Jan Hinrichs

Oliver Musshoff

Economic Hysteresis in Hog Production

Keywords: economic hysteresis, risk, real options, hog production economic hysteresis, risk, real options, hog production

published or not. The documents may come   L'archive ouverte pluridisciplinaire

I. Introduction

Intensive livestock farming is characterized by two facts. Firstly, the production hardly seems to respond to the considerable price changes that have occurred during the past decades. Secondly, the spatial allocation of production is rather unequal, though no special natural conditions are required for this business. Such an unequal distribution is not desired by agricultural policy makers. Regions with a high concentration of hog production suffer from environmental problems and farmers face several restrictions when enlarging their capacity. On the other hand, there are also weakly developed regions where investments in livestock farming are appreciated in order to stabilize the rural economy. The question rises of how the observed inertia in hog production can be understood. A promising explanation is offered by the real options theory (see for example [START_REF] Chen | Protection and employment under uncertainty: a real options approach[END_REF] and the literature cited therein). This theory analyses 2 investments in a dynamic and stochastic environment. An important finding is that the optimal range of inaction widens when uncertainty and irreversibility are present. Both features exist in the case of hog production due to a volatile hog market and very specific investments in production facilities. In fact, [START_REF] Maung | Capital Investment under Alternative Marketing Scenarios in the Hog Industry: A Real Option Approach[END_REF] calculate option values for the Canadian pork industry and prove the significant effect of risk and flexibility associated with different marketing alternatives. [START_REF] Odening | Investment Decisions in Hog Production-An Application of the Real Options Approach[END_REF] apply the real options approach to investments in hog finishing and demonstrate that investment triggers are much higher than the traditional investment theory (i.e. the net present value) suggests. Moreover, it is shown that it may even be rational to tolerate temporary operative losses before giving up production.

However, their results are derived from a normative model and therefore little can be concluded about the actual explanatory power of the new investment theory. In contrast, our paper analyses the investment behaviour of German hog producers empirically. Dynamic adjustments in the pork industry have recently been studied by [START_REF] Pietola | Investment under Uncertainty and Dynamic Adjustment in the Finnish Pork Industry[END_REF] and [START_REF] Gardebroek | Capital adjustments on Dutch pig farms[END_REF] by means of a stochastic adjustment cost model. They find that uncertainty slows down structural adjustments, but their model does not allow to estimate investment and disinvestment hurdles explicitly. The objective of our analysis is twofold. Firstly, we intend to identify determinants that influence capacity adjustments in hog production. An understanding of the adjustment behaviour of hog producers is essential to predict or to control the structural change in this industry. Secondly, from a more theoretical viewpoint we wish to contribute to the empirical validation of real options models. Although more and more applications of this approach are emerging, only few papers try to test its hypotheses empirically (see for example Richards and Green, 2003[START_REF] Wossink | The Failure of Marketable Permit Systems and Uncertainty of Environmental Policy: A Switching Regime Model Applied to the Dutch Phosphate Quota Program[END_REF][START_REF] Schatzki | Options, uncertainty and sunk costs: an empirical analysis of land use change[END_REF][START_REF] Dong | He came, he saw, (and) he waited: an empirical analysis of inertia in technology adoption[END_REF]. We use a generalized ordered probit model to estimate dynamically optimal thresholds for the expansion and the contraction of production capacities in hog production. This model is applied to panel data from German farms. While standard probit models have already been employed to test for the relevance of the real options theory, to our knowledge this is the first time that a generalized ordered probit model is used in this context.

The paper is organized in five sections. Following this introduction we briefly review the theoretical framework of real options in section II. Section III introduces the econometric 3 approach. The model specification and some particular aspects of the data are discussed in section IV. The estimation results and their compatibility with hypotheses derived from the real options are reported in section V, before concluding in the final section.

II. Theoretical Framework

Consider an investor who has to decide between immediately investing in a project or waiting and deferring the investment decision. Investing causes sunk costs I and yields an infinite stream of stochastic returns R . A standard assumption is that the returns follow a geometric Brownian motion:

Rdz Rdt dR R σ µ + =
(1)

µ and R σ are the drift rate and the volatility respectively; dz represents a Wiener-process.

Formally, the decision problem has the structure of an optimal stopping problem and can be solved by dynamic programming. ( )

R F
denotes the value of the investment opportunity.

Assuming an infinite time horizon the Bellman equation of the stopping problem becomes:

( )

dF E rFdt =
(2) r stands for an exogenous interest rate. Carrying out of the common steps to solve the Bellman equation thereby taking into account appropriate boundary conditions yields the following expression for the option value (c.f. Dixit and Pindyck 1994):

( ) b AR R F = (3)
A is a constant and b is given by

1 2 2 1 2 1 2 2 2 2 > +         - + - = R R R r b σ σ µ σ µ (4)
The continuation region, where the optimal decision is to keep the investment option alive, and the stopping region, where it is optimal to invest immediately, are separated by a threshold * R , the so-called investment trigger (trigger return, hurdle rate). This critical value is given by

( )I r b b R µ - - = 1 * (5)
The factor

( ) 1 1 / > - b b
is termed the option multiple. Obviously, the optimal trigger return exceeds the classical Marshallian trigger ( )I

0 > dK if * ) ( u R t R > rI C + > 0 = dK if * * ) ( u l R t R R < < 0 < dK if * ) ( l R t R < rL C - < (6)
Herein K denotes the capital stock, C the variable costs of production, * Uncertainty and flexibility however, drive a wedge between the classical triggers and as a consequence the range of inaction widens. (6) forms the basis for the econometric model that we describe as follows.

III. Econometric model

From the previous discussion it becomes apparent that the investment and disinvestment triggers are crucial to the optimal capital adjustments. Hence we attempt to estimate the optimal decision rule in terms of

≤ + - = it lit it R R ε ) Pr( * it lit it R R - ≤ = ε ) ( * it lit R R - Φ = ε Inaction ) 0 Pr( = it dK ) Pr( * * it uit it lit it R R R R - < < - = ε ) ( ) ( * * it lit it uit R R R R - Φ - - Φ = ε ε Investment ) 0 Pr( > it dK ) 0 Pr( * ≥ + - = it uit it R R ε ) Pr( * it uit it R R - ≥ = ε ) ( * it uit R R - Φ = ε (7)
* it it it l u R X dK L L β β = )) ) (( log( 0 * ε ε σ ∑ < - Φ = it dK it lit R R )) ) ( ( ) ) (( log( * 0 * ε ε ε ε σ σ it lit dK it uit R R R R it - Φ - - Φ + ∑ = )) ) (( 1 log( 0 * ε ε σ ∑ > - Φ - + it dK it uit R R (9)
It is well known that the marginal effects of the regressors on the probabilities in an ordered

IV. Data and Model Specification

The analysis utilizes panel data of specialized hog producers from the German Farm Accountancy Data Network (FADN) 1 . The sample consists of an unbalanced panel of 211 farms over a period from 1996 to 2002. To define the dependent variable of the ordered probit model we measure changes of the production capacity for each farm and period. An extension of the production capacity indicates that the expected returns of an investment exceed the investment threshold. Conversely, a reduction of the production capacity indicates that the expected returns fall below the exit trigger. If no adjustment of the production capacity is observed it implies that the expected returns of hog production lie in the inaction region, i.e. between the investment and the disinvestment trigger. To be specific, a farm is assigned to the investment regime, if the average stock of hogs increases more than 20 percent from one year to the other and the total capital stock of the farm increases at the same time. A decline of the average stock of hogs of more than 20 percent together with a non-increase of the total capital (after depreciation) are interpreted as disinvestment while all other cases are considered as inaction. Admittedly, this definition is arbitrary in a way, but additional calculations with alternative rules for the assignment to the three regimes did not change the results significantly.

The functions u f and l f in (8) are approximated by linear functions, i.e. In this respect our approach is similar to that of [START_REF] Richards | Economic Hysteresis in Variety Selection[END_REF] or [START_REF] Moel | When are real options exercised? An empirical study of mine closings[END_REF]. The independent variables X it cover the following areas: investment returns, investment costs and production costs, uncertainty and flexibility. Table 1 summarizes the definitions and some descriptive statistics of the exogenous variables as well as their hypothesized impact on the (dis)investment trigger.

Table 1 about here

Investment and production costs

Investment costs ) ( 1x I ≡ are derived from the position "buildings" and "technical equipment" shown in the balance sheets of the farms. Both the real options theory and the traditional investment theory predict a positive effect of investment costs on the investment trigger.

