Michael Konstantinos

Konstantinos Maris

Konstantinos George Nikolopoulos

Vassilis Giannelos

Assimakopoulos

Options trading driven by volatility directional accuracy

Keywords: Decision Support, Options Trading, Forecasting, Volatility, Directional Accuracy Decision Support, Options Trading, Forecasting, Volatility, Directional Accuracy

come

Introduction

Efficient valuation of options is of crucial importance for practitioners in any financial market [START_REF] Chen | Option straddle trading: Financial performance and economic significance of direct profit forecast and conventional strategies[END_REF][START_REF] Yoshida | The valuation of European options in uncertain environment[END_REF][START_REF] Andersen | How Options Analysis Can Enhance Managerial Performance[END_REF], Buckley et. al 2002[START_REF] Grace | Black-Scholes option pricing via genetic algorithms[END_REF][START_REF] Pedersen | Capturing all the information in foreign currency option prices: solving for one versus two implied variables[END_REF]). Options during the last decade became a key component in the majority of investment portfolios. This development is reflected by the fact that both the turnover and the volume of these products have experienced phenomenal growth since the 1970s [START_REF] Bjork | Arbitrage Theory in Continuous Time[END_REF].

Option pricing is based on a variety of factors. From the main components that affect the premium of an option the only component that cannot be observed directly is the volatility of the underlying asset. Volatility measures the amount by which an underlying asset is expected to fluctuate in a given period of time. It significantly impacts the price of an option's premium and heavily contributes to an option's time value [START_REF] Hull | Options, Futures and Other Derivatives[END_REF].

Volatility can be viewed as the speed of change in the price of the underlying instrument. The higher the volatility, the more chance an option has of becoming profitable by expiration. Reviewing volatility levels can help traders determine the right option strategy [START_REF] Caner | Sources of volatility in stock returns in emerging markets[END_REF][START_REF] Bautista | How volatile are East Asian stocks during high volatility periods?[END_REF][START_REF] Kim | Stock market volatility and trading activities in the KOSPI 200 derivatives markets[END_REF][START_REF] Fofana | GARCH option pricing with implied volatility[END_REF][START_REF] Bautista | Stock market volatility in the Philippines[END_REF][START_REF] Arago-Manzana | Monthly seasonality of the returns and volatility of the IBEX-35 index and its futures contract[END_REF][START_REF] Bahmani-Oskooee | Does black market exchange rate volatility deter the trade flows? Iranian experience[END_REF]. Forecasting financial market volatility has absorbed the interest of many academics in the last decade [START_REF] Sabanis | Stochastic Volatility[END_REF][START_REF] Fouque | From the Implied Volatility Skew to a Robust Correction to Black-Scholes American Option Prices[END_REF][START_REF] Skiadopoulos | Volatility Smile consistent Option Models A Survey[END_REF][START_REF] Lux | Volatility Clustering in Financial Markets A Microsimulation of Interacting Agents[END_REF]. The present study discusses an empirical option trading methodology based on volatility direction forecasts. Although in most cases accurate volatility forecasts are hard to obtain (Maris et. al 2004a), forecasting the direction is a bit easier. Increase in the directional accuracy leads to profitable investment strategies. The net gain is always depended on the size of the changes as well, however accuracy over 60% was found to guarantee profitable investment. In order to evaluate the proposed methodology weekly data from CAX, DAX and the Greek FTSE/ASE 20 stock indices were used. This study builds on earlier results presented in a study with data from the Greek market (Maris et. al 2004b) where volatility point forecasts were produced with the Theta model (Nikolopoulos and[START_REF] Nikolopoulos | Theta Intelligent Forecasting Information System[END_REF][START_REF] Assimakopoulos | The Theta model: a decomposition approach to forecasting[END_REF].

The study is structured as follows: the next section aims to introduce the reader to the options. In section three the options trading methodology is presented, while in the fourth section follows an evaluation in both terms of volatility directional accuracy and investment revenue. The last section summarizes the conclusions and future research.

Options

Options confer upon the holder the right to buy or sell an asset in the future for a given price. There are two basic types of options: A Call (C) gives the holder the right to buy while a Put (P) gives the holder the right to sell. The price at which the future transaction may be carried out is known as the strike price or exercise price. There are two sides to every option contract. On one side is the investor who has taken the long position (has bought the option) and on the other side is the investor who has taken the short position (has sold or written the option). The writer of the option receives cash upfront but has potential liabilities later. In order to ensure that writers of calls and puts are able to honour their obligations to sell or buy the underlying item, writers have to make a security deposit (margin). The net margin is calculated daily on the basis of the client's options and futures account. The important feature of options is that they do not have to be exercised [START_REF] Hull | Options, Futures and Other Derivatives[END_REF].

There are numerous strategies available for taking advantage of increases or decreases in volatility. These strategies are called non-directional strategies or volatility strategies. They are delta neutral strategies, where delta ( ) is one of the sensitivity factors that measure how an option's value changes with respect to a change in the price of the underlying asset [START_REF] Hull | Options, Futures and Other Derivatives[END_REF]. Volatility is subject to the forces of supply and demand. As a result volatility will tend to rise during periods when demand from options buyers is strongest and will fall when demand is weakest.

Various delta neutral strategies have been proposed in the bibliography [START_REF] Hull | Options, Futures and Other Derivatives[END_REF][START_REF] Briys | Options, Futures and Exotic Derivatives, Theory, Application and Practice[END_REF][START_REF] Mcmillan | Options As a Strategic Investment (4th Edition Study Guide)[END_REF]

Options Trading Methodology

The proposed options trading methodology is consisted of a number of necessary sequential steps in order to reach an investment decision, as presented in figure 1 and analysed below:

Weekly Closing Values (WCV) of the underlying instrument are obtained from the relevant markets. A new value is inserted each period to the database in order to update the time series.

