Arto Luoma
email: arto.luoma@uta.fi

Jani Luoto

Quantitative Methods, C22 -Time-Series Models < C2 -Econometric Methods: Single Equation Models < C -Mathematical and Quantitative Methods, D83 -Search|Learning|Information and Knowledge < D8 -Information and Uncertainty < D -Microeconomics, D84 -Expectations|Speculations < D8 -Information and Uncertainty < D -Microeconomics

Keywords: learning models, inflation expectations, survey data learning models, inflation expectations, survey data

In this paper we discuss a few models developed to explain the general public's inflation expectations formation and provide some relevant estimation results. Furthermore, we suggest a simple Bayesian learning model which could explain the expectations formation process on the individual level. When the model is aggregated to the population level it could explain not only the mean values, but also the variance of the public's inflation expectations. The estimation results of the mean and variance equations seem to be consistent with the results of the questionnaire studies in which the respondents were asked to report their thoughts and opinions about inflation.

In recent empirical literature of inflation expectations formations, Branch (2004 a) developed a promising model of heterogeneous agents, in which the general public forms its inflation expectations using a prediction function from a set of costly alternatives. Specifically, he assumes that consumers use three alternative types of forecast functions in their formation process: VAR, adaptive and naïve type models. His relatively contradictory results have lead scientists to think more closely about the process of consumers' inflation expectations formation. We, for example, find the assumption that households have access to VAR estimates to be unrealistic 2 . This is because the ordinary person cannot perceive the causes of inflation. [START_REF] Shiller | Why Do People Dislike Inflation[END_REF] in his questionnaire study, asks the respondents to list causes of inflation. The responses to this question were diverse and almost equally represented. Most assumed 'factors' of inflation were of a general type, such as 'greedy' or 'government'. Thus, identification of any more or less complex econometric or economic models seems to be an overwhelming task for ordinary people. In addition, we of course agree with Branch (2004 a) and many others in that the agents are heterogeneous. However, we believe that heterogeneity is mainly concerned with the thought process of individuals and is therefore hardly identifiable. More importantly, it is unclear how important this heterogeneity is in the evolution of aggregate consumer expectations. [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] explores the causality of the Michigan households' mean inflation expectations and the Survey of Professional Forecasters (SPF) mean inflation forecasts. 2 One may assume that the VAR forecasts are almost same as the forecasts of professionals made available to the public trough news articles, but they cannot be directly compared since there is no cost to read those news articles. Using the standard Granger causality test he finds that the professional forecast Granger-causes the household forecast, but that there is no Granger causality in the opposite direction. This evidence of Granger causality plays an essential role in his theory of epidemiological expectations formation. In his epidemiology model, households form their expectations when they randomly come into contact with the relevant information set which Carroll assumed to consist of news articles about professional forecasters' forecasts. This epidemiology model is closely linked to the sticky information model of [START_REF] Mankiw | Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF], for which [START_REF] Khan | Estimates of the Sticky-Information Phillips Curve for the United States, Canada and the United Kingdom, Bank of Canada Working paper 2002-19[END_REF] and [START_REF] Mankiw | Disagreement About Inflation Expectations[END_REF] acquire empirical estimates. All these authors employ different identification schemes, and estimate that individuals update their information sets on average every 12 months. If this is the case, a large proportion of the population always uses lagged news media forecasts as their information set.

Consequently, inflation expectations of the general public should be modelled as a function of lagged professional expectations. Finally, Branch (2004 b) compares these 'sticky information' models to the model uncertainty approach of Branch (2004 a) and states that model uncertainly is a more robust element of the Michigan data.

In this paper, we show that the Michigan inflation expectations data support neither Carroll's epidemiological model nor the sticky information model of [START_REF] Mankiw | Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF]. Moreover, we suggest a simple Bayesian learning model for the formation process of inflation expectations and show that by using this type of a boundedly rational model we can describe individuals' opinions and their uncertainty about them.

When the model is aggregated from the individual to national level and certain assumptions are made it can explain not only the mean values, but also the variance of the public's inflation expectations. The estimation results of the mean and variance 4 equations seem to be consistent with the results of the questionnaire studies in which the respondents were asked to report their thoughts and opinions about inflation.

In the inflation expectations literature, there has been almost no work testing learning models using actual empirical data. An important exception is [START_REF] Caskey | Modeling the Formation of Price Expectations: A Bayesian Approach[END_REF], who in his excellent paper uses a learning model, similar to ours, for professional forecasters' views about future inflation. However, formation of inflation expectations requires these professionals to assimilate media reports, personal observations, macroeconomic data, and other forms of information that might be generated in obscure ways.

Therefore, the use of an econometric model or some simple alternative behaviour model to explain their expectation formation might be problematic (see [START_REF] Manski | Measuring Expectations[END_REF].

However, the expectation formation of the general public is likely more straightforward.

A typical individual observes inflation through news media reports, which are mainly based on annualized monthly inflation figures, and perceives the process of inflation on a very superficial level. Thus, modelling inflation expectations using a simple, welldefined random process might be ideal in this case.

Our report is organized as follows. In Section II, we explore the empirical relationship between the professionals' and consumers' forecasts. In Section III, we discuss the formation process of the general public's inflation expectations and present a Bayesian learning model. In Section IV, we test how well the outcomes of this model can explain the mean and variance of inflation expectations. Finally, in Section V we conclude the paper.

F

where M t and S t are operators that yield the population means (or medians) of the Michigan and SPF inflation expectations at time t, respectively, and t is an error term.

The estimates obtained using the mean and median series are presented in Table 1.

The estimates of 3 in the mean and median cases are positive and significant at the 5% and 1% levels, respectively. This suggests that annualized monthly inflation, which is the most commonly reported inflation figure in the news media, is an important factor to [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] finding that inflation has no influence on an individual's expectation formation process. In our opinion, his finding arises, first, from the high correlation (0.865) between recent annual inflation and the lagged value of the Michigan series, and second, from using the annual inflation series instead of the monthly annualized inflation series.

Surprisingly, when we look at the estimate of 2 in the median case, its estimate is not statistically significant. Therefore, we could possibly exclude the lagged value of the Michigan series from the regression equation ( 3). This empirical finding causes a real problem to Carroll's epidemiology model. Moreover, the reader should note that as [START_REF] Curtin | Procedure to Estimate Price Expectations[END_REF] and [START_REF] Mankiw | Disagreement About Inflation Expectations[END_REF] argue, the long tails of the Michigan expectation series are not particularly informative and, therefore, the results acquired using median values might be more sensible. Therefore, in the following we will focus on the median values of the Michigan series. [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] argues that the constant term in equation 3 is spuriously significant because it implies, for example, that if both actual inflation and the professional's expectations were to go to zero forever, people would continue to expect a positive inflation rate forever i.e. they wouldn't eventually learn. However, this is only true when we expect that individuals form their expectations as Carroll assumes. For example, if individuals form their expectations using learning models, the presence of a positive constant in regression poses no problem. Unfortunately, the results presented above are not very reliable, because using nonstationary time series in regression analysis may yield spurious regression and inconsistent parameter estimates (see, for example, [START_REF] Hamilton | Time series analysis[END_REF]. On the other hand, if the series are cointegrated, the ordinary least squares (OLS) estimates might be biased due to endogeneity and serial autocorrelation (see Banerjee et al, 1993, Chapter 7).