Differences occur with respect to the influence of the investment costs on the disinvestment or contraction trigger. In a static context only the variable costs and the scrap value determine the disinvestment trigger. In a dynamic view adopted by the real options theory, the investment costs also play a role. An active farmer will wait longer before giving up or shrinking production if re-entry or expansion induces sunk costs again. This of course is only true, if a costless temporary suspension of production is impossible.

Since we express the trigger values in terms of revenues of hog production (and not as gross margins), variable production costs ) ( 2x C ≡ have an influence on these thresholds.

Unfortunately, the complete variable production costs are not shown in the financial statements.

The costs for farrows, which constitute a major part of the variable costs, are used as a proxy.

Nevertheless, it is likely that further cost components not covered by 1

x and 2

x influence the (dis)investment decision. For example, costs for planning and building permission arise. x , is included in the estimation model.

Another variable that may impact on the costs and thereby affect the (dis)investment trigger is the financial structure of the farm. Standard real options models implicitly assume perfect capital markets, i.e. money can be borrowed or invested at a risk free rate without restrictions.

However, Lagerqvist and Olson (2001) prove empirically that a higher financial leverage reduces the investment activities in US farms. The explanation they offer is that debt financing causes higher adjustment costs. Following this line of argumentation we include the debt share of the farms, 4

x , into the set of explanatory variables.

Investment returns and uncertainty

The investment returns are derived from the revenues from hog sales that are displayed in the income statements. Total revenues are translated into revenues per place assuming a turnover rate of 2.6. However, these figures are silent about the way of how farmers build their expectations of future returns and their volatility. The standard real option model presumes a geometric Brownian motion. Applying a Dickey-Fuller test to average annual revenues from hog production in Germany provides empirical evidence for this assumption in the present case.

The consideration of risk is of particular importance for the validation of the real options theory.

Several authors emphasize the sensitivity of option values and investment triggers with respect to the volatility of the investment returns (e.g. Schatzki, 2003 or Moel and[START_REF] Moel | When are real options exercised? An empirical study of mine closings[END_REF], but it is often difficult to control for this variable in econometric models. The use of panel data in the present application offers the opportunity to estimate farm specific volatilities. This is advantageous, because different marketing and risk management strategies leading to differences in the risk exposure of individual producers are taken into account. section II, the investment trigger increases with increasing volatility. Moreover, it can be shown that the disinvestment trigger falls when the project returns become more volatile. This means that increasing risk widens the optimal range of inaction.

Flexibility

The valuation of real options is closely connected to the measurement of flexibility. If no flexibility prevails, the new and the traditional investment theories coincide. The standard real options model in section II considers the option to defer an investment and assumes that this option does not expire. This simplifying assumption allows to derive the closed form solution

(3), but it is not a very realistic one. Investment opportunities may vanish in the course of time for different reasons. To illustrate this point, think of tightening environmental regulations that will rule out certain types of intensive animal husbandry in the future. Moreover, the farmer's flexibility to time the investment optimally will diminish with his increasing age, at least in family farms which constitute the majority in our sample. But if we concede that flexibility varies between farms and over time, this aspect should enter the empirical model. There are some attempts to quantify flexibility in the context of real options. For example, [START_REF] Ramezani | Real options, corporate performance, and shareholder value creation[END_REF] measures managerial flexibility by the firms' expenditures for research and development.

We prefer a narrower interpretation of flexibility in the sense of it measuring the time until the (dis)investment option expires. Option pricing theory tells us that the change of the option price with respect to the passage of time, i.e. the option theta is usually negative. In other words: the time value of the option decreases in the course of time and the value of the unexercised option converges to the intrinsic value. Quite analogously, the trigger values converge on their classical counterparts. It is tempting to approximate the time period to maturity of the (dis)investment option by the farmer's age, but the loss of flexibility will be interfered by another effect. The older a farmer is, the more likely it is that he does not receive the full returns of the investment.

In order to get an unambiguous relation between the age and the investment trigger we suggest using the absolute deviation between 45 and the farmer's age, 8

x . This proposal is motivated by the observation that the investments considered have an average operating life of about 20 years and that farmers usually retire at the age of 65.

Fixed effects and random effects

A prevalent problem related to the analysis of panel data is unobserved heterogeneity in the population. That means individual effects exist for each case (farm), which are not covered by the explanatory variables of the regression model. Ignoring these effects can lead to biased or inefficient parameter estimates. In the present application such effects may arise from differences in the farm manager's education, in the location or the legal status of the farm. Two main approaches are discussed in the literature to cope with this issue, the fixed effects approach and the random effects approach [START_REF] Arellano | Panel Data Econometrics[END_REF]. Fixed effects models assume that differences between individuals are constant over time and can be captured by differences in the constant term of the regression model, i.e. by dummy variables. Due to the fact that our sample includes more than 200 farms, it is practically unfeasible to assign a dummy variable to each unit. A step in that direction is to distinguish between intensive production regions (Lower Saxony and North Rhine-Westfalia,

1 5 = i x
) and less intensive production regions (all other states,

0 5 = i x ).
This distinction is motivated by possible differences in the production costs. Moreover, according to [START_REF] Porter | The competitive Advantage of nations[END_REF] cluster theory a high regional concentration of an industry can lead to cost advantages.

The second approach, the random effects model, views individual specific terms as randomly distributed across the units. This view seems more appropriate to our case, since the farms under consideration are a sample drawn from a larger population. Random individual effects are taken into account by including a second error term in the model. The relevance of individual random effects can be tested by a Lagrange-Multiplier test [START_REF] Breusch | The LM Test and its Applications to Model Specification in Econometrics[END_REF]. For our data we obtain an LM test statistic of 2.10 which falls below the critical value on a 95 percent significance level, 3.84. Hence the null hypothesis of no individual effects cannot be rejected. This finding justifies to conduct a pooled regression.

V. Results and discussion

As mentioned above, the empirical residuals of the generalized ordered probit model ( 7) neither show any significant correlation nor an autocorrelation between farms. Hence the maximum likelihood method will provide asymptotically efficient estimates. The log likelihood function ( 9) is maximized with respect to u β and l β using (10). it X is specified as described in the previous section. Table 2 summarizes the estimation results.

Table 2 around here

First of all, a pseudo R 2 value of 0.71 indicates a good overall fit of the model. Before we turn to the discussion of the partial effects of the explanatory variables we calculate the average β = 0.03 can be interpreted as a (risk free) interest rate. The impact on the disinvestment trigger is negligible. This result is not implausible, since in practice a reduction of the production capacity does not always go along with a disinvestment, but can also be the result of a temporary suspension of the production. The costs for such an interruption (e.g. transaction costs, contract penalties) are not necessarily related to the investment costs. The coefficients of the variable costs ( 2x ) have the correct sign and are significant, at least for the investment case.

Hog producers with a high stock rate and farms located in intensive production regions do not have higher investment triggers. This indicates that the aforementioned potential advantages and disadvantages of an intensive and spatially concentrated production balance out. It is remarkable that the disinvestment trigger is lower in the two regions with intensive hog production.

The hypothesis of leveraged farms exhibiting higher investment reluctance is rejected by the data: the coefficient 4 u β is not significant. Apparently additional debt capital can be acquired without increasing marginal costs -a result that seems to contradict previous research on the impact of the capital structure on the investment behaviour in agriculture (e.g. Barry et al., 2000). It should be noted, however, that the financial leverage of the investing farms is rather low on average (0.23). Moreover, a detailed analysis of the relation between capital structure and the investment behaviour requires considering the investment volume and the availability of internal financial funds. These factors were not taken into account in the present analysis.

Conclusions from the relevance of the new investment theory are usually based on the investigation of the sign and the significance of the estimated parameters of the risk variable. In fact, the coefficients have the sign that is predicted by the real options theory Multiplication with the two coefficients results in an average increase (decrease) of the investment trigger (disinvestment trigger) of 79 euros (163 euros) compared to a situation with certain returns. Hence the investment risk is a key factor for the understanding of the inertia in this sector. Unfortunately, a negative relationship between the investment activity and uncertainty cannot be uniquely attributed to the existence of real options. Alternatively, such a finding could simply be explained by the risk aversion of decision makers. While this problem has been described in the literature it has not been solved yet. As a way out we propose to look at the interaction of uncertainty and flexibility. In the context of the new investment theory, both uncertainty and flexibility are required to increase the range of inaction. Simple risk aversion on the other hand, works independently of flexibility. This distinction permits to separate the two causes of investment reluctance. For an implementation of this idea we divide the sample into two subsets, the one showing high and the other low flexibility. Again, flexibility is defined in terms of the expiration time of the (dis)investment option, which is approximated by the farmer's age. At the same time the variable 8

x is removed from the model. A separate estimation of the model with the two data sets reveals that the impact of risk is more pronounced if farms have higher flexibility: the coefficients of the risk variable 7 x are 7 u β = 3.98 and 7 l β = -6,96 for the more flexible group, whereas the corresponding values of the less flexible group are 0.31 and -0.74. That means, the observed inertia of the capacity adjustment can be (at least partially) assigned to option-like hysteresis.