From WCV series two volatility (annual) series are calculated, the Historical Volatility Series (HVS) and the Imply Volatility Series (IVS) where the Black & Scholes formula is used [START_REF] Hull | Options, Futures and Other Derivatives[END_REF]).

One step-ahead forecast is produced for HVS with two different extrapolating methods. The Naïve method that performs very well for short-term forecasting and a Moving Average of thirteen periods-MA13 (13 weeks = one term) that performs well for the medium-term [START_REF] Assimakopoulos | Financial Volatility Forecasting[END_REF].

A two-layer Artificial Neural Network (ANN) is trained with the Backpropagation algorithm [START_REF] Haykin | Neural Networks: A Comprehensive Foundation (International Edition)[END_REF] to combine these forecasts in order to produce as accurate forecasts as possible in terms of directional accuracy. We are interested in getting right the direction for the next period rather than the actual value itself. So we combine two point forecasts from different approaches (one short-term and one medium-term oriented) in order to get one efficient forecast for the direction of the series. The directional accuracy of the combination is better than the directional accuracy of the two methods that are weighted by the ANN (Naïve and MA13). In order to produce profitable investments accuracy over the threshold of 60% should be achieved. It must F o r P e e r R e v i e w 6 be noted that the majority of Academics in the forecasting field are in favour of combining, a empirical principle that was also verified in the largest ever forecasting competition, the M3-competition [START_REF] Makridakis | The M3-Competition: Results, conclusions and implications[END_REF]; an equal weighted combination of three exponential smoothing approaches outperformed the performance of each method separately. However it is not always the case that a combination can outperform any individual method, as proved by the performance of the Theta model -a single univariate method that outperformed all combinations in the very same competition [START_REF] Assimakopoulos | The Theta model: a decomposition approach to forecasting[END_REF]. Overall we are in favour of the combinatory approach in this study as it comes for the minimisation of risk as well as the usually increased accuracy.

The one step-ahead forecast is then compared with the last actual value of the two volatility series HVS and IVS. In some cases IVS has to be transformed so as to be in the same level (mean) with HVS and make comparisons feasible.

If the forecast is greater than the last observed actual then the trader is adopting a Combination of Strategies for Increasing Volatility (CSIV), otherwise a Combination of Strategies for Decreasing Volatility (CSDV) is taken. These two sets of positions CSIV & CSDV are explained in detail in table 1. Since there are two volatility series, two comparisons are made and consequently two trading suggestions are produced. In the case that the trading suggestions are in the opposite direction (the HVS series comparison suggest CSIV positioning while the IVS series a CSDV one or vice versa) then no action is made at all for this period and the trader waits for the next period. Thus, the CSIV trading order is consisted of two Short Calls (selling two buying options) and one Long Put (buying one selling option) with strike price lower than the "at the money" price of the underlying asset, three Long Calls and six Long Puts "at the money", and three Long Calls and three Short Puts with strike price greater than the "at the money" price. The maximum profit from this portfolio is infinite while the maximum loss is:

[INSERT TABLE 1 ABOUT HERE]

r = (P X1 + 3C X2 +6P X2 +3C X3 )-(3P X3 +2C X1 ).
On the other hand CSDV is exactly the complimentary position where this time as expected the maximum loss is infinite and the maximum profit equal to r.

Evaluation

The proposed methodology was evaluated based on the directional accuracy of volatility forecasts, as well as the financial success of the trading suggestions.

Directional accuracy

The The rational behind the choice of such a small holdout (relatively to the length of the series) comes from a financial economics perspective. The trading strategy should be able to be compared with actual yearly or 6-months bonds and investment portfolios; that is why 26 weeks were selected, however 52 weeks could be an alternative holdout. In terms of the standard practise in forecasting literature [START_REF] Makridakis | Forecasting Methods and Applications[END_REF], usually holdouts of about 20% -40% of the series are selected; however this is the practice in blind competitions, where the source of the data is unknown and holdouts of specific length do not make any real difference.

[INSERT FIGURE 2 ABOUT HERE]

Assimakopoulos and Vafopoulos ( 2000) conducted an extensive survey of available forecasting techniques for stock market volatility. In the present study a forecasting competition was conducted with eleven different approaches from that study: the random walk model (NAÏVE); the mean model (MEAN); the exponential smoothing model (SES) [START_REF] Makridakis | Forecasting Methods and Applications[END_REF]; Moving Averages of 4, 8, 13 and 26 weeks (MA4, MA8, MA13, MA26); and four models from the ARCH family (ARCH, GARCH, EGARCH, TARCH) [START_REF] Alexander | Risk Management and Analysis[END_REF].

Those methods were proven inadequate for the Greek market in an earlier study (Maris et al. 2004a). Having in mind that the financial evaluation is going to be conducted only in the Greek Market where detailed data are available, the authors decided to used ANN as mentioned earlier in order to combine the forecasts from some of these simpler approaches. Instead of challenging the forecasting accuracy of these models in terms of pointforecasts oriented error metrics (RMSE or MAPE, [START_REF] Makridakis | Forecasting Methods and Applications[END_REF]) the authors decided to use Directional Accuracy measures. The rational behind this decision is twofold: First it is much easier to forecast whether volatility is going to increase or decrease rather than estimating a point forecast, and secondly the trading strategies that will be used are based on the sign of the volatility change.

The directional accuracy is measured as a percentage of the times you get right the direction of the volatility forecast divided by the times you make a forecast. For our research we conducted 26 forecasts for each Stock Market. So the Average Percentage is calculated as the ratio of the successful volatility direction over the 72 attempts across the three different markets. The average ranking is calculated a bit differently. The methods are ranked for each separate market according to their directional accuracy and then an average of these three positions is taken. The combination from an ANN of forecasts from the NAIVE method and MA13 proved to be the best with both average measures (Table 2, Average Percentage 67.95% and Average Ranking 2.33) as a result of taking the first place in CAC40 (Directional Accuracy 80.77%), the fourth place in DAX (Directional Accuracy 57.69%) and the second place in FTSE20 (Directional Accuracy 65.38%). The NAÏVE method provides by definition 50% directional accuracy as it does not provide sign.