Therefore, we studied whether the series are unit root processes. The results of the augmented Dickey-Fuller test are shown in Table 2. Since the null hypothesis of a unit root is not rejected in either case of an expectation series and only slightly rejected in the case of the annualized inflation series, we model them as I(1) processes.

If the expectations series move together in the long-run, which seems to be a reasonable assumption, they can be modelled using co-integrated vector autoregression (CVAR).

Let therefore

y t = (M t [ t+4 ] S t [ t+4 ] t m
)' be the vector of the SPF median inflation forecast, the Michigan household median inflation expectation and annualized monthly inflation, respectively. Then the CVAR model can be parameterized in the error correction form

= + + + = 1 1 1 ' p i t t i t i t y y y , (4)
where is a vector of parameters, a matrix/vector of adjustment coefficients, a cointegrating matrix/vector and i :s parameter matrices. The error vectors t are assumed to be independent over time and normally distributed with zero mean and covariance matrix6 . We will use the Bayesian approach and posterior density simulations to make exact inference on the parameters. To see whether the data confirm the existence of a cointegrating relation between the Michigan, professional and actual inflation series and to find proper lag length for the model (4) we follow [START_REF] Corander | Bayesian Assessment of Dimensionality in Reduced Rank Regression[END_REF] and compute approximate fractional marginal likelihoods (FML). The FML results (not reported here in order to save space) indicate that the proper lag length is 1 and cointegration rank 2.

However, we restrict our model to include only one co-integrating vector and write the long-run relationship in an informative form

[ ] [ ] t 2 4 1 4 z + + = + + m t t t t t S M , (5)
where z t is a stationary term; that is, we use the parametrisation = (-1 1 2 )´. as a sign of noncausality, since professional forecasters should use the information offered by consumer expectations when they form their forecasts. For example, they might expect that the high inflation expectations of the general public cause consumer inflation to rise. The estimates of the CVAR model are presented in Table 1. Since more than 4% of the probability mass of 1 lies below zero, one must be careful when stating that the general public uses professional forecasters' forecasts when they form their expectations. On the other hand, the high CVAR estimate 2 = 0.349 confirms our earlier results that annualized monthly inflation is an important factor in the public's inflation expectations formation process. One can also interprete the estimated cointegrating relation so that the expectations of the public are more closely connected to annualized monthly inflation figures than the professionals' forecasts, since professionals also use other information in their forecasts, such as unemployment rates and lagged inflation estimates. See also the estimates of equation ( 6) in Table 1, where annualized inflation is excluded from regression. The link between the Michigan and SPF expectations does not seem strong here either, since the 95 % posterior interval of 1 includes zero. [START_REF] Khan | Estimates of the Sticky-Information Phillips Curve for the United States, Canada and the United Kingdom, Bank of Canada Working paper 2002-19[END_REF], [START_REF] Mankiw | Disagreement About Inflation Expectations[END_REF] and [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] ) we estimate the CVAR model using four lags.

The estimates of this model are shown in Table 1 (equation ( 6)). As the lag length estimate indicates, the posterior density of 21 (i) has a lot of its probability mass close to zero. Thus, the cumulative effect of the lagged SPF series on the Michigan series is not economically or statistically significant 7 . It seems that the data do not support [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] epidemiology model nor [START_REF] Mankiw | Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF] sticky information model.

Finally, Table 3 shows the medians and standard errors of the cross coefficients 21 (i) (i = 1,…,p) and their sums when standard Bayesian vector autoregressive (BVAR) models with a noninformative Jeffrey's prior distribution and different lag lengths 8 are used.

We can see from the table that the parameters 21 (i) are not significantly different from zero except in the model with one lag. However, as Carroll's Granger causality test indicates, the cumulative effect of the SPF forecast on the Michigan series is positive with high probability. Thus, there seems to be a relation between the professional's and the general public's forecasts, but this relation is probably a kind of long-run comovement in which the general public adjusts its expectations as the significant estimate for the adjustment parameter 1 = 0.487 indicates (see Equation 6in Table 1).

However, households do not necessarily adjust their expectations toward the forecasts 7 Note also that no one of the parameters 21 (i) had a posterior distribution deviating significantly from zero (results were similar when we use mean series). We also estimated the error correction model with the assumption that the SPF series is exogenous and the results looked similar. 8 The model is of the form In summary, we do not find that the data support [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF] epidemiology model or [START_REF] Mankiw | Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF] sticky information model. Therefore, there is a need for some alternative theory for the general public's inflation expectations.

III Modelling the Consumers' Formation of Inflation Expectations

In our candidate theory, which offers an alternative explanation for the general public's inflation expectations formation process, we assume that each individual has his own personal beliefs about the process of inflation. They update this prior knowledge regularly using annualized monthly inflation figures and possibly some other variables offered by the news media and use the updated information to form their expectations.

We find several reasons why inflation expectations of the general public should modelled using a well-defined random process with personal probabilities about the parameter values of the process. Firstly, individuals cannot observe inflation directly but through the news media, since in everyday life they observe the prices not the inflation.

Secondly, it is well known that typical individuals' views about the inflation process are relatively poor. They may not have any clear idea about the causes of inflation. It is very descriptive that the most common answer was 'greed' or 'greedy', when [START_REF] Shiller | Why Do People Dislike Inflation[END_REF], in his questionnaire study, asked people to list the causes of inflation. Thirdly, we, unlike [START_REF] Mankiw | Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF] or [START_REF] Carroll | Macroeconomic Expectations of Households and Professional Forecasters[END_REF], expect that most people follow economic news daily or at least regularly. We agree with [START_REF] Shiller | Why Do People Dislike Inflation[END_REF] who argues: 'Because the word "inflation" is so much a part of everyday lives, it has many 13 associations and connotations to ordinary people. Moreover, because shopping, and thereby noticing prices, is an everyday activity for ordinary people, thinking about prices is also a major part of people's thinking, and the subject "inflation" is one of great personal interest for most people'. Furthermore, when Shiller (1997) asked people if they find news stories about inflation interesting, 89% reported that inflation news reports are very or somewhat interesting (see more discussion on individuals' expectation behaviour: Kahneman and Tverky, 1979[START_REF] Nisbett | Human Inference: Strategies and Shortcomings of Social Judgment[END_REF][START_REF] Gleitman | Basic Psychology[END_REF], Mahmoud, El-Gamal and Grether, 1995[START_REF] Shiller | Why Do People Dislike Inflation[END_REF][START_REF] Akerlof | Near-Rational Wage and Price Setting and the Optimal Rates of Inflation and Unemployment[END_REF][START_REF] Manski | Measuring Expectations[END_REF]. Therefore, we assume that a typical individual believes that the process of inflation is captured by the model

t t t B X + = 4 , ( 7
)
where t is a normally distributed error term with zero mean and 2 variance and X t-4 is a row vector which includes annualized monthly inflation and other possible explanatory variables. We believe that a simple univariate process describes the public's views about the process of inflation better than a multivariate process, since ordinary people seem to fail to understand the concept of general equilibrium (see [START_REF] Shiller | Why Do People Dislike Inflation[END_REF].