VI. Summary and Conclusions

The understanding of the dynamics of capacity adjustments in agriculture is an important issue, since (dis)investments determine the direction and the velocity of structural changes.

Accordingly, many attempts have been made in agricultural economics to explain these decisions, technological, financial as well as sociological models being amongst them 2 . In the present paper a real options framework is used for analyzing capacity adjustments in the hog sector. Real options models allow to disentangle the joint effects of irreversibility and uncertainty concerning (dis)investment decisions. In our view this is an advantage compared to F o r P e e r R e v i e w 14 alternative approaches, in particular adjustment cost models. We employ a generalized ordered probit model for an empirical validation of the real options approach. It turns out that many implications of the new investment theory are in harmony with the empirical facts reflected in our data. Empirical evidence for real option models frequently is devaluated by the equivocal effect of uncertainty about investment decisions. One might object to the assertion that it is difficult to distinguish between options effects and simple risk aversion. However, an important feature of our model is the separation of both impacts of uncertainty. We provide evidence that real options actually play a role for the optimal timing of the expansion and contraction of production capacities in the German hog industry.

Of course, the existing real options in hog production cannot fully explain the emergence of production clusters. Nevertheless, real options help to understand why structural adjustment processes in hog production take place rather slowly. Our results draw the attention to sunk costs and uncertainty. An important implication of our results is that the observed inertia in capacity adjustments need not to be interpreted as a kind of inefficiency. The farmers' reluctance to invest does not necessarily express ignorance of profit opportunities or market frictions. It rather is compatible with dynamically optimal behaviour. Hence, a slow capacity adjustment per se provides little justification for state intervention. Such measures should for instance be justified by environmental or regional policy targets. If, on the other hand, it is desirable to speed up adjustment processes and structural changes in intensive livestock production for whatever reasons, the considerable inertia which can be attributed to this sector, has to be taken into account. This knowledge is helpful for the design of measures falling into the second pillar of the CAP like for example investment programmes and retirement programmes. for making the data available.

2 [START_REF] Boehlje | Alternative Models of Structural Change in Agriculture and Related Industries[END_REF] provides an overview of these models.

Page 19 of 19

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Submitted Manuscript

R

  the disinvestment trigger. L is a lump-sum cost, which the firm must incur in case of a disinvestment. If the firm earns a liquidation value, L is negative. Clearly, reveals that the sole presence of sunk costs already causes economic hysteresis.

  has the structure of an ordered probit model. This relation becomes clear if we consider it it R ε + as the latent variable of the probit model and realize that the investment trigger is always larger than the disinvestment trigger. Note that the thresholds * uit R and * lit R are not constant but depend on economic variables it X which may be firm specific and/or time varying.In general, the relation between the triggers and the vector of control variables can be β are parameter vectors that have to be estimated.[START_REF] Pudney | Gender, Race, Pay and Promotion in the British Nursing Profession: Estimation of a Generalized Ordered Probit Model[END_REF] introduced the term 'generalized ordered probit model' for this class of models. Our model is a special case showing a trivial structure of the latent variable. Under the assumption that the errors it ε are independent and normally distributed with standard deviation ε σ

  equal to the parameters u β and l β . Moreover, it is not the impact of the regressors on the probabilities simply by inspecting the sign of the coefficients, at least not for the inaction case 0 = it dK (cf.Greene, 2000, p. 877).This complicates the interpretation of the results in general. A peculiarity of our model is that a change of the independent variables it X does not shift the distribution of the latent variable but the thresholds * uit R and * lit R . Due to this fact, the effect of a regressor on the probability of being inactive is unambiguous, if the corresponding coefficients have opposite signs (increase (decrease) of * uit R and decrease (increase) of * lit R ). If, in contrast, the coefficients are both positive or both negative it is not clear whether the probability of observing inaction increases or decreases.

  investment and disinvestment trigger by multiplying the parameter estimates with the average values of the regressors it X . The corresponding values are 553 and 127 euros respectively per place. That means, an average farmer extends his production capacity whenever the returns in hog finishing exceed 553 euros per place and year. Conversely, the production capacity is reduced, if the returns fall below a threshold of 127 euros per place and year. In order to assess the magnitude of these figures a comparison with the classical Marshallian triggers would be helpful. Since the empirical model does not allow for an endogenous calculation of the classical triggers you have to derive them separately. According to average planning data for Germany, variable costs of hog finishing amount to 260 euros. This value constitutes the classical exit trigger. Apparently the estimated disinvestment trigger only covers 50 percent of the variable costs. The classical investment trigger is approximated as follows: The average investment costs in our sample are 604 euros. An assumed operating life of 20 years, an interest rate of 6 percent and a wage rate of 15 euros per hour lead to fixed costs of 78 euros per place and year. Adding fixed and variable costs gives a classical total expense of 338 euros, which is considerably less than the estimated value of 553 euros. Hence our results confirm the hypothesis that the endogenously calculated investment triggers (disinvestment triggers) in hog production exceed (fall below) their classical counterparts. In average the range of inaction is more than five times higher compared with a situation without uncertainty and flexibility. parameter estimates support the hypotheses of the real options theory. As expected, investment costs ( 1 x ) increase the investment trigger. The corresponding parameter estimate 1 u

  ( 7 u β = 3.01, 7 l β = -6.19). The average volatility of the returns from hog production amounts to 26 percent.

1

  We are grateful to the Federal Agricultural Research Centre (FAL Braunschweig), Germany

Table 1 : Summary of the independent variables

 1

	Variable	Mean	Standard	Hypothesized impact on	Definition
			deviation Investment	Disinvestment
				trigger	trigger
	R	327.5074	65.1633	-	-	Fattened hog revenues
		€				p.a. and place
	1 x	€ 515.2717	643.9740			Investment costs
	2 x	€ 147.9929	31.2609			Farrow costs p.a. and place
	x 3	3.9740 LU/ha	2.0288		?	Number of livestock units per ha
	x 4	19.7391 %	22.3674		?	Debt share in percent of total assets
	x 5			?	?	Dummy variable accounting for regional differences
	6 x	% 1.1760	4.7096			Drift rate of hog revenues
	7 x	% 26.2583	6.3470			Volatility of hog revenues
	x 8	7.9201 years	5.5996		/	Absolute deviation of farmers´ age from 45 years
	= Trigger increases		= Trigger decreases	? = Effect unclear
	Total number of observations = 839
	Number of observations with investment: 64
	Number of observations with inaction: 748
	Number of observations with disinvestment: 27

Table 2 : Maximum Likelihood estimation results

 2

	Variable	Investment Parameter Estimate 1	Disinvestment Parameter Estimate
	1 x	β	1 u	0.0302** (2.5385)	β	l	1	0.0000 (0.0000)

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Elena Marquez

Ana R Martinez Cañete

Ines Perez

Soba Aguilar

INTERTEMPORAL PREFERENCE PARAMETERS FOR SOME EUROPEAN MONETARY UNION COUNTRIES

Keywords: intratemporal non-separability of preferences, intratemporal elasticity of substitution, intertemporal elasticity intratemporal non-separability of preferences, intratemporal elasticity of substitution, intertemporal elasticity of substitution, durable and nondurable consumption. JEL classification: E44, G12

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The fundamental goal of this paper is the estimation and analysis of the intertemporal preference parameters, that is the subjective discount factor and intertemporal elasticity of substitution, shown by investors-consumers in Germany, Spain and France in the long term.

These preference parameters have often been estimated within the context of the consumption-based capital asset pricing model, CCAPM, developed by [START_REF] Lucas | Asset Prices in an Exchange Economy[END_REF]. In different cases, their empirical estimation has given rise to puzzling intertemporal elasticity of substitution estimates; specifically, the estimated values of this parameter can be considered abnormally low 1 , and are even negative in some cases, such as in the work of [START_REF] Hall | Intertemporal Substitution in Consumption[END_REF] and [START_REF] Hansen | Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors[END_REF] for the North American economy. Focusing on the countries we have mentioned, we find puzzling estimates of the parameter in the work of, among others, [START_REF] Rubio | Testing the CCAPM on Spanish Data: A New Approach[END_REF] and Rodríguez [START_REF] Rodríguez López | Modelos Intertemporales de Valoración de Activos: Análisis Empírico para el Caso Español[END_REF] for Spain, [START_REF] Lund | GMM and Present Value Tests of the C-CAPM: Evidence from the Danish, German, Swedish and UK Stock Markets[END_REF] and [START_REF] Meyer | Intertemporal Asset Pricing. Evidence from Germany[END_REF] for Germany, [START_REF] Girardin | Private Consumption Behaviour, Liquidity Constraints and Financial Deregulation in France: a Nonlinear Analysis[END_REF] for France, and [START_REF] Cuthberston | Resurrecting the C-CAPM: Evidence from France and Germany[END_REF] for Germany and France.