[INSERT TABLE 2 ABOUT HERE]

Position Evaluation

In order to evaluate the proposed trading methodology, we made transactions of 100 contracts on the FTSE/ASE 20 index in a period of 26 weeks (six months), from the 24/10/2003 to 16/4/2004. The index multiplier is 5. The cost of a contract in Euros is given by multiplying the price with the index multiplier. A week later we closed our positions by taking the opposite positions no mater if we had a loss or a profit.

Similarly we conducted transactions with directional forecasts form other forecasting approaches over 26 weeks and computed the total profit/loss of our positions. The results of this real-data simulation are shown in Table 3.

[INSERT TABLE 3 ABOUT HERE]

All the results presented in table 3 are extracted using the same trading strategy. The only difference in each case is the method that produced the forecasts for the direction of the volatility. It is clear that the best method (ANN_NAÏVE_MA13) in terms of directional accuracy did not produce the best financial results. However it produced better financial results than established methods (as the ARCH family) and better results than all the simple methods with the exception of the moving average of twelve weeks This result was partially expected, as a successful directional forecast does not guarantee maximisation of the profit. This is due to the fact that one successful forecast for only one period could cause major profit, more than two or three other successful forecasts. This has to do with the fact that not only the direction counts but the size of the volatility moves as well. Thus, the next step of the methodology should be to find the best method in terms of directional accuracy percentage but restricted to 11 those directional moves sized over a certain threshold i.e. 5%; those that resulted in having a large profit. Nevertheless, the fact that the proposed methodology was profitable over a period of half a year, with 26 continuous trades, is by all means very promising.

Conclusion

This study presented an empirical option trading methodology based on forecasts for the direction of the volatility of the underlying financial index. The proposed methodology is easy to apply, easy to embed in an Information System and requires standard inputs available freely via the Internet for the majority of stock markets.

A high directional accuracy leads to profitable investment strategies, however the net end result always depends on the size of changes as well. An empirical threshold of 60% of successful volatility forecasts was found to be sufficient for creating profitability within a period of six calendar months. The proposed volatility forecasting approach was validated on weekly data obtained from CAX40, DAX and the Greek FTSE/ASE 20 stock indices while the trading strategy using data only from the Greek index.

For the production of volatility forecasts an ANN was employed in order to combine the forecasts from two simpler approaches: the short-term oriented Naïve method and the mid -term oriented Moving Average of thirteen weeks model. This method proved to perform best across the three different markets. The forecasting method is by definition more robust due to the combinatory nature. The proposed methodology produced profit for a period of six months (26 weeks). For each week the methodology provides two trading suggestions -one based on the historical volatility and another on the implied one. The robustness of the method is once more verified, as both trading orders are on average profitable over the testing period. However, while applying the same trading strategy to volatility forecasts from less accurate models, some interesting results came up; some simpler approaches produced better financial results. This was partially expected, as a successful directional forecast does not guarantee maximisation of the profit. This is due to the fact that one successful forecast for only one period could cause major profit, more than two or three other successful forecasts.

Future research should be focused towards finding the best method in terms of directional accuracy but restricted to those directional moves over a certain margin; these changes are expected to result in big profits. Also more practical issues should be addressed in order to test the methodology with more frequent data i.e. daily data or intraday data. Finally the proposed methodology should be embedded in a prototype information system in order to be widely tested in other stock markets (FTSE, DJIA, NASDAQ), and become more generic. Nevertheless, the evaluation results and the simplicity of the proposed approach make it rather attractive and by all means worth expanding.

  time-series under consideration consist of weekly observations (Friday closing values) from three stock indices: CAC40, DAX and the Greek FTSE20. All three series stand for annual volatility (calculated on the relative underlying stock indices, Hull 1997). The graph of the DAX series follows in figure 2. The sample period of the time-series under examination covers 238 weeks. The first 212 weekly observations were used for the estimation of the models' parameters, from the period starting on the 27/08/1999 to the period ending on the 17/10/2003 (weeks t: 1, 2, ... 212). The authors held out the last 26 observations (weeks t: 213, … 238) up to the period ending on the 16/4/2004, in order to evaluate the models out of sample one-stepahead forecasting accuracy. Thus, the average out of sample forecasting accuracy was calculated over 26 one-step-ahead errors.

Figure 1 .

 1 Figure 1. Flow diagram for the proposed methodology.

Table 1 .

 1 Combination of Strategies for Increasing Volatility (CSIV) Annual volatility (calculated on the German DAX stock index)

	Comparison of Last Actual
	Transformed Imply Volatility with
	1-step ahead Volatility Forecast

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK +:Buy, -: Sell, C: Call, P: Put Page 17 of 20 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 2 .

 2 CAC40, DAX, FTSE20 -Directional Accuracy (Rolling over 26 oneweek ahead forecasts)

	Page 19 of 20	Submitted Manuscript
	METHOD		Average Percentage	Average Ranking
	ANN_NAIVE_MA13		67.95%	2.33
	ANN_NAIVE_SES		64.10%	3.00
	ANN_SES_MA13		62.82%	3.33
	MA13		60.26%	4.00
	ANN_NAIVE_ARCH		58.97%	4.33
	ANN_NAIVE_EGARCH	58.97%	4.33
	MA8		57.69%	4.67
	MA26		57.69%	4.67
	GARCH		56.41%	5.00
	TARCH		56.41%	5.00
	ARCH		55.13%	5.33
	EGARCH		55.13%	5.33
	MEAN		55.13%	5.33
	MA4		51.28%	6.33
	NAÏVE		50.00%	6.67
	SES		42.31%	8.67

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

Table 3 .