However, the opinions about the parameter values of the above process may vary strongly among individuals. To allow for this kind of disagreement, we further assume that every individual has his own personal beliefs about the parameters of the model (7).

Moreover, we assume that the personal prior distribution of the ith individual for the parameter vector B i is multivariate normal: (  )

i i i V B N B 1 0 2 0 , ~ , (8)
where B 0 is the individual's prior estimate of B and matrix

( ) i V 1 0
is a measure of his uncertainty, relative to 2 . If, for example, the ith individual believed that inflation follows a random walk process, the parameter of recent inflation in B 0 would be equal to 1 and the corresponding diagonal entry in 1 0

V very small. The parameters of other variables in B 0 would be zero and the corresponding variances in 1 0

V very small. Thus we have a very flexible behavioural model which covers the observed disagreement about the causes of inflation and explains the variance of inflation expectations among households (see [START_REF] Shiller | Why Do People Dislike Inflation[END_REF]Mankiw, Reis and[START_REF] Mankiw | Disagreement About Inflation Expectations[END_REF].

We further assume that the ith individual forecasts inflation on the basis of his evolving beliefs about B (confer [START_REF] Caskey | Modeling the Formation of Price Expectations: A Bayesian Approach[END_REF]. Each period he obtains new information on annualized monthly inflation and other possible explanatory variables from news articles he uses it to update his beliefs about the parameter vector B. This updating process can be best described using the following recursive equations of the Kalman filter:

( ) where vector K t is the so-called Kalman gain. We do not expect that individuals fully remember the observations of possible explanatory variables, presented in past news articles; however, our point is that this kind of a recursive system might be the best description of their learning process. The model also covers the possibility that some people have such strong prior beliefs that they do not change them.

i t t t t i t i t B X K B B 1 4 1 ˆ + = (9) ( ) ( ) ( ) i t t i t i t i t V X K V V 1 1 4 1 1 1 ˆ = (10) ( ) ( ) 1 4 1 1 4 4 1 1 1 ' ' ˆ + = t i t t t i t i t X V X X V K (11)
Finally, assuming that the ith individual uses a quadratic loss function in his forecasts and taking into consideration that his thought processes cannot be fully replicated, we model his inflation expectations as

( ) i t i t t t i t u B X E + = + 4 , ( 12
)
where the operator

[ ] ( ) ( ) ( ) i t t i t t t i t u X B X E Var var ' ĉov 4 + = + , (14)
where

( ) i t
B ĉov is the covariance matrix measuring the dispersion of opinions among the general public.

Equation ( 13) implies that the population variance of inflation expectations is a function of annualized monthly inflation and possibly some other variables reported in the news media and of the variances and covariances of the individuals' parameter estimates.

IV Empirical test of the Bayesian Learning Model

The respondents of the monthly Michigan surveys have learning paths with different lengths and starting points. Therefore, it seems reasonable to assume that the mean

vector { } i t B m ˆand dispersion matrix ( ) i t B ĉov
in equations ( 13) and ( 14) stay constant over time. Then we can estimate them using OLS. However, the reader should note that we can not trust the standard t-statistics related to these parameters, since the time series involved in these models are unit root or nearly unit-root processes. However, our main objective is to investigate how well the outcomes of the Bayesian learning model can predict the mean and variance series of the actual Michigan inflation expectations. We suggest that the key things here are the correct signs of the variance estimates and the prediction power of the estimated models. To proceed further, we set 9

[ ] ( ) [ ] ( ) ( ) ( ) error u X B X error E M i t t i t t t i t t t + + = + = + + var ĉov ' var var 4 4 , ( 15
) [ ] [ ] { } { } { } error u m B m X error E m M i t i t t t i t t t + + = + = + + 4 4 . ( 16
)
Moreover, we assume that the most probable components of X t are annualized monthly inflation t m and the 3-month T-bill rate, since most commonly published economic news articles on the subject concern these figures and since the public seems to perceive the relation between inflation and the interest rate [START_REF] Shiller | Why Do People Dislike Inflation[END_REF]. The results for the variance and mean equations are summarized in Table 4. We can see that the variance model based on inflation and the 3-month T-bill rate and the variance model based on inflation alone give similar correlations between the predicted variance 9 To analyze the predicted variance of the learning model we need a longer sample period than the period 1981/3-2004/1 for which the professionals' CPI inflation forecast series is available. To obtain a longer forecast period 1970/1-2004/1 we used SPF's GDP deflator forecast series. We regressed the CPI inflation forecast series on the GDP deflator inflation forecast series and a constant and predicted the CPI inflation forecast series for the period 1970/1-1981/2 using the estimated regression model. The parameter estimates were 0.68 and 0.89 for the constant and the GDP deflator forecast series, respectively). 4). These findings are in line with [START_REF] Shiller | Why Do People Dislike Inflation[END_REF] questionnaire study, in which he observes that most people seem to fail to think of economic models; people do not tend to see any connection between inflation and unemployment, i.e. the Phillips curve, or between inflation and money growth, i.e. the quantity theory of money.

The variance model based on inflation and unemployment and the model based on inflation and the SPF series give us the highest correlations between the predicted and actual variance series (0.88 and 0.9). However, if we take a closer look at the parameter estimates of these models, we find that in both these models the estimates of var(u)+var(b 0 ) are negative, which of course does not make sense. One plausible explanation for the high correlation between the professionals' forecast series and the Michigan variance series (cov(b 2 ,b 0 ) = 14.7) is that there is a higher probability for individuals who believe inflation to be random walk to give lousy forecasts when inflation is rationally expected to increase rapidly than during a stable low inflation period.

In summary, based on the weak relation between the SPF and Michigan median series, as found when estimating equations ( 5) and ( 6) in Section 2, and the results presented in the current section, we conclude that a Bayesian learning model based on annualized monthly inflation series and the 3-month T-bill rate offers us a more plausible explanation for the general public's inflation expectations than the limited information flows models based on rational or nearly rational forecast series.