The literature provides different explanations for the difficulties with which the consumption-based capital asset pricing model adjusts to empirical evidence. In the first place, some authors consider that the specification of preferences normally used since [START_REF] Hansen | Large Sample Properties of the Generalized Method of Moments[END_REF]Singleton (1982, 1983) is inappropriate, so the resolution of the abnormal values detected would require alternative agent preference specifications 2 . On the other hand, the omission of durable consumption in the estimation of preference parameters, a common practice which may not be appropriate insofar as preferences which are intratemporally inseparable could introduce a downwards bias into the estimates of intertemporal elasticity of substitution. This is the fundamental reason presented by [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF]Reinhart (1998a, 1998b) to explain abnormally low estimates of intertemporal elasticity of substitution, and the same line is followed by [START_REF] Dunn | Modelling the Term Structure of Interest Rates under Non-Separable Utility and Durability of Goods[END_REF], [START_REF] Eichenbaum | Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data[END_REF]Hansen (1990), López Salido (1993), [START_REF] Mamaysky | Interest Rates and the Durability of Consumption Goods[END_REF], [START_REF] Okubo | Intertemporal Substitution and Consumer Durables: an Analysis Based on Japanese Data[END_REF], [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF], [START_REF] Wirjanto | Exploring Consumption-Based Asset Pricing Model with Stochastic-Trend Forcing Processes[END_REF] and [START_REF] Yogo | A Consumption-Based Explanation of Expected Stock Returns[END_REF] 3 .

Our research is therefore based on the hypothesis of the impact that durable consumption might have on the estimation of certain preference parameters in the context of the CCAPM model. We have to analyse the degree to which preferences are intratemporally separable, since only if this is confirmed can durable consumption be omitted from the analysis. We therefore estimate the intratemporal elasticity of substitution between nondurable and durable consumption followed by an estimation of the subjective discount factor and intertemporal elasticity of substitution with the consumption data identified as most appropriate by the intratemporal separability analysis.

These estimates are performed for three European countries, Germany, Spain and France, with a two-fold purpose: on the one hand, we aim to verify whether the results are robust; and on the other, since they are members of a monetary union and monetary policy is therefore common to them all, we aim to analyse the possible differences between the values of the preference parameters of the different economies involved; should such differences exist, they could help us to understand the diverse effects that such a common policy could have on saving in the different countries. Besides studying these three economies, and unlike the other empirical studies examined, we also introduce an analysis of current preferences between durable and nondurable consumption when they are not homothetic. The analysis becomes more robust from an econometric perspective because the model is tested using two different cointegration methods, [START_REF] Park | Canonical Cointegrating Regressions[END_REF] and [START_REF] Johansen | Likelihood-Based Inference in Cointegrated Vector Autoregressive Models[END_REF].

The paper is organised as follows: firstly, in section 2, we briefly describe the theoretical model and econometric methods used in the estimation. Section 3 contains the results of our estimation of the intratemporal elasticity of substitution between durable and nondurable consumption following the approach adopted by Ogaki and Reinhart (1998a) and [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF]. In section 4, we go on to use the two-stage Generalised Method of Moments (GMM) to estimate the Euler Equation resulting from the intertemporal maximisation of investors, using consumption data considering the flow of services generated by durable consumption and thus obtaining intertemporal elasticity of substitution estimates for the countries considered. Finally, section 5 contains our conclusions. The Appendix provides details of the consumption series employed.

The model and the testing methods

The model

We follow the model adopted by Ogaki and Reinhart (1998a).

Intertemporal preferences are expressed as

[1] ( ) 1 1 0 0 1 , 1 t t t U E u σ σ β σ ∞ - = ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ = - ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ - ⎣ ⎦ ∑
where 0 σ > is the intertemporal elasticity of substitution and 0 β > is the subjective discount factor. Intratemporal utility is given by a function with constant elasticity of substitution (CES function):

[2]

1 1 1 1 1 1 1 , 0, 0. t t t u aC S a ε ε ε ε - - - ⎡ ⎤ = + > > ⎢ ⎥ ⎣ ⎦ t C
= + + + < <
where 1 - is the rate of depreciation of durable goods and t D is the expenditure on durable consumption in period t.

The maximisation of the intertemporal utility of the agents would be represented by the following Euler equation,

[4] 1, 1 1 1, 1, , t i t t t UMa E R i UMa β + + ⎡ ⎤ ⎢ ⎥= ∀ ⎢ ⎥ ⎣ ⎦
where

1 i t
R + is the gross rate of return of asset i during period t and 1,t UMa is the marginal utility of the consumption of nondurable goods and services in period t.

Since this is a model with two goods, it is possible to exploit the first-order condition that shows that, for each period t, the relative price of the assets, t P , must be equal to the marginal rate of substitution between them, as follows:

[5] [ ] 2, 0 1, t t t t E U M a P UMa τ τ τ τ β δ ∞ + = ∑ = where 2,
UMa τ is the marginal utility of the flow of services generated by durable consumption.

Multiplying the two members of the previous expression by ( ) ( ) ( )

1 1 1 1, 1, 0 1 t t t t t t t t t t UMa C S C P E D a D C U M a τ ε ε ε τ τ τ τ τ β δ ∞ - - - + + + = = ⎡ ⎤ ⎛ ⎞ ⎡ ⎤ ⎢ ⎥ ⎟ ⎜ ⎢ ⎥ ⎟ ⎢ ⎥ ⎜ ⎟ ⎜ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ∑
This expression is the basis for estimating the intratemporal elasticity of substitution between the two types of asset. When ε σ = , we could converge to the separable model, because in this case the intertemporal marginal rate of substitution would only depend on the consumption of nondurable goods 5 .

In the above Ogaki and Reinhart model, the current preferences are homothetic. [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF] contemplates the possibility of the two types of asset being considered actually having a low degree of substitutability, and being largely complementary, since it seems sensible to assume that joint consumption of durable and nondurable assets would increase agent utility.

Pakos also analyses the possibility of the income effect playing an important role in the determination of relative consumption. The current utility function proposed by Pakos is as follows:

[7]

{ }

1 1 1 1 ( , ) ( ) , 0 t t t t u C S aC S ε η ε ε ε η - - - = + >
where  is the quotient of the income elasticities of nondurable,  1 , and durable consumer goods,  2 . In this case, the first-order condition equivalent to equation [6] would be:

[8]

( ) ( )

1 1 1 1 1, 1 1 1 1 1, 0 1 1 t t t t t t t UMa C S C P E D C D U M a a η ε ε ε τ τ τ τ η η τ τ ε ε η β δ ε + ∞ - - - + + - = - = - ⎡ ⎤ ⎛ ⎞ ⎟⎛ ⎞ ⎜ ⎢ ⎥ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎢ ⎥ ⎜ ⎜ ⎟ ⎟ ⎝ ⎠ ⎜ ⎟ ⎜ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ ∑
Once again, under certain assumptions, we could estimate parameters ε and η with a cointegration approach. Ogaki and Reinhart (1998a) show that, under certain assumptions, the right- where, again, b is a constant and t v is a zero mean stationary process. It is possible to show that, although the ordinary least squares estimator is superconsistent, it is not asymptotically efficient, so we will estimate the parameters involved using a cointegration approach.

Econometric method

Specifically, following Ogaki and Reinhart (1998a), we have estimated the intratemporal elasticity of substitution using the canonical cointegration method proposed by [START_REF] Park | Canonical Cointegrating Regressions[END_REF] 7 . We will also use the ( , ) H p q test proposed by [START_REF] Park | Testing for Unit Roots and Cointegration by Variable Addition[END_REF] for the cointegration analysis. This test enables us to test both the determinist (0,1) H and stochastic (1, ) H q 8 cointegration hypothesis.

We have also estimated the parameters according to the [START_REF] Johansen | Likelihood-Based Inference in Cointegrated Vector Autoregressive Models[END_REF] method. The essential idea is to analyse the degree to which the results obtain change according to the method of estimation employed and, when applicable, confirm these results 9 . The Johansen method is based on considering a VAR of order p which can be expressed in the form of an error correction model as

[11] 1 1 1 1 1 ... t t p t p t t Y Y Y Y e µ - - -+ - ∆ = +Γ ∆ + +Γ ∆ + Π + ,
where t Y is a vector of m variables I(1).