 3 Position evaluation over 26 weeks in Euros (FTSE20)

				Page 20 of 20
	Forecasting Method	Trading Order 1 Trading Order 2 EVALUATION
	ANN_SES_MA13	63140	109020	172160
	MA12	-16280	186360	170080
	ANN_NAIVE_SES	78040	84000	162040
	ANN_NAIVE_EGARCH	105940	41440	147380
	ANN_NAIVE_MA13	58440	65840	124280
	ARCH	-184160	255000	70840
	EGARCH	-184160	255000	70840
	SES	121480	-69420	52060
	GARCH	-184160	161960	-22200
	ANN_NAIVE_MA5	-197840	-31280	-229120

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

Submitted Manuscript

Buckley, A., Tse, K., Rijken, H. and Eijgenhuijsen, H. (2002) Stock Market Valuation with Real Options: lessons from Netscape, European Management Journal, 20

Acknowledgement

The authors would like to thank Mr. Michael C. Handrinos from Lancaster University for his comments and suggestions in the final revision of this paper.

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


Keywords: monetary integration, real option, calibration

We examine the real option implicit in countries'decisions of whether to join a monetary union and calibrate our theoretical model for the core ASEAN/AFTA group of Indonesia, Malaysia, Philippines, Singapore and Thailand. None of the countries would be prepared to join a monetary union amongst them at present, and most have low to negligible probabilities of ever wanting to do so.

Introduction

With the European Monetary Union in operation since 1999, focus has shifted to other areas of the world, particularly Asia, to examine whether similar ventures might be viable or desirable there. [START_REF] Barro | Rules, discretion and reputation in a model of monetary policy[END_REF] Policymakers are generally concerned about in ‡ation performance, possibly because a time inconsistency problem in monetary policymaking can cause an undesirable in ‡ation bias to persist. [START_REF] Dixit | The art of smooth pasting[END_REF] If the future evolution of such in ‡ation preferences is uncertain, the decision to join a monetary union represents a real option due to policymakers'reluctance to commit to a largely irreversible move that could later prove less advantageous than initially thought. In this paper we extend and apply the theoretical model of Strobel (2002, 2005) in examining this real option implicit in countries'decisions of whether to join a monetary union when the costs of later leaving it again are considered prohibitively high and there is uncertainty over the future bene…ts of such a move. We calibrate our model for the core ASEAN/AFTA countries of Indonesia, Malaysia, Philippines, Singapore and Thailand by proxying policymakers' stochastic in ‡ation biases with unemployment rates, derive the proxied trigger values of relative in ‡ation bias parameters for di¤erent time horizons and contrast them with the corresponding actual ratios for 2003, our reference period. We …nd that none of the countries considered would be prepared to join a monetary union amongst them at present, most of them have low to negligible probabilities of ever wanting to do so, whilst also not expecting that event to occur in …nite time. Those countries thus appear too heterogenous and variable at the moment to make formation of a monetary union much of a realistic prospect in the near future.

Section 2 now presents the model; the results of our calibration exercise are reported in section 3, and section 4 concludes the paper.

The model

Policymakers in countries c and the potential wider union u are assumed to be exclusively concerned with in ‡ation performance; they face instantaneous loss rates l it = it , where exogenous in ‡ation biases it 0 follow geometric Brownian motions4

d it = i it dz it ; i = c; u (1)
with i > 0 , dz it = " it p dt are increments of Wiener processes with " it NID(0; 1) , and E t (dz ct dz ut ) = dt with the coe¢ cient of correlation between the processes z it (and 1 < 1). The expected present discounted value of losses associated with in ‡ation performance is then5

F o r P e e r R e v i e w L it = E t Z 1 t l i e ( t) d = it (2)
where > 0 is the (possibly subjective) discount rate.

The decision of a country c on whether or not to join the wider monetary union u then involves solving the Bellman equation for the optimal stopping problem

F (L c ; L u ) = max L c L u ; 1 dt E t [dF (L c ; L u )] (3)
where F (L c ; L u ) is the value to country c of the option of joining the wider monetary union u , and L c L u is the expected discounted bene…t of such a move when any other cost/bene…ts are abstracted from. [START_REF] Strobel | Monetary integration and in ‡ation preferences: a real options analysis[END_REF] Note that this implicitly assumes that joining a monetary union is an irreversible process, so that the costs of possibly later leaving it again are considered prohibitively high. We can then obtain Proposition 1 Country c will want to exercise the option of joining the wider monetary union u if

u c u c = 1 1 1 where 1 = 1 2 0 @ 1 + 1 q 1 8 3 8 3 + c 2 2 c u+ u 2 1 A
Otherwise it will keep the option unexercised, with expected time and probability of future exercise of

T u c = 8 < : 1 if u 2 c 2 ln u c ln u c 1 2 ( c 2 u 2 ) if u 2 > c 2 P u c = 8 > < > : 1 if u 2 c 2 exp ln u c ln u c ( c 2 u 2 ) c 2 2 c u+ u 2 if u 2 < c 2 6
We drop time subscripts for ease of notation. Proof. See Appendix. Country c perceives exercise of the option of joining the wider monetary union u as desirable only when the current value of relative in ‡ation bias parameters u c is less than (or equal to) its trigger value u c ; intuitively, the higher a country's in ‡ation bias relative to the potential wider union's, the more it stands to gain from giving up its monetary independence. While

u c > u c
applies, on the other hand, country c strictly prefers to leave the option of monetary integration unexercised and remains outside the wider union for the time being; in this case, we can further derive the expected time and probability of its potential future exercise of that option.

A simple calibration

We proceed to calibrate the model in Section 2 for the core ASEAN/AFTA countries of Indonesia, Malaysia, Philippines, Singapore and Thailand by proxying national policymakers'inherent in ‡ation biases c with unemployment rates; this re ‡ects the familiar rationale for the potential bene…ts of surprise in ‡ation based on the expectational Phillips curve. 7 Using annual data for the period 1986-2003 drawn from the Asian Development Bank's Key Indicators 2004, 8 we calculate the required moments from the respective transformed series ln( xt x t 1 ) to re ‡ect our distributional assumption of eq. ( 1); these are reported in Table 1. The potential monetary union's in ‡ation bias u is for these purposes constructed as the simple arithmetic mean of the constituent countries'proxied values; this mimics a bargaining outcome over the union's monetary policy where individual member countries have equal votes.