VI Conclusion

In this paper, we have empirically shown that a simple Bayesian learning model is a feasible explanation for the general public's inflation expectations formation. We have also shown that the Michigan Survey data do not support models of limited information flows, discussed the theoretical basis of the Bayesian model and come to the conclusion that it gives a more realistic picture of individuals' expectation behaviour in the case of inflation than some new models presented in the literature, such as models of limited information flows or models with uncertainty approach. Learning models have, of course, many variants, but the advantage of Bayesian models is that by using personal and 10% levels, respectively. In the Bayesian analysis part we report the posterior median and the share of posterior mass which lies above (below) zero when the median is positive (negative). The median is given in bold face when zero is not included in the 95% posterior interval).

Sample 1981/Q3 -2004/Q1

  and professionals, because these two groups use different methods and resources to form their expectations (for example, see results of Schiller, 1997).

  mean and median series. Our estimates are in disagreement with

  i :s are parameter matrices and t is the normally distributed error term with zero mean and covariance.

  Rather, both professionals and the general public adjust their expectations toward actual annual inflation i.e. both groups correct their expectations toward the fully rational outcome.

  Our alternative candidate series, which may compensate for the T-bill series, are those which are most probably regularly reported by all major media in the US: a) SPF forecast b) Unemployment rate c) Annualized quarterly growth of GDP d) Annualized monthly growth of M1

  actual Michigan variance. However, the actual mean series has a remarkably higher correlation with the predicted mean series based on inflation and the T-bill rate than with the predicted series based on inflation alone. These results suggest that a part of the population always believes the process of inflation to be random walk, which causes the variance of the Michigan survey to be high, while another part of them is aware of the relationship between inflation and the interest rate (confer[START_REF] Shiller | Why Do People Dislike Inflation[END_REF]. The model based on monthly inflation and the 3-month T-bill rate gives relatively high correlation coefficients between the predicted and actual Michigan mean series, compared to the models based on inflation and unemployment, inflation and the quarterly growth rate of GDP or inflation and the monthly growth rate of M1. The drop of the correlation coefficient from the mean model based on inflation and the T-bill rate to the mean model based on inflation and the unemployment rate is quite large, about 11%. Moreover, the correlation between the predicted mean series based on annualized monthly inflation and the actual Michigan mean series is 0.645, which suggests that the growth of money, growth of GDP or unemployment series add practically nothing to the learning model expectations based on monthly inflation (compare correlations reported in Table

Table 1 :

 1 can describe individuals' opinions and their willingness to update them. From our point of view, Bayesian learning models are worth further development in the context of the public's inflation expectations. Estimation Results for Equations 3, 5 and 6

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

Table 2 :

 2 Augmented Dickey-Fuller Tests

	Augmented Dickey-Fuller Test for Michigan Median Inflation Expectations
	Series, Professional Forecasters' Inflation Forecast Series and annualized
	monthly inflation series.
	Variable	t-adf
	Michigan mean series	-1.993
	Michigan median series	-1.529
	Survey of Professional Forecasters mean series	-0.5551
	Survey of Professional Forecasters median series	-0.7668
	Annualized monthly inflation (Realtime)	-3.201*
	Sample 1981/Q3 -2004/Q1
	* indicates statistical significance at the level of 5%

Table 3 :

 3 Point Estimates of BVAR Models Prior and Different Lag Lengths (p =1,…,4) where y t = (M t [ t+4 ] S t [ t+4 ])'

	Model
	y	t	=	p	i	y	t	i	+	t
			i	= 1
	with Jeffrey's number of lags		parameter(lag)	median
	1			21 (1)				0.31
										(0.07)
				21 (1)				0.29
										(0.23)
	2			21 (2)				-0.03
										(0.21)
			sum 21 (i)			0.25
										(0.09)
				21 (1)				0.31
										(0.24)
	3			21 (2)				0.06 (0.33)
				21 (3)				-0.11
										(0.21)
			sum 21 (i)			0.27
										(0.10)
				21 (1)				0.27
										(0.25)
				21 (2)				0.12
	4			21 (3)				(0.35) -0.11
										(0.34)
				21 (4)				-0.03
										(0.23)
			sum 21 (i)			0.25
										(0.10)
	standard deviations in parentheses

Table 4 :

 4 Estimation Results for Variance and Mean Equations

	Variance Model
	var	(	M	t	[ ] ) t + 4	=	X	'	t	( ) X B i t ĉov	t	+	var	( ) error u i t +
															correlation
															between
				Variables					var(u)+var(b 0 )	var(b 1 )	cov(b 1 ,b 0 )	var(b 2 )	cov(b 2 ,b 0 )	cov(b 1 , b 2 )	predicted
															and actual
															variance
															series
	monthly inflation					21.617	0.591	-0.272	-	-	-	0.842
													(1.698)	(0.082)	(0.110)
	monthly inflation and			3.178	0.292	3.836	0.116	3.278	-0.406	0.842
	T-bill										(5.034)	(0.110)	(1.318)	(0.136)	(1.473)	(0.214)
	monthly inflation and			-20.636	0.573	1.994	0.216	14.679	-1.351	0.908
	SPF forecasts						(6.530)	(0.148)	(1.380)	(0.534)	(3.504)	(0.493)
	monthly inflation and			-69.320	0.131	12.172	-0.498	17.485	-1.302	0.875
	unemployment						(19.495)	(0.072)	(1.999)	(0.382)	(5.497)	(0.267)
	monthly inflation and			24.828	0.162	3.281	0.028	-2.669	0.318	0.809
	growth of GDP						(3.956)	(0.091)	(1.290)	(0.065)	(0.930)	(0.123)
	monthly inflation and			14.348	0.143	4.036	-0.161	3.625	0.053	0.818
	growth of M1						(3.638)	(0.087)	(1.235)	(0.403)	(1.875)	(0.306)
															Sample 1970/Q1 -2004/Q1
	Mean Model
	M	t	[ ] t +	=	X	t	{ } { } error u m B m i t i t + + 4
															correlation
										Variables		b 0	b 1	b 2	between predicted
															and actual mean
															series
	monthly inflation (b 1 )				3.176	0.295	-	0.645
															(0.142)	(0.037)
	monthly inflation (b 1 ) and T-bill (b 2 )	2.341	0.149	0.228	0.852
															(0.129)	(0.023)	(0.023)
	monthly inflation and SPF forecasts	1.516	0.054	0.678	0.918
															(0.130)	(0.025)	(0.044)
	monthly inflation and unemployment	1.658	0.270	0257	0.757
															(0.293)	(0.032)	(0.045)
	monthly inflation and growth of GDP	3.369	0.291	-0.070	0.668
															(0.165)	(0.036)	(0.032)
	monthly inflation and growth of M1	3.101	0.298	0.053	0.651
															(0.158)	(0.037)	(0.048)
															Sample 1981/Q3 -2004/Q1

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

data are available at http://www.phil.frb.org/econ

data are available at http://www.phil.frb.org/econ/forecast/readow.html

data are available at http://econweb.rutgers.edu/nswanson/realtime.htm

Note that we do not assume the SPF nor inflation series to be exogenous. For example, even if the lagged values of the Michigan series do not help forecast the future SPF values, one should not take this


