Variable Adj. t-Stat Observed Adj. t-Stat 5% Critical Value Unit Root

-3.468542 -3.510740 Yes

-1.790911 -3.510740 Yes

-0.694769 -3.510740 Yes

-0.529551 -3.510740 Yes

-1.960378 -3.510740 Yes

-2.219752 -3.510740 Yes

-2.922993 -3.510740 Yes

Appendix 2.2: Philips-Perron Tests on First Differences

P.P. Tests on First Difference: Trend and Intercept

Variable Adj. t-Stat Observed Adj. t-Stat 5% Critical Value Unit Root

-16.01222 -3.513075 No

-7.529985 -3.513075 No

-7.557408 -3.513075 No

-7.921821 -3.513075 No

-5.766999 -3.513075 No

-5.871099 -3.513075 No

-9.361443 -3.513075 No

81

Appendix 2.3: Random Walk Results & Tests

2.3.1: Hall’s log-linear random walk model with drift

2.3.1.1: Regression Results

Dependent Variable: LOG(CONS)

Method: Least Squares

Date: 04/12/12 Time: 09:18

Sample (adjusted): 2000Q2 2011Q2

Included observations: 45 after adjustments


C(1) 0.418638 0.332372 1.259545 0.2146

LOG(CONS(-1)) 0.936892 0.050593 18.51818 0.0000


Adjusted R-squared 0.885988 S.D. dependent var 0.067947

S.E. of regression 0.022943 Akaike info criterion -4.668207

Sum squared resid 0.022634 Schwarz criterion -4.587910

Log likelihood 107.0346 Durbin-Watson stat 2.171761

82

2.3.2: Model 1: Hall’s log-linear random walk model without drift

2.3.2.1: Regression Results



Date: 04/12/12 Time: 10:14




LOG(CONS(-1)) 1.000559 0.000515 1942.497 0.0000






2.3.2.2: Wald Test

Wald Test: Equation: RW

Test Statistic Value df Probability t-statistic 1.086055 45 0.2832

F-statistic 1.179515 (1, 45) 0.2832 Chi-square 1.179515 1 0.2775

Null Hypothesis: C(1) = 1 Null Hypothesis Summary:

Normalized Restriction (= 0) Value Std. Err. -1 + C(1) 0.000559 0.000515 Restrictions are linear in coefficients.

83

2.3.2.3: White’s Heteroscedasticity Test

White Heteroskedasticity Test:

F-statistic 1.384361 Probability 0.261422

Obs*R-squared 2.782713 Probability 0.248738

Test Equation:

Dependent Variable: RESID^2


Date: 04/14/12 Time: 10:46

Sample: 2000Q2 2011Q3

Included observations: 46


C 1.916376 1.284201 1.492270 0.1429

LOG(CONS(-1)) -0.582286 0.391132 -1.488719 0.1439

(LOG(CONS(-1)))^2 0.044239 0.029779 1.485545 0.1447




Sum squared resid 2.53E-05 Schwarz criterion -11.32492

Log likelihood 266.2162 F-statistic 1.384361

Durbin-Watson stat 2.150232 Prob(F-statistic) 0.261422

84

2.3.2.4: Breusch-Godfrey Serial Correlation LM test

Breusch-Godfrey Serial Correlation LM Test: F-statistic 5.318254 Prob. F(3,42) 0.0034

Obs*R-squared 12.66351 Prob. Chi-Square(3) 0.0054

Test Equation: Dependent Variable: RESID Method: Least Squares Date: 04/12/12 Time: 15:38 Sample: 2000Q2 2011Q3 Included observations: 46 Presample missing value lagged residuals set to zero.