The proxied trigger values of relative in ‡ation bias parameters u c , from Proposition 1, are then computed for time horizons of 10 and 25 years by applying discount rates of 12.5% and 5.5%, respectively, to allow for varying degrees of policymakers' myopia. 9 2 and3 both for a potential monetary union comprising all …ve countries (All) as well as a narrower one (MST) consisting only of Malaysia, Singapore and Thailand (the low-unemployment group in our reference period). Table 4 then gives the expected times and probabilities, from the second part of Proposition 1, of the option of monetary integration potentially being exercised at some point in the future for those di¤erent constellations.

From Table 2 we observe that none of the countries considered would be prepared to join a monetary union comprising the whole group at present, irrespective of time horizon. time horizon, none of them ever expects wanting to do so. Malaysia and Indonesia have otherwise the highest probabilities of ever wanting to join a monetary union comprising the whole group, while those probabilities are negligible for Singapore and Thailand, particularly for the longer time horizon where uncertainty leads to signi…cantly more cautious behavior. We observe similar results for the sub-group of Malaysia, Singapore and Thailand: Table 3 shows that none of them would be prepared to join a narrow monetary union between them at present either, irrespective of time horizon. While Malaysia expects future joining dates that lie only very substantially above the time horizons considered, Singapore and Thailand never expect wanting to join at all, and it is then only Singapore for the 10 year horizon that has a non-negligible probability of ever wanting to be part of such a union.

To sum up the results of our simple calibrations: the …ve ASEAN/AFTA countries considered appear at present too heterogenous and variable to make formation of a monetary union amongst them much of a realistic prospect in the near future, as the value of waiting associated with such a major regime shift proves rather substantial for the criteria considered.

Conclusion

We examined the real option implicit in countries' decisions of whether to join a monetary union and calibrated our theoretical model for the core ASEAN/AFTA group of Indonesia, Malaysia, Philippines, Singapore and Thailand. We found that none of the countries considered would be prepared to join a monetary union amongst them at present and that most of them have low to negligible probabilities of ever wanting to do so. Those countries thus appear too heterogenous and variable at the moment to make formation of a monetary union much of a realistic prospect in the near future. as the di¤erential equation that characterizes the evolution of f ( ) in that region. We solve equation ( 5) by standard methods, using the value-matching and smooth-pasting conditions f ( ) = 1 and @f ( ) @ = 1 , plus the boundary condition f (0) = 0 , 12 and thus obtain

3

 3

=

1

 1 as the critical (trigger) value . From the de…nition of it then follows that u

Table 1 :

 1 These results, together with the proxied Standard deviations & correlation coe¢ cients

		StDev	Corr w/ All	Corr w/ MST
	Indonesia	0.205	0.574
	Malaysia	0.143	0.728		0.706
	Philippines	0.105	0.588
	Singapore	0.259	0.621		0.763
	Thailand	0.511	0.683		0.790
	All	0.129	1.000
	MST	0.206			1.000
	Source: Asian Development Bank (ADB) -Key Indicators 2004
	F o Ratio w/ All ('03) r	Trigger ratio w/ All 10 year 25 year
	Indonesia Malaysia Philippines Singapore Thailand	0.620 1.630 P 0.583 1.253 e e 3.824	0.109 0.228 0.209 0.078 0.020	0.011 0.031 0.027 0.008 0.002
			r
			R e
				v
				i
				e
					w

Source: Asian Development Bank (ADB) -Key Indicators 2004

Table 2 :

 2 Ratios & trigger ratios with All

	values for the relative in ‡ation bias parameters u c	for 2003, our reference
	period, are presented in Tables

  Table 4 further indicates that, apart from the Philippines which has expected joining times hundreds of years above the discount rate of 2.5% over those …nite time horizons.

	Ratio w/ MST ('03)	Trigger ratio w/MST
			10 year	25 year
	Malaysia	0.909	0.137	0.015
	Singapore	0.699	0.110	0.012
	Thailand	2.132	0.027	0.002
	Source: Asian Development Bank (ADB) -Key Indicators 2004
	F o
	r
	P
	e e
		r
		R e
			v
			i
			e
			w
		5

Table 3 :

 3 Ratios & trigger ratios with MST

			All					MST
		10yrs		25yrs		10yrs		25yrs
		Prob Time Prob Time	Prob Time Prob Time
	Indonesia	0.210	inf	0.028	inf
	Malaysia	0.486	inf	0.233	inf	1.000 171.6 1.000 370.9
	Philippines 1.000 359.4 1.000 1076.6
	Singapore	0.036	inf	0.002	inf	0.196	inf	0.027	inf
	Thailand	0.001	inf	0.000	inf	0.001	inf	0.000	inf
	Source: Asian Development Bank (ADB) -Key Indicators 2004

Table 4 :

 4 Probabilities & expected times

See e.g. Eichengreen/Bayoumi (1999).

See e.g.[START_REF] Barro | Rules, discretion and reputation in a model of monetary policy[END_REF].

See e.g. Dixit/Pindyck (1994).

Similar frameworks are used in[START_REF] Strobel | Leaving a monetary union: expected time and probability[END_REF][START_REF] Strobel | Monetary integration and in ‡ation preferences: a real options analysis[END_REF].

See e.g.Dixit (1993, eq. (2.7)).