Sergio Jara-Diaz
email: jaradiaz@cec.uchile.cl

Beatriz Tovar
email: btovar@daea.ulpgc.es

Lourdes Trujillo
email: lourdes@daea.ulpgc.es

Sergio Jara-Díaz

On the proper modelling of multioutput port cargo handling costs

Keywords: multiproduct, economies multiproduct, economies of scale and scope, port and cargo handling. JEL Classification system: L9 multiproduct, economies of scale and scope, port and cargo handling. JEL Classification system: L9

The importance of multi output of cargo handling activities in the port

Introduction: Cargo handling in multipurpose port terminals

Up to now, the analysis of cargo handling and port activities has, in general, relied on an aggregate measure of output such as total tons moved or its value, as in Chang (1978), Rekers et al. (1990), Tongzon (1993), Kim andSachis (1986) andMartínez Budría (1996). In this paper we first follow this tradition, analyzing cargo handling activities through the estimation of a cost function with output described as total volume handled and we derive marginal costs, scale economies as well as some policy conclusions from this initial estimation. Then we compare these "traditional" results with those arising from an explicit modelling of the heterogeneity of the output. This comparison allows us to document that various ways in which the analysis based on a synthetic output indicator misleads policymaking.

Data and aggregate model formulation

We focus on a cost function C(W,Y) which represents the minimum expenditure necessary to produce output Y at given input prices W. Its estimation requires data on expenditure, production and input prices for one or more firms during one or more periods. Our data was collected directly from three private medium size firms operating within the port area of Las Palmas de Gran Canaria, one of the largest in the Spanish port system. They deal mainly with containers (87% of total volume), but also operate roll-on/roll-off cargo (ro-ro, 3%) as well as general break-bulk (general) cargo (10%). We collected 264 monthly observations from 1991 through 1999 (not all years available for all three firms).

The productive factors have been grouped into four categories: personnel, total area, capital and intermediate inputs. The personnel working in port terminals may be classified in two categories: stevedores or port workers, who handle cargo, and non-port workers, who do not (administratives, executives, maintenance and control personnel, among others). In turn, port workers are divided into two categories: those who are on the payroll (ordinary employment) and those who are not (special employment). This latter category can be recruited on a provisional basis by any company to work 6-hour shifts, under the management of the Sociedad Estatal de Estiba y Destiba (SEED).

Capital encompasses all the components of tangible assets of the company -i.e. buildings, machines, etc. The monthly cost results from the addition of the accounting depreciation for the period plus the return on the active capital of the period. This rate of return evidences the compensation earned by risk-free capital, which is made up of bank interest plus a risk premium. For the period under analysis the return for both concepts amounts to 8% per annum. Lastly, the rest of the productive factors used by the company that have not been included in any of the three preceding categories, such as office supplies, water, electricity, and the like, have been classified as intermediate consumption.

Regarding occupied space, each terminal can make use of an area that has been granted under concession, which may be increased by provisionally renting -upon prior request-additional area from the port authority, turning area into a variable factor With this information, a quadratic long run cost function (1) was estimated along with the input expenses equations (2) obtained using Shephard's lemma

0 1 2 1 1 1 1 1 ( ) ( ) ( ) 1 1 ( ) ( )( ) 2 2 ( )( ) ( )( ) ( )( ) ( )( ) n i i i i n n ij i i j j i j n n j j j i i i j i N i i i

CT A y y p p T T y y p p p p y y p p y y T T p p T T T T T T D

µ = = = = = = = + + + + + + + + + + (1) 2 ( ) ( ) ( ) ( ) m i i i i i i i i i i j j j i i j i G p x p p p p p y y T T µ = = + + + +
(2)

The aggregate (single) output cost

In this section, we follow the tradition of the last 30 years or so in the sector and we estimate a cost function estimated for a single synthetic output. Table 1 shows all the first order coefficients that are relevant for our interpretation of results.

All first order parameters are statistically significant and have the expected signs with the exception of the trend coefficient that has a counterintuitive positive sign indicating that, everything else constant, cost increases with time. The dummy variables are both negative and similarly small, indicating that the smaller firms would exhibit some 2.3% less costs than the larger one if the three produced the mean amount. The single marginal cost estimated at the mean is 715 pesetas/ton and the corresponding value of the degree of economies of scale (the inverse of the cost-product elasticity) is S=1.959, indicating clear increasing returns. These results are fairly compatible with the average cost curve presented in Figure 1 based on the aggregated production volume. The curve looks as a traditional long run one, and graphically suggests the presence of economies of scale and, therefore, marginal costs that should fall below the average figures, i.e. less than 750 pesetas/ton, as obtained.

Marginal cost calculated at the mean production of each firm (terminal) yields little variation (from 706 to 724 pesetas/ton), but scale economies at each mean do vary, yielding 2.38, 3.01 and 1.22 for firms 1, 2 and 3 respectively, monotonically decreasing with average production. According to these results, all three firms should be encouraged to increase production to take advantage of scale economies. All three occupy neighbouring sites. Pushing the three firms to merge and operate as one could be convenient. If optimal prices were a target, charging marginal cost per ton would require a modest subsidy or, if this is not wanted, a single second best price equal to the average cost in the neighbourhood of 1420 pesetas could be set, accepting a modest social loss.

Regulation would play an important role.

INSERT

The multi-output cost function. 1

In this section, we use the same information to estimate a long run cost function where outputs are individually identified, namely, the volume of containers, general cargo and ro-ro and modelled explicitly. The model specification is just as the previous function (1) and equations (2) but in this case we have a vector of outputs and each output is identified as y i .with i going from 1 to 3, making this a multioutput cost function. ro-ro are definitely larger than the maximum single figure that could be expected from the pseudo average cost curve in Figure 1.

The differences among the estimated marginal costs by product are fully consistent with the underlying technical aspects. Handling general cargo presents complicated operations to a degree where machines are less important than labour.

Nevertheless, the figures per firm suggest that volume plays a role as well, as the firm that moves a larger quantity (firm 2) exhibits the lowest marginal cost for this output (see Table 3 below).

On the other hand, the marginal cost estimates for ro-ro (some 40% larger than those of the containers) seem to respond to two effects. In general, operations are simpler than those for containers, making some stages disappear, and they require less equipment. However, space is fundamental for this type of movement and its volume is lower, which seems to influence marginal cost.

INSERT TABLE 2 ABOUT HERE

The trend variable is negative, as expected, and the firm specific dummies are both small and close to 2,5 % of the cost at the mean. The global degree of scale economies is 1.64 and the product specific degree of returns to scale is practically one for all three outputs. This suggests that economies of scope are present, as these magnify specific scale economies.