Variable Coefficient Std. Error t-Statistic Prob. LOG(CONS(-1)) 0.000111 0.000455 0.244623 0.8079

RESID(-1) -0.221866 0.154338 -1.437536 0.1580 RESID(-2) -0.540759 0.139600 -3.873644 0.0004 RESID(-3) -0.063289 0.159955 -0.395668 0.6944

R-squared 0.275294 Mean dependent var 4.78E-05

Adjusted R-squared 0.223529 S.D. dependent var 0.022957 S.E. of regression 0.020229 Akaike info criterion -4.880424 Sum squared resid 0.017188 Schwarz criterion -4.721411 Log likelihood 116.2497 Hannan-Quinn criter. -4.820857 Durbin-Watson stat 2.010601

85

2.3.2.5: Normality Test

0

1

2

3

4

5

6

7

8

9

-0.04 -0.02 0.00 0.02 0.04 0.06

Series: ResidualsSample 2000Q2 2011Q3Observations 46

Mean 4.78e-05Median -0.002242Maximum 0.062191Minimum -0.036092Std. Dev. 0.022957Skewness 0.609662Kurtosis 3.199029

Jarque-Bera 2.925527Probability 0.231595

86

2.3.2.6: Ramsey RESET Test

Ramsey RESET Test:


Log likelihood ratio 1.953048 Probability 0.162259

Test Equation:



Date: 04/14/12 Time: 11:11

Sample: 2000Q2 2011Q3



LOG(CONS(-1)) 1.068697 0.049326 21.66587 0.0000

FITTED^2 -0.010355 0.007496 -1.381433 0.1741






2.3.2.7: Chow Breakpoint Test

Chow Breakpoint Test: 2009Q1 Null Hypothesis: No breaks at specified breakpoints Varying regressors: All equation variables Equation Sample: 2000Q2 2011Q3

F-statistic 0.501484 Prob. F(1,44) 0.4826

Log likelihood ratio 0.521314 Prob. Chi-Square(1) 0.4703 Wald Statistic 0.501484 Prob. Chi-Square(1) 0.4788

87

Appendix 2.4: Error Correction Model Results and Tests

2.4.1: Long Run Equations Regression Results

2.4.1.1: Equation 4.3, Function with Disposable Income

Dependent Variable: LOG(CONS) Method: Least Squares Date: 04/13/12 Time: 11:48 Sample (adjusted): 2000Q2 2011Q2 Included observations: 45 after adjustments


LOG(YD) 0.170792 0.058300 2.929521 0.0056 LOG(W) 0.141766 0.023318 6.079801 0.0000

LOG(HHLR) -0.082098 0.025263 -3.249756 0.0024 LOG(CC(-1)) -0.037793 0.007527 -5.021238 0.0000

LOG(PE) 0.057550 0.008644 6.657524 0.0000 R-squared 0.940967 Mean dependent var 6.573243

Adjusted R-squared 0.933399 S.D. dependent var 0.067947 S.E. of regression 0.017535 Akaike info criterion -5.125649 Sum squared resid 0.011992 Schwarz criterion -4.884760 Log likelihood 121.3271 Durbin-Watson stat 1.835597

88

2.4.1.2: Equation 4.4, Function with Employee Compensation

Dependent Variable: LOG(CONS) Method: Least Squares Date: 04/13/12 Time: 11:06 Sample (adjusted): 2000Q2 2011Q2 Included observations: 45 after adjustments


LOG(ECOMP) 0.576885 0.224065 2.574628 0.0139 LOG(W) 0.112542 0.031107 3.617876 0.0008

LOG(HHLR) -0.063217 0.025094 -2.519171 0.0160 LOG(CC(-1)) -0.034505 0.007787 -4.431025 0.0001

LOG(PE) 0.061602 0.009038 6.816257 0.0000 R-squared 0.938440 Mean dependent var 6.573243

Adjusted R-squared 0.930547 S.D. dependent var 0.067947 S.E. of regression 0.017907 Akaike info criterion -5.083729 Sum squared resid 0.012505 Schwarz criterion -4.842841 Log likelihood 120.3839 Durbin-Watson stat 1.758500

2.4.2: Philips-Perron Test on Residual of Long Run OLS

Null Hypothesis: RESIDMODEL2 has a unit root Exogenous: None Bandwidth: 26 (Newey-West automatic) using Bartlett kernel

Adj. t-Stat Prob.* Phillips-Perron test statistic -7.134490 0.0000

Test critical values: 1% level -2.618579 5% level -1.948495 10% level -1.612135 *MacKinnon (1996) one-sided p-values.