E52 -Monetary Policy (Targets, Instruments, and Effects) < E5 -Monetary Policy, Central Banking, and the Supply of Money and Credit < E -Macroeconomics and Monetary Economics, F33 -International Monetary Arrangements and Institutions < F3 -International Finance < F -International

Appendix

Proof. (Proposition 1) For country c , not joining the wider monetary union u for a further instant dt is optimal in the continuation region of the optimal stopping problem eq. ( 3), giving the relevant Bellman equation as

Applying Ito's Lemma to eq. ( 4) and noting that the value function F (L c ; L u ) should be homogeneous of degree 1, 10 so that F (L c ; L u ) = L u f ( ) where Lc Lu , 11 we obtain 7


JEL Code: Q12 -Micro Analysis of Farm Firms, Farm Households, and Farm Input Markets < Q1 -Agriculture < Q -Agricultural and Natural Resource Economics

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

Introduction

In rural areas of China one of the main effects of the economic reforms has been to enhance the role of market forces in farm household production and consumption decisions. A fundamental change was the replacement of the commune system with the "household responsibility system" (HRS) whereby land and production responsibilities were placed under contract with individual farm households. To encourage private investment and the sustainable use of natural resources the land contract was expanded in the early 1980s from 1-3 years to 15-25 years (Davis et al. 2000); the Rural Land Contracting Law (2003) further extends the contract period to 30 years in most areas. The nature of the reforms led inevitably to a research agenda that tended to concentrate on the impact on farm household production and productivity. Designing an effective agricultural policy programme, however, depends not only on the "correctness" of the policy itself but also on understanding the response of the participants (farm households) in the policy implementing process.

Moreover, as government investment targets and priorities are increasingly based on consumer demand forecasts, reliable estimates of, household demand for different commodities are important in informing policy design. This paper explores rural household food consumption behaviour using a data set from Jilin Province in Northern China. It aims partially to fill a gap in the literature on the nature of household demand for livestock products in rural China. Jilin Province has a population of about 26 million and occupies a "middle" position in nationwide rural development indices. It is recognised as a predominantly agricultural province and is one of the main grain producing areas in China. The paper focuses in particular on the effects of household income and household characteristics on consumption behaviour. The work has two novel features. Firstly it The paper begins with a brief review of previous household demand studies in China.

It then moves to a consideration of data issues and outlines the classification of the data for analytical purposes into four main food groups-Grain, Vegetable Products, Animal Products and Other Foods. A household food demand system is estimated using a Linear Approximation of the AIDS (LA-AIDS) model-incorporating four household characteristics-based on the assumption of a three-stage budgeting procedure. Expenditure elasticities for a range of food groups are reported, with a particular focus on Animal Products.

Household demand studies in China

This section is a non-exhaustive overview of earlier studies of household demand in China. Apart from a study by [START_REF] Houthakker | An International Comparison of Household Expenditure Patterns, Commemorating the Centenary of Engel's Law[END_REF] The early studies in the reform era mainly used the Engel function and Linear Expenditure Systems (LES) to estimate expenditure and/or consumption patterns, mainly because of its simplicity and intuitiveness of economic interpretation. For example, [START_REF] Chow | The Chinese Economy, Harper and Row[END_REF], Van De Gaag (1984), and[START_REF] Li | Structure of China's Domestic Consumption Analysis and Preliminary Forecasts[END_REF] used the Engel function and the LES to estimate consumption patterns in rural households in Hubei province and urban households in Beijing in 1981and 1982[START_REF] Chow | The Chinese Economy[END_REF] estimated Engel functions for food, clothing, housing, and miscellaneous items using the 1981 expenditure data for rural households in 28 provinces of China. Using the pooled time-series and cross-sectional data from China's urban and rural household surveys for the year 1982 to 1985, [START_REF] Lewis | Household Demand in China[END_REF] estimated the Chinese urban and rural household expenditure and income elasticities for a broad group of food, clothing, daily articles, other commodities, and non-commodities, and also for a subfood groups of grain, pork, poultry and fish. None of these studies, however, took account explicitly of the household rationing system even though we would expect it to influence demand and consumption estimates. Gao, Wailes, and Cramer (1996), however, attempted to take account of rationing by using a differential Rotterdam mixed-demand system to estimate China's urban household food demand using aggregated data from 1987 to 1991. Their results showed that a mixed-demand model system performed better than those that ignored the rationing issue.

By the end of 1993 the grain rationing system had been abolished in most cities and towns. At about the same time the SSB household survey was reviewed and more than 400 items were added including rural household income and consumption indices. Both of these developments removed some of the constraints experienced by earlier household studies. This was followed by a growth in the number of household demand and consumption studies that gradually adopted more theoretically plausible [START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF][START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF]; Fan et al. (1994); Li, and Samuel (1994); [START_REF] Fan | Household Demand in Rural China: A Two-stage LES-AIDS Model[END_REF]; [START_REF] Wu | Food Consumption in Urban China: An Empirical Analysis[END_REF]; Wan (1996a[START_REF] Wan | Income Elasticities of Household Demand in Rural China[END_REF]; [START_REF] Mittelhammer | Accounting for Aggregation Bias in Almost Ideal Demand Systems[END_REF]; and Gao et al. (1996aGao et al. ( , 1996b)).

Only a few studies have tried to take household characteristics into account. [START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF] used cross-section data for 1990 and the demographic translating method in a two-stage AIDS model to analyze rural household consumption behaviour in Guangdong province. They incorporated sociodemographic dummy variables for example geographical location, topography, households with or without rural leaders and/or government staff workers and education levels. They found that most of the socio-demographic dummy variables in the model were significant. For example, households with members who were rural leaders and/or government staff tended to spend more money on durable goods because their income levels were higher. Households with higher education levels spent a much higher proportion of their income on non-food items than they did on food items. [START_REF] Wu | Food Consumption in Urban China: An Empirical Analysis[END_REF] examined the consumption patterns of urban households using aggregated 1990 household consumption data from 33 cities in China. By using a two-stage budgeting procedure, which incorporated an AIDS model in each stage, they estimated a six commodities (rice, pork, vegetables, fish, eggs and fruits) demand system. In this case, however, household characteristics were not taken into account. Gao et al. (1996) used an AIDS model on micro-level 1990 data from Jiangsu Province. They also used the demographic translating method to evaluate economic and demographic effects on rural household demand for nine food commodities and five non-food commodities groups. They found that households with family members

The data

We obtained data from the Provincial Statistical Bureau for a total of 1,520 rural households for each year from 1991 to 1995. The data were obtained from a rural sample survey covering 19 counties. Sampling is conducted in a multi-stage systematic way with a random start. The Provincial Statistical Bureau selects sample counties, then sample villages and finally sample households within the selected villages. The sampling method at each stage is controlled and is identical.