The product specific degrees of scale economies are all close to unity, which suggests that the reason for the difference between the global figures on scale, are due to the possible presence of economies of scope, which magnifies scale, something impossible to verify with the aggregate approach. If we analyse all possible orthogonal partitions of the product set into two firms, one handling a single output and the other handling the other two, the degree of economies of scope are all close to 0.39. This means that it is better to handle all three cargo types with one firm than to create an additional firm to take care of one output, provided that all three outputs have to be handled. This merits further discussion.

Product specific scale economies close to one mean that the incremental cost (cost of the addition of that product to the line) is similar to the marginal variation of total cost, which fits intuition. But it also means that are economies of scope what causes overall economies of scale, due to the presence of common (non operative) costs related to non port personnel and general expenses, plus some complementarities in production provoked by common use of the surface space, labour managed by the firm, shore cranes used for containers and some form of general cargo, and so on.

Finally, scale economies are noted for the two smallest firms as the calculated values for S are 2.26 and 2.13. For the largest one, this value is 1.08, reflecting nearly constant returns to scale. These results coupled with those regarding scope suggest that the two small firms could be allowed to merge, as they are located in neighbouring sites. This would maintain some degree of competition in the market.

Comparisons and discussion.

The comparison of the results of the cost functions estimated from the two specifications of product offers a wide range of insights along various dimensions, including the dispersion of marginal costs of the various outputs, the economies of scale as well as the economies of scope as seen in Table 3. These should be of interest to a wide range of policy makers, including reformers, regulators and competition agencies.

Table 3 shows that the marginal cost estimates for containers are some 4% each firm. The most impressive differences are found for general cargo, where marginal costs are more than 170% larger for the disaggregate model than for the original one. Moreover, note that for the disaggregated models, the differences in marginal cost estimates among terminals are very small and the order is the same.

The similarity of the figures for marginal costs for the aggregate estimate of the fist model and the estimate for containers in the second model seems to be a consequence of the important volume of containers at each terminal, which vary from 76 to 97%.

INSERT TABLE 3 ABOUT HERE

The firm specific dummies become some 10% more negative than in the aggregate model. It keeps a relatively low value for the constant, which is an estimate of the cost of the largest firm at the mean. However, the time coefficient becomes negative, as expected.

Regarding scale economies with multiple outputs (see Appendix), the overall figure of 1.64 is smaller than the 1.96 obtained with the aggregate model. But this hides even larger differences when individual firms are considered, as the three figures drop from 2.38, 3.01 and 1.22 to 2.26, 2.13 and 1.08 respectively when output is correctly specified. This means that the largest terminal has reached constant returns. Therefore, the policy conclusions change dramatically, as the aggregate results suggest that merging could be desirable from a cost viewpoint, charging an optimal price of about 1420 pesetas per ton moved, while the disaggregate model would

Conclusions.

Port activities have been usually analysed describing output through some synthetic measure of total volume of cargo moved. Inputs required, however, differ according to the type of cargo handled. Furthermore, input combinations also vary depending on the packaging. When output is described as a scalar hiding multiple outputs, the observed variation in total output (volume) may reflect a wide range of variations in each of the individual outputs This causes various important problems. For instance, if product specific marginal costs are actually very different, a single synthetic figure will mislead any discussion on optimal pricing. Also, the impossibility of estimating economies of scope will bias the estimate of scale economies, because potential advantages (or disadvantages) of joint production will not be captured properly. These problems have various policy implications.

The first is from the viewpoint of a regulator concerned with the optimal pricing of the sector activities. In this context, this note shows how important it is to recognize the consequences of the failure to model explicitly the cost diversity associated with the output diversity. This failure can lead to very significant distortions in resources allocations in an industry in which residual monopoly power or at least the risks of collusion between a few operators can be quite From the viewpoint of a competition agency, the note clearly illustrates the value of making better use of the information available on the composition of the output. Indeed, in the case analyzed here, the multioutput approach makes a clear case to allow only two of the three terminals to merge while with the single output model would have endorsed the merger of the three operators.

From the point of view of a sector reformer, in addition to providing some evidence on the existence of a limit to the unbundling into terminals of port activities, the paper also shows that reformers should consider more carefully the limits to specialization in the sector. Indeed, the information on the economies of scope generated by the multioutput approach provides some guidance on the optimal market structure for the industry. It shows that the operators are better off not specializing, competing on the three main business lines available instead. This is an important consideration in an industry undergoing, or subject to pressure to undergo, restructuring around the world and in which specialization is often one of the expected outcomes.

Overall, what this note highlights is that the proper approach to analyse port activities is multi-productive, and the consequences of not taken into account

Introduction

Up to now, the analysis of cargo handling and port activities has, in general, relied on an aggregate measure of output such as total tons moved or its value, as in Chang (1978), Rekers et al. (1990), Tongzon (1993), Kim andSachis (1986) andMartínez Budría (1996). In this paper we first follow this tradition, analyzing cargo handling activities through the estimation of a cost function with output described as total volume handled and we derive marginal costs, scale economies as well as some policy conclusions from this initial estimation. Then we compare these "traditional" results with those arising from an explicit modelling of the heterogeneity of the output. This comparison shows that the usual type of analysis based on a synthetic output indicator can mislead policymaking, particularly in terms of marginal costs, which affects pricing, and economies of scale and scope, which helps detecting optimal industry structure.

Variables description and cost model

We focus on a cost function C(W,Y) which represents the minimum expenditure necessary to produce output Y at given input prices W. Its estimation requires data on expenditure, production and input prices for one or more firms during one or more periods. Our data was collected directly from three private medium size firms operating within the port area of Las Palmas de Gran Canaria, one of the largest in the Spanish port system. They deal mainly with containers (87% of total volume), but also operate roll-on/roll-off cargo (ro-ro, 3%) as well as general break-bulk (general) cargo (10%). We collected 264 monthly observations from 1991 through 1999 (not all years available for all three firms). Capital encompasses all the components of tangible assets of the company -i.e. buildings, machines, etc. The monthly capital cost results from the addition of the accounting depreciation for the period plus the return on the active capital of the period. This rate of return evidences the compensation earned by risk-free capital, which is made up of bank interest plus a risk premium. For the period under analysis the return for both concepts amounts to 8% per annum. The price of capital is calculated as the ratio of the capital cost over the active capital of the period (net fixed assets under exploitation for a given period).

Regarding occupied space, each terminal can make use of an area granted under concession by the port authority. This surface may be increased by provisionally renting additional area from the port authority, turning the total area used by the operator into a variable production factor, as it can be accommodated on demand. It is measured in square meters, and its price is calculated as the ratio of the area-related monthly expenses over the total area used that corresponding month.

Lastly, the rest of the productive factors used by the company that have not been included in any of the three preceding categories, such as office supplies, water, electricity, and the like, have been classified as intermediate consumption.

The price of electricity has been used as an index of the price of intermediate consumption, as the price of the other components do not undergo changes. The total monthly production expenses for each of the terminals result from the aggregation of expenses over all the productive factors defined above.