89

2.4.3: ECM Regression Results

2.4.3.1: Equation 4.5 ECM

Dependent Variable: D(LOG(CONS))


Date: 04/13/12 Time: 14:59




C(1) 0.004646 0.003122 1.488221 0.1452

D(LOG(YD)) 0.116207 0.079922 1.454008 0.1544

D(LOG(W)) -0.122480 0.107445 -1.139925 0.2616

D(LOG(HHLR)) -0.035989 0.048304 -0.745053 0.4609

D(LOG(CC(-1))) -0.024303 0.008196 -2.965250 0.0053

D(LOG(PE)) 0.045347 0.009956 4.554911 0.0001

RESIDMODEL2(-1) -0.816071 0.154283 -5.289444 0.0000






90

2.4.3.2: Equation 4.6 ECM (Model 2)

Dependent Variable: D(LOG(CONS)) Method: Least Squares Date: 04/24/12 Time: 17:59 Sample (adjusted): 2000Q3 2011Q2 Included observations: 44 after adjustments


D(LOG(CC(-1))) -0.020325 0.007669 -2.650183 0.0115 D(LOG(PE)) 0.043975 0.009866 4.457190 0.0001

RESIDMODEL2(-1) -0.791513 0.155846 -5.078826 0.0000 R-squared 0.529342 Mean dependent var 0.004266


2.4.4:Variance Inflation Factors (VIF) Test

Variance Inflation Factors Date: 04/24/12 Time: 18:19 Sample: 2000Q1 2011Q3 Included observations: 0

Coefficient Uncentered

Variable Variance VIF C(1) 6.35E-06 1.015991

D(LOG(CC(-1))) 5.88E-05 1.027393 D(LOG(PE)) 9.73E-05 1.038872

RESIDMODEL2(-1) 0.024288 1.044293

91

2.4.5: White’s Heteroscedasticity Test

White Heteroskedasticity Test:


Obs*R-squared 15.73028 Probability 0.072732

Test Equation:

Dependent Variable: RESID^2


Date: 04/24/12 Time: 18:21

Sample: 2000Q3 2011Q2



C 0.000238 5.62E-05 4.230474 0.0002

0.003158811984*(D(LOG(CC(-1)))) -0.058116 0.057673 -1.007692 0.3207

0.003158811984*(D(LOG(PE))) -0.037427 0.061564 -0.607929 0.5473

0.003158811984*RESIDMODEL2(-1) -1.064630 0.910641 -1.169100 0.2505

(D(LOG(CC(-1))))^2 0.000368 0.000165 2.224104 0.0329

(D(LOG(CC(-1))))*(D(LOG(PE))) 0.001302 0.000566 2.302035 0.0276

(D(LOG(CC(-1))))*RESIDMODEL2(-1) -0.013372 0.014968 -0.893412 0.3779

(D(LOG(PE)))^2 -0.000553 0.000485 -1.138515 0.2629

(D(LOG(PE)))*RESIDMODEL2(-1) 0.001378 0.011081 0.124346 0.9018

RESIDMODEL2(-1)^2 0.037947 0.106386 0.356692 0.7235




Sum squared resid 2.56E-06 Schwarz criterion -12.96154

Log likelihood 304.0748 F-statistic 2.102090

Durbin-Watson stat 1.752224 Prob(F-statistic) 0.057236

92

2.4.6: Breusch-Godfrey Serial Correlation LM test

Breusch-Godfrey Serial Correlation LM Test: F-statistic 1.466431 Prob. F(3,37) 0.2395

Obs*R-squared 4.675656 Prob. Chi-Square(3) 0.1971

Test Equation: Dependent Variable: RESID Method: Least Squares Date: 04/24/12 Time: 18:23 Sample: 2000Q3 2011Q2 Included observations: 44 Presample missing value lagged residuals set to zero.