Households maintain logbooks that separately record cash transactions-in value and volume terms-and own consumption/goods in kind exchanges. The Appendix table provides a statistical summary of the basic features of the sampled households and quantities of food consumed. In budget terms food was by far the largest item, accounting on average for almost 60 per cent of household expenditure in 1995.

Clothing and housing costs were the next largest items accounting for a further 20 per cent of expenditure. Within the food category grain consumption was by far the largest item accounting for 45 per cent of the total food budget followed by meat and meat products at 14 per cent and vegetables at about 10 per cent [START_REF] Jiang | Rural Household Food Demand: A Microeconomic Analysis of Jilin Province[END_REF]. The data set is extremely large and in order to make the analysis feasible we assume that households adopt a three-stage budgeting procedure. In Stage I Food is treated as a separate budgeting category from other principal categories such as Clothing and Housing. In Stage II within the Food category households are assumed to budget separately for four categories: Grains; Vegetable Products; Animal Products; and Other Foods. In Stage III there is further separation of each category, for example the Animal Products category is sub-divided into three groups: Meat; Aquatic Products; and Eggs. In treating the data in this way we assume weak separability of preferences (Deaton and Muellbauer, 1980a). A utility function is weakly separable if and only if the goods can be partitioned into subsets in such a way that every marginal rate of substitution involving two goods from the same subset depends only on the goods in that subset. This means, for example, that the demand for a particular Food subgroup-say Animal Products-can be expressed as a function of the prices of the items in that sub-group and total expenditure on those items. Expenditure on and the prices of goods outside the Food group enter the demand functions for Food only through their effect on total expenditure on food. In this particular study, data availability allowed us to analyse Stage III budgeting only in the case of Animal Products.

We incorporate household characteristics into the estimation using the demographic translating method developed by [START_REF] Pollak | Estimation of Complete Demand Systems from Household Budget Data: The Linear and Quadratic Expenditure Systems[END_REF]. In this method, translation parameters, d i , are first defined as depending on demographic characteristics such that

d i = D i (h) (i = 1,…, n)
where, h = (h 1 , h 2 , …, h j ) is a vector of demographic characteristics.

The modelling approach

We use the Linear Approximation of the Almost Ideal Demand System, the so-called LA-AIDS model introduced by Deaton and Muellbauer (1980b). In the budget share form of the model we have: where, w i is the household budget share on the ith commodity;

w i = α i + β i log( Y P * ) + ∑ j γ ij logP j …………………..(1)
α i , β i, γ ij are parameters of the system; and

γ ij = 1 2 (γ* ij + γ* ji )
Y is total household income or expenditure; p j is the price of the jth commodity;

Y/P is "real expenditure"; and P* is the Stone Price index given by, log P * = ∑ i w i logP i where, i is the ith commodity group, w i is the expenditure share of ith commodity group, P i is the aggregate price for the ith commodity group.

The name, Almost Ideal Demand System, stems from the properties associated with the system. Deaton and Muellbauer (1980b) As discussed above the incorporation of household characteristics follows the demographic translating method as follows:

α i = ρ i0 + ∑ d s=1 ρ is H s ..…………..(2)
where, H s are the demographic variables of which there are d (s = 1,…,d).

ρ i0 and ρ is are parameters to be estimated.

α i is the intercept term in LA-AIDS model .

By substituting (2) into (1) we have an enhanced LA-AIDS model incorporating household characteristics:

w i = ρ i0 + ∑ d s ρ is H s + β i log ( Y P * ) + ∑ j γ ij logP j
Now, ρ i0 is the new intercept term.

According to [START_REF] Alston | Estimating Elasticities with the Linear Approximate Almost Ideal Demand System[END_REF], the uncompensated own-price, cross-price, and expenditure elasticities for this system are,

ε ii = -1 + (γ ii / w i ) -β i ε ij = (γ ij / w i ) -β i (w j / w i ) η i = 1 + β i /w i
and the household variable elasticitity is, We assume that all w i > 0, thus we have a limited dependent variables model. A Tobit model is used for solving this problem, which takes the form,

δ is = H is ρ is / w i .
w ih = ρ i0 +∑ s ρ is H s +β i (log Y h -logP h ) + ∑ j γ ij logP jh + µ i if, w ih > 0
and, w ih = 0 if, w ih <= 0. Now, µ i is an independently distributed error term assumed to be normally distributed with zero mean and variance σ 2 . Thus we use the Seemingly Unrelated Regression (SUR) method-developed by [START_REF] Zellner | An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias[END_REF]-in LIMDEP 7 for model estimation.

Results

Results are presented for Stage II and Stage III expenditure (income) elasticities. In

Stage III we restricted our analysis to the Animal Products group (Stage II) due to the better availability of data for this group. But we also felt that this group (Meat, Eggs and Aquatic Products) is particularly interesting due to anticipated future growth in household demand, especially for meat.