If the range of matrix Π is less than m, this matrix can be broken down as

[12] β α ′ = Π F o r P e e r R e v i e w
where β contains the cointegration ratio parameters and α contains the adjustment parameters. The range of Π indicates the number of cointegration ratios and can be tested by the maximum likelihood estimation of the trace test 10 .

The asymptotic distributions of the trace test change depending on the hypotheses constructed on the deterministic terms in the error correction model. In this respect, [START_REF] Nielsen | Similarity Issues in Cointegration Page 26 of 36[END_REF] showed that, if the data contains linear trends (which would lead to [ ] 0

≠ ∆ t Y E
), testing the cointegration rank starting with a specification including a trend restricted to the cointegration vector induces "similarity" in the testing procedure, meaning that the critical trace test values do not depend on the values of the parameters. It is subsequently possible to test whether this trend is significant or not and, if not, estimate the model using a specification comprising a constant not restricted to the cointegration vector. However

, if [ ] 0 = ∆ t Y E
(there is no trend in the data), according to this similarity argument, the cointegration rank should be tested considering a constant restricted to the long-term ratio 11 . In this paper, the specification of the deterministic terms has been based on this procedure.

Intratemporal elasticity of substitution in

Germany, Spain and France

Unit root test

The first step before applying the cointegration approach consists of analysing whether the series involves are stationary or not. Estimation of intertemporal elasticity of substitution by the GMM method also requires the series employed to be stationary. For these two reasons, we use the usual unit root tests in order to analyse whether the series employed meet the required 1970[START_REF] Campbell | Consumption-Based Asset Pricing[END_REF]for Germany, 1964[START_REF] Mamaysky | Interest Rates and the Durability of Consumption Goods[END_REF]for Spain and 1960[START_REF] Mamaysky | Interest Rates and the Durability of Consumption Goods[END_REF] for France. To calculate the relative price of durable and nondurable consumer goods, we first calculate the deflator for each type of good and then find the ratio between them. As for the rate of return of the risk-free asset, for Germany it corresponds to the annual 3-month interest rate on the interbank market published by the IMF. For Spain, we take the mean interest rate of the different one-year treasury bond issues (1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001) and the internal stock market return on electric bonds 12 (1964-1986); the data comes from the Bank of Spain. For France, we use the rate of interest on government bonds (one year or more) provided by the IMF. Finally, as a proxy variable of the rate of return on risk assets, we have taken the market yield for each of the countries considered. For Germany, we have considered the annual mean of the Total DAX30 Index, for Spain, the Total General Madrid Stock Market Index (IGTBM) and for France, the Paris stock exchange CAC40 index. In all these cases, we use the variation in the nondurable consumer good expenditure deflator to calculate both the real interest rate and the real rate of return.

As we can see on Table 1, the results of the augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests for the relative price logarithm t p , and the logarithmic difference of the two types of consumption ( )

t t c d -
show that consumption and relative price are variable (1) I both for Spain and for Germany (for a 5% level of significance). The procedure proposed by [START_REF] Holden | Unit Roots and Cointegration for the Economist[END_REF] to determine the true data generating process enables us to confirm the non-stationarity of relative consumption for these

F o r P e e r R e v i e w
two countries. The same applies to France. Therefore, we can conclude that both consumption and relative price are I(1) series in the countries analysed.

Note that this is a condition required in order to apply the cointegration approach.

With regards to the real interest rates 13 , the tests employed indicate that this variable is I(1) for France. In Germany and Spain, however, it can be considered I(0), because the existence of unit root cannot only be rejected in the model including neither a constant nor a trend, which can be dismissed as the true data generating process if we use the Holden and Perman procedure mentioned earlier.

As for each country's representative rate of return on risk assets, we cannot dismiss the existence of unit root in model ( 3), which again fails to correspond to the true data generating process.

In sum, the rates of return on risk assets are stationary in the three countries considered, whereas this only applies to the real interest rate in Germany and Spain.

Results of the estimation according to the Park and Johansen cointegration methods

The cointegration tests performed with the canonical cointegration method and the Johansen maximum likelihood method, and the results of the intratemporal elasticity of substitution estimations, are shown on Tables 2 and3, respectively.

Germany

As Table 2 shows, Park's ( , ) H p q test does not enable us to dismiss the existence of both determinist and stochastic cointegration between the variables. The estimated value of µ is significantly different from zero but,

F o r P e e r R e v i e w
although the sign is correct, the intratemporal elasticity of substitution is not significant.

According to the Johansen method, there is a cointegration ratio between relative consumption and prices 14 . The model has been specified with a constant restricted to the cointegration vector because, in the German case,

[ ]= - ∆ ) ( t t d c E -0.002 and [ ]= ∆ t p E
-0.005. Is can be seen that the constant is significant (on the 10% limit) but it cannot be dismissed that price t p is not part of the long-term ratio; in other words, that ε is not significantly different from zero 15 .

The fact that the estimated value of the intratemporal elasticity of substitution is not significant (Table 3), has led us to consider the specification of the utility function proposed by [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF], which analyses the possibility of the income effect playing an important role in the determination of relative consumption 16 .

In this case, Park's Hp, q test rejects the null hypothesis of determinist cointegration, but not stochastic cointegration. The results show that, in this case, ε it is significantly different from zero, like parameter η . The fact that this is less than a unit, indicates that  1   2 ; in other words, that the income elasticity of nondurable consumer goods is smaller than that of durable goods. In model (1), the cointegration rank is r =1. Parameters ε and η are significant and they are also positive, as expected. The first of them is somewhat greater than results from canonical cointegration, whereas the second is very similar. With regards to model (2), we have also considered r =1.

The trend is not significant so, according to the similarity argument mentioned earlier, once the rank was determined we have estimated the parameters, accepting that the data trend is cancelled in the cointegration vector and therefore considering a constant not restricted to the latter. Both the estimated parameters are positive and significant and closer to those obtained with canonical cointegration.

Spain

The [START_REF] Park | Testing for Unit Roots and Cointegration by Variable Addition[END_REF] test shows that the null hypothesis of both stochastic and determinist cointegration cannot be rejected for a 1% level of significance in any of the cases considered, although determinist cointegration is rejected for a 5% level of significance (Table 2). The estimated values of both µ and ε are significantly different from zero. On the other hand, the results do not enable us to reject the null hypothesis 1 ε = , so we cannot dismiss the Cobb-Douglas utility function as valid for the Spanish case.

As for the Johansen method, a study of the series does not point to the existence of a data trend and we also With a view to comparing the results with the German case, we have also estimated the utility function proposed by [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF] 17 . This model is rejected for Spain by the Park test in nearly all the cases considered. The sign of parameter ε is also incorrect, although it is not significant. With the data available, therefore, this model does not appropriately reflect the performance of relative consumption in Spain.

obtain [ ]= - ∆ ) ( t t d c E -0.
Neither are non-homothetic preferences supported by the results obtained with the Johansen method, since the estimated price coefficient is negative when considering both a constant and a trend restricted to the cointegration vector (the fact that [ ]= 1) and r =2 in model ( 2) 18 . In the former, the price coefficient is significant, although this is not the case in the latter 19 .

France

The Park test does not enable us to reject the null hypothesis of both determinist and stochastic cointegration. The results of the estimation of intratemporal elasticity of substitution again indicate that both µ and ε are significantly different from zero and that the intratemporal elasticity of substitution also has the correct sign. On the other hand, as in the Spanish case, it is not possible to reject the null hypothesis 1 ε = , so the Cobb-Douglas utility function cannot be dismissed as valid for France.

According to the Johansen method, observation of the series indicates that we can rule out the existence of a determinist trend, especially in relative consumption. The mean of the series in differences is also close to zero and considering the possibility of it existing (model 2). According to model (1), the most appropriate cointegration rank is r =2. The results are not too satisfactory because we have obtained that one of the cointegration rations could come from the fact that durable consumption is stationary and the other does not appropriately link the model's variables, since both the price and durable consumption parameters are unexpectedly negative. As for model (2), the cointegration rank is r=1 and we obtain that the trend restricted to the cointegration vector is not significant. We therefore estimate the model considering an unrestricted trend, which does not provide the results expected because it cannot be rejected that ε is both significant and negative. To estimate the intertemporal elasticity of substitution, we will employ the Generalised Moments Model in two stages proposed by Ogaki and Reinhart (1998a) as a deviation from the Generalised Method of Moments [START_REF] Hansen | Large Sample Properties of the Generalized Method of Moments[END_REF]. In our model, and with the simplifying assumption that 1 a = , the Euler Equation [7] takes on the following form in the case of homothetic preferences

(specifically, [ ]= - ∆ ) ( t t d c E -0.