D(LOG(CC(-1))) 0.006397 0.008243 0.776017 0.4427 D(LOG(PE)) -0.000473 0.010753 -0.044021 0.9651

RESIDMODEL2(-1) 0.092115 0.330102 0.279051 0.7818 RESID(-1) -0.078008 0.348754 -0.223677 0.8242 RESID(-2) -0.342519 0.179034 -1.913149 0.0635 RESID(-3) -0.147094 0.189534 -0.776080 0.4426

R-squared 0.106265 Mean dependent var -1.71E-18

Adjusted R-squared -0.038665 S.D. dependent var 0.015996 S.E. of regression 0.016302 Akaike info criterion -5.250135 Sum squared resid 0.009833 Schwarz criterion -4.966287 Log likelihood 122.5030 Hannan-Quinn criter. -5.144870 Durbin-Watson stat 1.976470

93

2.4.7: Normality Test

0

1

2

3

4

5

6

7

8

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Series: ResidualsSample 2000Q3 2011Q2Observations 44

Mean -1.71e-18Median -4.37e-05Maximum 0.032775Minimum -0.030079Std. Dev. 0.015996Skewness -0.018067Kurtosis 2.448656

Jarque-Bera 0.559691Probability 0.755901

94

2.4.8: Ramsey RESET Test

Ramsey RESET Test:


Log likelihood ratio 0.262774 Probability 0.608221

Test Equation:

Dependent Variable: D(LOG(CONS))


Date: 04/24/12 Time: 18:25

Sample: 2000Q3 2011Q2



C(1) 0.002325 0.003074 0.756474 0.4539

D(LOG(CC(-1))) -0.019403 0.007975 -2.432923 0.0197

D(LOG(PE)) 0.041971 0.010790 3.889663 0.0004

RESIDMODEL2(-1) -0.763932 0.167387 -4.563866 0.0000

FITTED^2 2.944061 6.091172 0.483332 0.6316






5.2.1:

2.4.9: Chow Breakpoint Test

Chow Breakpoint Test: 2009Q1 Null Hypothesis: No breaks at specified breakpoints Varying regressors: All equation variables Equation Sample: 2000Q3 2011Q2

F-statistic 0.196463 Prob. F(4,36) 0.9386

Log likelihood ratio 0.950151 Prob. Chi-Square(4) 0.9173 Wald Statistic 0.785851 Prob. Chi-Square(4) 0.9403

95

Appendix 2.5: Testing the Random Walk Hypothesis

2.5.1: Model 2 Re-estimation Regression Results

Dependent Variable: D(LOG(CONS)) Method: Least Squares Date: 04/24/12 Time: 18:41 Sample (adjusted): 2000Q3 2009Q4 Included observations: 38 after adjustments


D(LOG(CC(-1))) -0.021171 0.007264 -2.914774 0.0063 D(LOG(PE)) 0.043897 0.009425 4.657634 0.0000

RESIDMODEL2(-1) -0.836518 0.165840 -5.044111 0.0000 R-squared 0.565988 Mean dependent var 0.004733


2.5.2: Actual and Forecasted Consumption Regression Results

Dependent Variable: D(CONS) Method: Least Squares Date: 04/24/12 Time: 19:00 Sample: 2010Q1 2011Q3 Included observations: 7

Variable Coefficient Std. Error t-Statistic Prob. D(CONSF) 0.841639 0.384541 2.188684 0.0712 R-squared 0.443680 Mean dependent var -0.435714


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