Among those factors, labor shows the largest share of terminal expenditure in the sample, representing an average of 53% of the monthly expenses 1 . Note that this is the same figure obtained by [START_REF] Cullinane | A Stochastic Frontier Model of the Productive Efficiency of Korean Container Terminals[END_REF] for Korean container terminals.

This data was used to estimate a quadratic long run cost function (1) and the input expenses equations (2) obtained using Shephard's lemma

0 1 2 1 1 1 1 1 ( ) ( ) ( ) 1 1 ( ) ( )( ) 2 2 ( )( ) ( )( ) ( )( ) ( )( ) n i i i i n n ij i i j j i j n n j j j i i i j i N i i i

CT A y y p p T T y y p p p p y y p p y y T T p p T T T T T T D

µ = = = = = = = + + + + + + + + + + (1) 2 ( ) ( ) ( ) ( ) m i i i i i ii i i ij j j i i j i G p x p p p p p y y T T µ = = + + + + (2)
where y is the amount of output, p i is input i price, n is the number of inputs, D i are firm specific dummies to capture specific effects, N is the number of firms and T is time trend, included to capture possible technical change. Variables with a horizontal bar on top are sample means.

The aggregate (single) output cost

In this section, we follow the tradition of the last 30 years or so in the sector and we estimate a cost function for a single synthetic output. Table 1 shows all the first order coefficients that are relevant for our interpretation of results.

All first order parameters are statistically significant and have the expected Marginal cost calculated at the mean production of each firm (terminal) yields little variation (from 706 to 724 pesetas/ton), but scale economies at each mean do vary, yielding 2.38, 3.01 and 1.22 for firms 1, 2 and 3 respectively, monotonically decreasing with average production.

According to these results, all three firms should be encouraged to increase production to take advantage of scale economies. As they occupy neighbouring sites, pushing the three firms to merge and operate as one could be convenient. If optimal prices were a target, charging marginal cost per ton would require a modest subsidy. If it is not a goal, a single second best price equal to the average cost in the neighbourhood of 1420 pesetas could be set, accepting a modest social loss. For synthesis, the single output approach yields clear implications for regulation, as increasing returns suggest that a single operator would be cost-efficient, but price regulation should be imposed. We will see in the next section that this is not necessarily so.

INSERT

The multi-output cost function. 3

In this section, we use the same information to estimate a long run cost function where outputs are individually identified, namely, the volume of containers, general cargo and ro-ro, which are modelled explicitly. The model specification is just as the previous function (1) and equations ( 2) but in this case we have a vector of outputs and each output is identified as y i .with i going from 1 to 3, making this a multioutput cost function.

Table 2 contains all the relevant coefficients of this long run multioutput cost function. It shows very clearly that marginal cost estimates do vary across products. It also shows the expected ranking: containers exhibit the lowest value, followed by ro-ro cargo and general cargo. As average cost figures are undefined in a multioutput context, these results were compared against maximum tariffs currently applied at the port, grouped by type of cargo. They happen to follow the same relative ranking and to be always above our marginal costs estimates, which reinforces the quality of the estimation. Note that the marginal costs for both general cargo and ro-ro are definitely larger than the maximum single figure that could be expected from the pseudo average cost curve in Figure 1.

INSERT TABLE 2 ABOUT HERE

The differences among the estimated marginal costs by product are fully consistent with the underlying technical aspects. Handling general cargo presents complex operations to a degree where machines are less important than labour. Nevertheless, the figures per firm suggest that volume plays a role as well, as the firm that moves a larger quantity (firm 2) exhibits the lowest marginal cost for this output (see Table 3 below).

On the other hand, the marginal cost estimates for ro-ro (some 40% larger than those of the containers) seem to respond to two effects. In general, operations are simpler than those for containers, making some stages disappear, and they require less equipment. However, space is fundamental for this type of movement and its volume is lower, which seems to influence marginal cost.

The trend variable is negative, as expected, and the firm specific dummies are both small and close to 2,5 % of the cost at the mean. The global degree of scale economies is 1.64 and the product specific degree of returns to scale is practically one for all three outputs. This suggests that economies of scope are present, as these magnify specific scale economies.

The product specific degrees of scale economies are all close to unity (see Table 3 below), which suggests that the reason for the difference between the global figures on scale, are due to the possible presence of economies of scope, which magnifies scale, something impossible to verify with the aggregate approach. If we analyse all possible orthogonal partitions of the product set into two firms, one handling a single output and the other handling the other two, the degree of economies of scope are all close to 0.39. This means that it is better to handle all three cargo types with one firm than to create an additional firm to take care of one output, provided that all three outputs have to be handled. This merits further discussion.

Product specific scale economies close to one mean that the incremental cost (cost of the addition of that product to the line) is similar to the marginal variation of total cost, which fits intuition. operative) costs related to non port personnel and general expenses, plus some complementarities in production provoked by common use of the surface space, labour managed by the firm, shore cranes used for containers and some form of general cargo, and so on.

Finally, note that the two smallest firms exhibit strongly increasing returns to scale as the calculated values for S are 2.26 and 2.13. For the largest one, however, this value is 1.08, reflecting nearly constant returns to scale. These results coupled with those regarding scope suggest that the two small firms could be allowed to merge, as they are located in neighbouring sites. This would maintain some degree of competition in the market.

Aggregate versus disaggregate models.

The comparison of the results of the cost functions estimated from the two specifications of product offers a wide range of insights along various dimensions, including the dispersion of marginal costs of the various outputs, the economies of scale as well as the economies of scope as seen in Table 3. These should be of interest to a wide range of policy makers, including reformers, regulators and competition agencies 4 .

Table 3 shows that the marginal cost estimates for containers are some 4% larger than the corresponding figures obtained from the aggregate model. However, ro-ro marginal costs are between 44% and 55% larger than the single figure for each firm. The most impressive differences are found for general cargo, where marginal costs are more than 170% larger for the disaggregate model than for the original one. Moreover, note that for the disaggregated models, the differences in marginal cost estimates among terminals are very small and the order is the same.

The similarity of the figures for marginal costs for the aggregate estimate of the The firm specific dummies become some 10% more negative than in the aggregate model. It keeps a relatively low value for the constant, which is an estimate of the cost of the largest firm at the mean. However, the time coefficient becomes negative, as expected.