Estimation of intertemporal elasticity

[13] ( ) 1 1 ( 1) 1 1 1 1 1 1 1 1 1 1 1 1 , , t t t i t t t t t C S C E R i C C S σ ε σ ε ε ε ε ε ε β - - - - - + + + + - - ⎡ ⎤ ⎛ ⎡ ⎤ ⎞ ⎢ ⎥ + ⎟ ⎜ ⎛ ⎞ ⎢ ⎥ ⎣ ⎦⎟ ⎢ ⎥ ⎜ ⎟ ⎜ = ∀ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ ⎜ ⎢ ⎥ ⎜ ⎡ ⎤ ⎝ ⎠ ⎟ + ⎟ ⎜ ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ and [14] 1 1 ( 1) 1 1 1 1 1 1 1 1 1 1 , t t t i t t t t t C S C E R i C C S σ ε η σ ε ε ε ε η ε ε β - - - - - + + + + - - ⎡ ⎤ ⎛ ⎞ + ⎛ ⎞ ⎟ ⎢ ⎥ ⎜ ⎟ ⎟ ⎜ ⎜ = ∀ ⎟ ⎟ ⎢ ⎥ ⎜ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎟ ⎜ ⎢ ⎥ + ⎝ ⎠ ⎣ ⎦
, for non-homothetic preferences. The idea in Ogaki and Reinhart (1998a) is to introduce the estimated values of the parameters in the previous stage in equations [13] and [14] to proceed to estimate σ . This method does not affect the asymptotic distribution of the estimators obtained by the Generalised Method of Moments 21 .

The only requirement of estimation by GMM to verify all the desirable properties of the estimators are for the variables employed to be stationary 22 .

On the other hand, estimation by the Generalised Method of Moments leads us to the need to consider the choice of instruments. From a theoretical perspective, the only requirement a variable has to meet to be an instrument is to be known by the agents at the time when they make their decisions. We have therefore completed the estimation considering two different groups of instruments, in order to analyse whether the results are sensitive to them. In order to mitigate the problem of temporal data aggregation on the estimations, following [START_REF] Hall | Intertemporal Substitution in Consumption[END_REF], [START_REF] Hansen | Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors[END_REF] and Amano and Wirjanto I1 : it includes a constant, the total consumption growth rate lagged two periods and the real interest rate lagged two periods 23 .

I2 : it includes a constant, the total consumption growth rate and the gross real rate of return of the stock exchange index considered in each case, both lagged two periods.

The estimations have been made jointly employing the real interest rate and the respective rate of return of the stock index of each country, except for

France because, as we saw in section 3, the interest rate is not stationary, so it does not meet the condition required for the GMM estimator to show all the desirable properties. In the French case, therefore, we have estimated the model only considering the real rate of return of the CAC40 index. The results are shown on Table 4.

In all cases, the estimated values of both intertemporal elasticity of substitution and the subjective discount factor have the correct sign and are significantly different from zero. On the other hand, the model is not rejected in any case using the Hansen test. Except for France, the estimations appear to be sensitive to the instruments used, since they significantly differentiate between them.

If we compare the estimates of intertemporal elasticity of substitution with those obtained in previous papers for the countries considered, we see that in our case they are clearly higher. With regards to Germany, for instance, Meyer values obtained here. Using the same technique, [START_REF] Cuthberston | Resurrecting the C-CAPM: Evidence from France and Germany[END_REF] also obtain intertemporal elasticity of substitution values lower than those shown on Table 4, although they are higher than those obtained by Meyer 25 .

On the other hand, Lund and Engstend (1996), using the GMM method, also obtain very low intertemporal elasticity of substitution values, which are in many cases not significantly different from zero. For Spain, [START_REF] Rubio | Testing the CCAPM on Spanish Data: A New Approach[END_REF], Jagannathan bounds, must be over 14, implying an intertemporal elasticity of substitution value of less than 0.07.

using
If we compare the results with those obtained using the same model for other countries, we see that the estimations of  for the Spanish and French cases are higher than those obtained by [START_REF] Wirjanto | Exploring Consumption-Based Asset Pricing Model with Stochastic-Trend Forcing Processes[END_REF] for Canada, [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF]Reinhart (1998a, 1998b) for the United States, and [START_REF] Okubo | Intertemporal Substitution and Consumer Durables: an Analysis Based on Japanese Data[END_REF] for Japan. In the German case, the results with group of instruments 2 I come quite close to those obtained by [START_REF] Wirjanto | Exploring Consumption-Based Asset Pricing Model with Stochastic-Trend Forcing Processes[END_REF] for Canada. It is important to emphasise that in these papers, the value of the subjective discount factor is taken as given in the estimation 26 . Since the subjective discount factor and intertemporal elasticity of substitution are negatively related, and since the estimated values of β in our case are lower than those established by Ogaki and Reinhart, it is not surprising to find that the estimated intertemporal elasticity of substitution Furthermore, in the German case, we can see that, although the subjective discount factor estimated with group of instruments I2 is close to that established by Ogaki and Reinhart, the estimated value of  is considerably higher. However, we must remember that while we consider non-homothetic preferences for Germany, Ogaki and Reinhart use homotheticity in their estimations.

If we compare the results obtained for the three countries analysed, we see that the estimated intertemporal elasticity of substitution is considerably lower in Germany than in Spain and France; this would mean that saving in Spain and France is more sensitive to real interest rate variations than in Germany.

Nevertheless, this result must be taken with caution, because the intertemporal model being considered for Germany is not the same as the model contemplated for the other two countries. Furthermore, we also have to consider that the sample periods considered, although close, are different, and this could also be affecting the estimates.

Since we now have an estimation of both ε and σ , we can test the intertemporal separability of the preferences; it is sufficient to test the null hypothesis σ ε = . In the German case, separability of preferences is rejected when we consider the estimates of σ obtained with group of instruments I1, but not with group of instruments I2. In the cases of Spain and France, however, the intratemporal separability of preferences is rejected in all the cases considered.

Conclusions

Intertemporal elasticity of substitution has been estimated in intertemporal models considering a single consumer good, specifically the consumption of nondurable goods, giving rise to values which are too low. The separable nature of the intratemporal utility function, which translates in practical terms into non-consideration of durable consumption expenditure, can bias preference parameter estimations. In this paper, we have estimated the intratemporal elasticity of substitution between durable and nondurable consumption for Germany, Spain and France, using the approach proposed by [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF]Reinhart (1998a, 1998b) in order to analyse whether the current utility is separable into the different consumption components. The estimation was performed considering annual consumption data and calculating the flow of services provided by durable consumption assuming that such goods generate services for a finite time and that the depreciation rate of durable consumption is greater the further away we are from the time of acquisition. We have also considered the utility function proposed by [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF], which considers non-homothetic intertemporal preferences.

With these premises, and using a cointegration approach, the results of this estimation for Germany, Spain and France show how intratemporal elasticity of substitution is significantly different from zero, although for Germany we have considered non-homothetic preferences, whereas for Spain and France we have estimated the elasticity value with homothetic preferences. Based on this result, we have considered it appropriate to introduce durable asset consumption in the intertemporal elasticity of substitution estimation.

The estimated intertemporal elasticity of substitution values for the three countries are all of the correct sign and significantly different from zero when the non-separable model is considered; the same occurs with the subjective discount factor which is also always less than 1. If we compare the estimations obtained in each of the countries analysed, we see that the estimated intertemporal elasticity of substitution values for Spain and France and higher than for Germany, showing that the reaction of consumers-investor to changes in the real interest rate is different in the countries considered. The results indicate that it is Spanish saving which reacts more strongly to shocks in the real interest rate and Germany saving which is less sensitive, although elasticity of substitution is positive in all cases, and over 1. Nevertheless, it is important to note that this result should be taken with caution because the current utility function used in the intertemporal elasticity of substitution estimation is different for Germany than for Spain and France. Not in vain, if we consider the intertemporal elasticity of substitution estimations for Spain and France with group of instruments I2, we can see how the estimated values are quite close, which is not the case for Germany. Finally, the separable model can be clearly rejected for Spain and France, although not so clearly for Germany, since we cannot reject the null hypothesis of equality between intratemporal and intertemporal elasticities of substitution when group of instruments I2 is used to estimate the latter. However, the estimation of the separable model has enabled us to see how the omission of a consumption expenditure component produces a downwards bias in the intertemporal elasticity of substitution estimations and, in this respect, the non-consideration of durable consumption could help to explain the puzzling estimates of this parameter obtained in previous works.

In sum, the results presented indicate a need to consider specifications of the current utility function which include durable good consumption as a utility-generating argument. We believe that this could help to improve the empirical results of macroeconomic models aimed at estimating intertemporal preference parameters and thus mitigate the different empirical puzzles detected when they are tested. On the other hand, there are significant differences in the parameters estimated for the three countries considered, which must be taken into account when analysing the impact that common EMU monetary policy could have on the different member countries. The scope of this paper would clearly be increased by applying the analysis to more member States and explicitly including both money and the monetary policy transmission mechanism in the model.

Appendix: consumption data

Unlike most other studies estimating preference parameters within the framework of the CCAPM model, our project requires distinguishing between expenditure on nondurable assets and services and expenditure on durable goods. To obtain the relevant information, we have referred to the National (2002). In this case, the base year is 1995.

Having homogenised the consumption expenditure series for the different countries, we distinguished between expenditure on nondurable goods and services and durable goods. For this purpose, nondurable consumer goods and services include the following concepts:

1. Food products, beverages and tobacco.

2.

Clothing and footwear.

3.

House rental, heating and lighting.

4.

Household entertainment goods and services.

5.

Medical and healthcare services.

6.

Maintenance and preservation of personal means of transport.

7.

Use of public transport.

9.

Entertainment, leisure and cultural services.

10.

Other goods and services.

On the other hand, durable consumer goods include the following concepts:

1. Furniture, accessories and household appliances.

2.

Purchase of vehicles.

3.

Leisure, sport and cultural articles.

4.

Books, newspapers and magazines.

5.

Teaching.

To calculate the service flows generated by durable consumption, we have calculated the following expression 10 0 , 1.

t t k t k t k S D δ δ - - = = =

∑

We have introduced two differences in relation to the work of [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF]Reinhart (1998a, 1998b):

1.

In the first place, we have considered that durable consumption generates services during a finite number of periods. We specifically assume that durable consumption generates services for 11 years. This number was selected considering the mean lifespan of the most typical of 1 Using the terminology typical of asset pricing literature, we could say that, to a certain extent and according to the specification of the preferences employed, the results reflect both the risk premium puzzle, [START_REF] Mehra | The Equity Premium. A Puzzle[END_REF], and the interest rate puzzle, [START_REF] Weil | The Equity Premium Puzzle and the Riskfree Rate Puzzle[END_REF]. A detailed analysis of the empirical puzzles of the CCAPM model, and of some of the solutions proposed, can be found, among others, in [START_REF] Campbell | Consumption-Based Asset Pricing[END_REF]. 2 We are referring to the consideration of phenomena such as durability or the formation of consumption habits, as in the case, among others, of [START_REF] Dunn | Modelling the Term Structure of Interest Rates under Non-Separable Utility and Durability of Goods[END_REF] or [START_REF] Campbell | Explaining the Poor Performance of the Consumption-Based Asset Pricing Models[END_REF] or to the rupture with the expected utility approach in the work of [START_REF] Epstein | Substitution, Risk Aversion, and the Temporal Behaviour of Consumption and Asset Returns: An Empirical Analysis[END_REF].

3 Focusing on the Spanish case, López [START_REF] López Salido | Consumo y ciclo vital: resultados para España con datos de panel[END_REF] analyses the intratemporal separability of preferences using microeconomic data from the Encuesta Continua de Presupuestos Familiares for the 1985-89 period. 4 Note that if 1 ε = , expression [2] converges to the Cobb-Douglas function, whereas if 0, ε = the current utility would converge to Leontief's utility function. For a detailed analysis, see [START_REF] Pakos | Asset Pricing with Durable Consumption Goods and Non-Homothetic Preferences[END_REF]. 5 We can therefore test the assumption of intratemporal separability by testing the null hypothesis . ε σ = 6 Specifically, Ogaki and Reinhart consider an endowment economy in which their logarithm is stationary. On the other hand, Ogaki and Reinhart (1998a) and [START_REF] Okubo | Intertemporal Substitution and Consumer Durables: an Analysis Based on Japanese Data[END_REF] show that, although the stationarity of is not necessarily derived from the model's assumptions, it is a valid assumption, at least from an empirical perspective. 7 For a detailed study of this technique, see, among others, [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF] and [START_REF] Ogaki | Structural Macroeconometrics[END_REF]. 8 The difference between the two concepts is based on the fact that the cointegration vector which eliminates the stochastic trends among the variables can also eliminate determinist trends or not. In the first case, we refer to determinist cointegration, whereas if the determinist trends are not eliminated by the cointegration vector, this is a case of stochastic cointegration. For details of the determinist and stochastic cointegration concepts, see, among others, [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF]. 9 Other methods also lead to estimators with all the desirable properties. This is the case for the methods of [START_REF] Phillips | Statistical Inference in Instrumental Variables Regression with I(1) Processes[END_REF] and [START_REF] Stock | A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems[END_REF]. 10 This method (the properties of which make it particularly useful in a multivariate context) also allows for stationarity tests on the series involved in the analysis, so it is possible to complete the study of their order of integration provided by unit root tests. 11 See [START_REF] Hendry | Explaining Cointegration Analysis, part. II[END_REF]. 12 In this respect, we have followed [START_REF] Esteve | Determinantes de los tipos de interés reales a largo plazo en España[END_REF].

13

, 1 f j t R + is the real interest rate of country j , j=Germany, Spain, France, and cannot be rejected as stationary, in line with the results of the ADF and PP unit root tests, when we consider a constant in the datagenerating process. In all the estimated long-term ratios, we have performed the relevant exclusion, stationarity and weak parameter exogeneity tests by means of LR tests distributed like a ) 2 ( 2 χ the degrees of freedom of which depend on the constraints established. We have also tested the VAR residues to verify that they present neither autocorrelation nor heterocedasticity and that they verify the hypothesis of normality (although, if this hypothesis is not confirmed, [START_REF] Gonzalo | Comparisons of Five Alternative Methods of Estimating Long-Run Equilibrium Relations[END_REF] showed that the results of the estimation would continue to be robust). According to the information criteria of Akaike and Schwarz, the number of lags used in the VAR is 1 in the estimations for Spain and Germany and 2 for France. 16 The results of the ADF and Phillips-Perron unit root tests for variables t c y t d show that we cannot reject them as non-stationary. The results are available upon request to the authors. 17 The unit root tests do not reject the stationarity of variables t c and t d for some of their specifications. The results of these tests are available upon request from the authors and they are confirmed to a certain extent by the results obtained for this specification of preferences with the Johansen method. 18 Since with r=2 the module with the greater characteristic root is not too close to 1 and, moreover, both price and durable consumption react significantly to deviations in the longterm ratio. 19 Moreover, in this case, it cannot be rejected that t c and t d are stationary variables.

1 i t R + is
20 With this level of significance, the stationary test applied enables us to reject that relative consumption is stationary.

21 For an explanation, see [START_REF] Ogaki | Unit Roots in Macroeconometrics: A Survey[END_REF][START_REF] Ogaki | Structural Macroeconometrics[END_REF].

22 See section 3. 23 In the case of France, since the real interest rate is not stationary, the variable on levels has been replaced by its gross growth rate. 24 We are referring to the [START_REF] Hansen | Large Sample Properties of the Generalized Method of Moments[END_REF]Singleton model (1982, 1983). 25 The results are somewhat less puzzling when we consider utility function specifications which are not intertemporally separable.

26 For example, Ogaki and Reinhart apply a value of β equal to 0.99 and 0.995 for quarterly data; in other words, the annual subjective discount factor takes on values of 0.9605 and 0.9801. 27 We are unaware of microeconometric estimations of this parameter for the other two countries considered. 28 We are referring to the Order of the Ministry of Economy and Public Finance of December 15, 1998, annex IV. In these tables, we have taken the number of years after which the vehicle in question is less than 15 per cent of its initial value. The parameters have been estimated considering larger and smaller periods of time, without the results varying significantly. All the results are available upon request from the authors. Since we are unaware of the existence of similar tables for Germany and France, we have applied the procedure used for Spain to these two countries. 29 Depreciation rates have been taken from the aforementioned tables.

  . We specifically apply the ADF test and the Phillips-Perron unit root test to the following series: relative consumption, relative price, real interest rate and real rate of return.The relative consumption data are annual for the three countries and cover

Furthermore

  005, the nondurable and durable consumption series point to a greater data trend possibility because , respectively. Therefore, as a pragmatic solution, we determine the cointegration rank according to the Johansen method, considering a constant restricted to the cointegration vector (model 1) and a trend likewise restricted (model 2), which also enables us to assess are very sensitive to the specification of the deterministic terms.