Regarding scale economies with multiple outputs, the overall figure of 1.64 is smaller than the 1.96 obtained with the aggregate model. But this hides even larger differences when individual firms are considered, as the three figures drop from 2.38, 3.01 and 1.22 to 2.26, 2.13 and 1.08 respectively when output is correctly specified. This means that the largest terminal has reached constant returns. Therefore, the policy conclusions change dramatically, as the aggregate results suggest that merging could be desirable from a cost viewpoint, charging an optimal price of about 1420 pesetas per ton moved, while the disaggregate model would call for the two smallest firms to join operations, keeping competition with the largest that has already reached constant returns. Different prices should be charged for the movement of one ton moved in a container, as a ro-ro, or as fractioned general cargo, with prices above 760, 1120 and 2040 pesetas/ton respectively, the extra charge depending on the price elasticity of demand.

analyzed scope and scale economies in multi-utilities; and [START_REF] Sav | Higher education costs and scale and scope economies[END_REF] applied this methodology to the higher education for public and private sector . Port activities have been usually analysed describing output through some synthetic measure of total volume of cargo moved. Inputs required, however, differ according to the type of cargo handled. Furthermore, input combinations also vary depending on the packaging. When output is described as a scalar hiding multiple outputs, the observed variation in total output (volume) may reflect a wide range of variations in each of the individual outputs This causes various important problems. For instance, if product specific marginal costs are actually very different, a single synthetic figure will mislead any discussion on optimal pricing. Also, the impossibility of estimating economies of scope will bias the estimate of scale economies, because potential advantages (or disadvantages) of joint production will not be captured properly. These problems have various policy implications.

The first is from the viewpoint of a regulator concerned with the optimal pricing of the sector activities. In this context, this paper shows how important it is to recognize the consequences of the failure to model explicitly the cost diversity associated with the output diversity. This failure can lead to very significant distortions in resources allocations in an industry in which residual monopoly power or at least the risks of collusion between a few operators can be quite important.

From the viewpoint of a competition agency, the paper clearly illustrates the value of making better use of the information available on the composition of the output. Indeed, in the case analyzed here, the multioutput approach makes a clear case to allow only two of the three terminals to merge while results with the single output model would have endorsed the merger of the three operators.

From the point of view of a sector reformer, in addition to providing some evidence on the existence of a limit to the unbundling into terminals of port activities, the paper also shows that reformers should consider more carefully the limits to specialization in the sector. Indeed, the information on the economies of scope generated by the multioutput approach provides some guidance on the optimal market structure for the industry. It shows that the operators are better off not specializing, competing on the three main business lines available instead if the three are to be produced. This is an important consideration in an industry undergoing, or subject to pressure to undergo, restructuring around the world and in which specialization is often one of the expected outcomes.

Overall, what this note highlights is that the proper approach to analyse port activities is multi-productive. • statistically significant at 5%.

Note: 1 € = 166.386 pesetas

  corresponding figures obtained from the aggregate model. However, ro-ro marginal costs are between 44% and 55% larger than the single figure for

  two smallest firms to join operations, keeping competition with the largest that has already reached constant returns. Different prices should be charged for the movement of one ton moved in a container, as a ro-ro, or as fractioned general cargo, with prices above 760, 1120 and 2040 pesetas/ton respectively, the extra charge depending on the price elasticity of demand.

Figure

  Figure 1. Average Cost Curve.

M

  C c o n ta in e rs (p ta s /to n ) o n ta in e rs 1 ,0 0 5 4 8 (*) E S g e n e ra l c a rg o 1 ,0 0 1 4 7 (*) E S ro -ro c a rg o 1 e l w ith a g g re g a te d o u tp u t M o d e l w ith d is a g g re g a te d o u tp u

Page

  signs with the exception of the trend coefficient that has a counterintuitive positive sign indicating that, everything else being constant, cost increases with time. The 1 Total area, capital and intermediate consumption represent 13%, 8%, and 26% both negative and similarly small, indicating that the smaller firms would exhibit some 2.3% less costs than the larger one if the three produced the mean amount. The single marginal cost estimated at the mean is 715 pesetas/ton and the corresponding degree of economies of scale (the inverse of the cost-product elasticity) is S=1.959, indicating clear increasing returns. 2 These results are fairly compatible with the average cost curve presented in Figure1based on the aggregated production volume. The curve looks as a traditional long run one, and graphically suggests the presence of economies of scale and, therefore, marginal costs that should fall below the average figures, i.e. less than 750 pesetas/ton.

2

  Note: 1 Euro (€) = 166.386 pesetas3 This section is based on Jara Díaz et al(2005)

Figure

  Figure 1. Average Cost Curve.

  * ) M C g e n e r a l c a r g o ( p ta s /to n ) e l w ith a g g re g a te d o u tp u t M o d e l w ith d is a g g re g a te d o u tp u

Table 2

 2

	contains all the relevant coefficients of this long run multioutput
	cost function. It shows very clearly that marginal cost estimates do vary across
	products. It also shows the expected ranking: containers exhibit the lowest value,
	followed by ro-ro cargo and general cargo. As the average cost figure is not useful
	in this case, these results were compared against maximum tariffs currently applied
	at the port, grouped by type of cargo. They happen to follow the same relative
	ranking and to be always above our marginal costs estimates, which reinforces the
	quality of the estimation. Note that the marginal costs for both general cargo and

Table 1 . First order coefficients from the long run aggregated model.

 1

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

this important fact are quite relevant for the adequate regulation in cargo handling port activities. Single output studies could suggest erroneous structures.

Table 2 . First order coefficients from the long run multioutput cost function

 2

	Parameter

Source: Jara-Díaz et al.

(2005)

.

Table 3 . Marginal costs (MC) and scale economies (ES) by firm for the two models

 3

TABLE 1

 1

	ABOUT HERE

  But it also means that are economies of scope what causes overall economies of scale, due to the presence of common (non

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

4

  The role that multioutput cost function estimation could play in the debate about regulation is recognised in other sectors as well. For example,Fraquelli et al. (2004)

	first model and the estimate for containers in the second model seems to be a
	consequence of the important volume of containers at each terminal, which vary
	from 76 to 97%.
	INSERT TABLE 3 ABOUT HERE
	F o r
	P
	e
	e r
	R e v
	i e
	w
	8

Table 1 . First order coefficients from the long run aggregated model.

 1 Ignoring this important fact may distort regulatory decisions in the cargo handling port activities. Single output studies could suggest erroneous structures. which ultimately would hurt the users of these port services.

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

Note: 1 € = 166.386 pesetas

Table 2 . First order coefficients from the long run multioutput cost function

 2

	Parameter

Source: Jara-Díaz et al.

(2005)

.

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

This section is based on Jara Díaz et al(2005)

Acknowledgements.

This research was partially funded with Grant 1050643 from Fondecyt-Chile, the Millenium Nucleus Complex Engineering Systems, and Gobierno Autónomo de Canarias.

Acknowledgements.

The authors era grateful to the reviewers of the journal for their suggestions. This research was partially funded with Grant 1050643 from Fondecyt-Chile, the Millenium Nucleus Complex Engineering Systems, and Gobierno Autónomo de Canarias.

General < L9 -Industry Studies: Transportation and Utilities < L -Industrial Organization, L98 -Government Policy < L9 -Industry Studies: Transportation and Utilities < L -Industrial Organization