  . The model has therefore been specified including a constant restricted to the cointegration vector. The cointegration rank is 1 and both the constant and the intratemporal elasticity of substitution are positive and significant, with the latter being slightly lower than is obtained with the Park method and very close to unit value.

  appears to indicate the possible presence of a trend in the series). The most appropriate cointegration rank is r =1 in model (

  012 and [ ]= ∆ t p E -0.012). We therefore estimate the homothetic preference model considering a constant restricted to the cointegration vector. The information used to determine the cointegration rank Page 13 of 36Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK is 1. The constant and price parameter are positive and significant, the latter to a 10% level 20 .Again, in order to compare these results with those obtained for Germany, we have also estimated the non-homothetic preference model, even though the proposal ofOgaki and Reinhart (1998) cannot be rejected. The model is rejected when we consider the Park test for a value of q≥3. Moreover, although the estimated value of ε is significantly different from zero, the sign is incorrect. In the French case, as for Spain, theOgaki and Reinhart (1998a) model appears to be the most appropriate.Neither does the Johansen method support the model based on nonhomothetic preferences. The evolution of the consumption series (of both durable and nondurable assets) does not enable us to clearly exclude the presence of a data trend (indeed, estimate the model both disregarding the trend in the series (model 1)

  among others, we have lagged the variables used as instruments two periods. The instruments considered are:

(

  1999), applying the Hansen and Jagannathan bounds technique to the basic CCAPM model 24 , obtains that the intertemporal elasticity of substitution values required for the model to adjust to the empirical evidence ranges, according to the consumption data employed, from 0.0006 to 0.0007, much lower than the

  the basic model, obtains aversion to risk parameter values of over 60, which implies intertemporal elasticity of substitution values of less than 0.016. The results obtained by Rodríguez López (1997) again show intertemporal elasticity of substitution values not significantly different to zero in some cases;the results are especially puzzling when the basic model is considered. Finally, for France,[START_REF] Girardin | Private Consumption Behaviour, Liquidity Constraints and Financial Deregulation in France: a Nonlinear Analysis[END_REF] present estimations of this parameter which are close to zero and[START_REF] Cuthberston | Resurrecting the C-CAPM: Evidence from France and Germany[END_REF] estimate that the relative risk aversion parameter values required for the model to satisfyHansen and

  On the other hand, it is important to mention that the estimated values of this parameter for Spain are consistent with the microeconometric estimations of the same parameter obtained by López Salido (1993) 27 .

  Accounts of the different countries concerned, specifically to the classification of consumption expenditure by function. The sample period covered in each case depends on the availability of data for the countries included in the analysis. The sources of information used and the sample period contemplated for the three countries are as follows: Germany: the data covers the 1970-2003 period. It is annual data taken from the Statistisches Bundesamt Deutschland. Data at constant prices is based on the year 1995. Spain: the data covers the 1964-2001 period. For 1964-1994, we have taken the series from Uriel et. al. (2000), whereas for 1995-2001, the data comes from the National Accounts, based on 1995, published by the INE. France: the data covers the 1960-2001 period and comes from the Institut National de la Statisque et des Études Économiques, INSEE

  In the table, (***) indicates that the estimated parameter is significantly different from zero at a 1 per cent, (**) 5 per cent and (*) 10 per cent level of significance. (a) In the case of Model (2) for Spain, it shows the estimated value of the trend

  hand side of expression [6] is stationary 6 , so if we take logarithms on the lefthand size of the expression, we could obtain that variables p t , c td t  are

	cointegrated, with (1, 1/ ) ε -	being the cointegration vector. To estimate this
	cointegration vector, we consider the following expression:
	[9]	t p	1 ( c t µ ε = +	-	t d	)	+	t v	,
	where t v is a zero mean stationary process and µ is a constant. In the case of
	non-homothetic preferences, equation [8] would lead us to the following
	cointegration regression
	[10]	t c	b = +	ε	t p	+	t d η	+	t v	,
	F o
	r
	P e
		e
			r
			R e
						v i
									e w

  the three countries considered. This result is confirmed on Table5, where we have estimated the separable model for Germany, France and Spain with group of instruments I1; in order to analyse the effect of omitting one of the components of consumption expenditure on the estimated intertemporal elasticity of substitution value, we have taken the estimated value of the subjective discount factor in the non-separable model as given. The results obtained confirm the initial hypothesis, since the estimated intertemporal elasticity of substitution values are significantly lower than those obtained in the non-separable model, and are even negative for France; furthermore, in the Spanish case, the model is rejected by the Hansen test.

	F o
	r
	P e
	e
	r
	R e
	v i
	e w

The results, then, appear to indicate the non-intratemporal separability of preferences among the different consumption components for

  durable consumption assets: cars. We referred to the Registered car, jeep and motorcycle depreciation tables published by the Ministry of Public Finance for

		Submitted Manuscript	Page 24 of 36
		F o F o F o F o F o F o
		r r r r r r
		P e P e P e P e P e P e
		e e e e e e
		r r r r r r
		R e R e R e R e R e R e
		v i v i v i v i v i v i
		e w e w e w e w e w e w
	Spain 28 .
	2.	Secondly, we assume that the rate of depreciation of durable
	consumer goods, t k δ -, increases the further we get from the period in
	which they were purchased. In other words, we assume a variable rate of
	depreciation 29 .
	Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  to calculate the nominal rates of return for Germany, Spain and France).14 To determine the cointegration rank, the information provided by the trace test in table 2 has been completed, in all cases, with an analysis of the roots of the characteristic polynomial and with the t statistics of the adjustment coefficients α . The critical values of the 95% trace

									the real
	gross rate of return of financial asset i,	i	=	DAX	30,	, IGTBM CAC	40	(abbreviations of the
	stock indices used test were obtained from Johansen (1995).
	15 According to the stationarity tests applied,	(	t c -	d	t	)

Page 33 of 36 Editorial

	Submitted Manuscript
	T Ta ab bl le e 4 4: : I IN NT TE
	F o
	r
	P e
	e
	r
	R e
	v i
	e w

Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

ER RT TE EM MP PO OR RA AL L E EL LA AS ST TI IC CI IT TY Y O OF F S SU UB BS ST TI IT TU UT TI IO ON N

  Notes: the values in square brackets are asymptotic p values Page 34 of 36 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Page 35 of 36		Submitted Manuscript Submitted Manuscript		Page 36 of 36
			T Ta ab bl le e 5 5: : S SE EP PA AR RA AB BL LE E M MO OD DE EL L
	Country	Stage 1 Country INSTRUMENTS β	σ	β	J-Test	σ	J-Test
		estimations GERMANY
	GERMANY	ε	η	0.9355 I1	0.0010 [0.0000]	8.3934 0.9355 [0.1358]	1.6353	5.2793
		0.7707 0.9881 SPAIN	I2 0.9478	[0.0000] 0.9706 [0.0000] 9.1375 [0.0032] 0.0081 [0.0103] [0.0000] 1.2979 [0.0000]	[0.2598] 5.8883 [0.2320]
	SPAIN	ε 1.4368 FRANCE	I1 0.8716 I2	0.9478 [0.0000] -0.2155 1.4122 0.9187 [0.0000] [0.4935] [0.0000] 3.2735 2.3714	3.8161 [0.4314] 3.8221
			[0.0000] Notes: the values in square brackets are asymptotic p values [0.0000]	[0.4307]
	FRANCE	ε		I1			0.8716	2.3018	0.2712
						[0.0000]	[0.0000]	[0.6025]
		0.9533 F o F o	I2		0.8826 [0.0000]	2.2196 [0.0000]	1.7750 [0.1827]
			r r
			P e P e
				e e
				r r
				R e R e
						v i v i
							e w e w

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UKSubmitted Manuscript

Notes: 1. In the table, (***) indicates rejection of the null hypothesis of existence of unit roots at a 1 per cent, (**) 5 per cent and (*) 10 per cent of significance level. The critical values were obtained from [START_REF] Mackinnon | Critical Values for Cointegration Tests[END_REF]. The number of lags chosen (in brackets) for the ADF test is the number for which the greatest lag of the variable in first differences is significant, starting with a lag of k = 4 , and for the Phillips-Perron test the number corresponding to the Newey and West procedure (1987).

2. Beneath columns (1), ( 2) and ( 3) are the results of the tests for the models with constant and trend, with constant, and without constant or trend, respectively.

GERMANY