We considered the theoretical restrictions of adding up, homogeneity and symmetry as they apply to demand systems. However, as the entire budget shares sum to unity, i.e. ∑ i w i = 1, the adding up restriction is inherent in the data and therefore did not need to be tested. We estimated the models in Stages II and III with and without the homogeneity and symmetry restrictions imposed. Using the log-likelihood ratio test we found that in both Stages the restrictions on the parameters caused the ratios to decline significantly-compared to the models without restrictions-in the case of and Muellbauer (1980b) and [START_REF] Hossain | Lithuania's Food Demand During Economic Transition[END_REF]. Moreover, when using the AIDS model on Spanish annual time-series food expenditure data, [START_REF] Molina | Food Demand in Spain: An Application of the Almost Ideal System[END_REF] found that the theoretical assumptions of homogeneity and symmetry were rejected, but that the model still provided plausible elasticities. Using the same approach we examined the impact of including household characteristics in the models. Chi-square tests suggested significant differences between the log-likelihood ratios at the 5per cent level for the models including the characteristics compared to those without.

This suggested that the AIDS model incorporating household characteristics should produce superior results.

Table 1 presents the estimated Stage II and Stage III conditional and total expenditure (income) elasticities for the selected food groups. A conditional value in Stage II for example refers to the elasticity of that food group with respect to total expenditure on the four food groups in that stage, the latter amount having been determined at Stage I under the assumption of weak separability. The total (or real) value is the expenditure elasticity of a particular group with respect to total household expenditure on food and non-food items. If we assume no saving behaviour then the total expenditure elasticity is the same as the income elasticity. The total value, of course, is the more relevant measure when considering possible future changes in demand and also for policy analysis purposes. effects in Stage II were on the conditional and total elasticities for Grain and on the conditional values for Animal Products. The differences, however, were not significant. In Stage III differences were apparent only in the case of eggs but again the magnitudes were relatively small. The total expenditure elasticity for Grain in

Stage II ranges from 0.64 to 0.67. This is substantially higher than estimates in previous studies of household demand in rural China. Wan (1996a) for example, using an Engel function on provincial rural household data, estimated an elasticity value of 0.4. [START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF], however, using and AIDS model estimated a value for rural Guangdong Province of 0.58. The total expenditure elasticity for vegetables is 0.45: which is substantially lower than the estimates in the Wan (1996a) and [START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF] studies of 1.04 and 0.91 respectively.

The highest Conditional and Total elasticity values were for the Animal Products group, 1.22 and 0.76 respectively. These are the only elasticity estimates that we are aware of in the literature for this particular (Stage II) food group. Within this group the elasticities were highest for the Meat sub-group at 1.14 and 0.87 respectively.

This estimate is somewhat lower than the [START_REF] Halbrendt | Rural Chinese Food Consumption: The Case of Guangdong[END_REF] estimate of 1.09 but consistent with the [START_REF] Fan | Household Demand in Rural China: A Two-stage LES-AIDS Model[END_REF] estimate of 0.9. It is also quite close to the estimate of 0.7 for meat in rural India by [START_REF] Abdulai | Household Food Demand Analysis in India[END_REF]. For a fuller review of elasticity estimates from previous studies see Jiang (2001). There seems likely to be four main reasons for the differences between the various elasticity estimates: (a) the most obvious is differences in coverage between urban, rural, region etc. We calculated the elasticity of household demand with respect to the four measured household characteristics. A number of the coefficients for the household characteristics were significant at the 95 per cent level. The absolute values of the elasticities, however, were relatively small. Perhaps of greatest interest was the negative impact of education level on Stage II household demand for Grains (elasticity -0.04), whereas it had a positive influence on demand for Animal Products (elasticity 0.06). The elasticity in Stage III for Meat was 0.04. These results are consistent with the occupational groups and roles of the more educated rural households in Jilin. Their members tend to be the cadres, rural teachers and village enterprise managers who frequently have important public relations roles to perform including the entertaining of guests and visitors.

Summary and conclusions

In this paper we have followed a three stage budgeting procedure, assuming weak separability of preferences, to allocate households' total expenditure within a complete consumption system. In Stage I we allocated total expenditure to food and non-food products. In Stage II food expenditure was allocated to four food groups: The relatively high positive expenditure elasticity for Grain confirms that it was a normal good during the period studied. Substantial growth in household demand, therefore, can be anticipated, particularly for fine grains such as rice and wheat, as per capita incomes continue to grow in rural areas. In the circumstances it is likely that the internal demand pressures will continue to keep the Grain "self-sufficiency" goal high on the list of policy priorities.

At the same time, rural households have been shifting their consumption from coarse grains in particular towards Animal Products. We found that this group had the highest expenditure (income) elasticities of all the groups studied. domestic demand for Grain will change but the added pressures from animal production will also serve to keep grain policy high on the political agenda.

Although we found that household characteristics did exert some influence on demand the overall impact of the variables we were able to use was relatively low.

  quality household data set for Jilin rural households and a rigorous and theoretically plausible modelling framework. Secondly it explores the impact of household characteristics such as family composition and education on household demand behaviour.

  -which estimated income and price elasticities for food, clothing, housing, and miscellaneous items in Beijing in 1927 and Shanghai in 1929-there were no statistical or econometric analyses of household demand and consumption in China before 1980. The main reasons were the poor availability and reliability of data and of course the existence of consumption rationing. The State Statistical Bureau (SSB) sample surveys, which started in 1955 and 1956 for rural and urban households respectively, were suspended in 1960 but commenced again after 1978.

  in particular the AIDS model, for example: Pinstrup-Andersen et al. (1990);

  , state industry, rural industrial enterprises or private business tended to have a higher standard of living than other households. They consumed more vegetables, poultry, fish, and fruit, and less grain. The educational level of household labour (usually meaning head of household) has no uniformly significant impacts on food consumption patterns. Thus whilst the number of household food demand studies in China has grown the literature remains relatively thin in relation to rural household demand for Animal Products. The paper aims partially to fill this gap using an extensive household database.

  can thus be added flexibly to the model. The translating method can be interpreted as allowing "necessary" parameters of the demand system to depend on household characteristics. Four such characteristics are selected for the estimation-based on the demographic information available in the data set: (a) number of people in the household; (b) proportion of household accounted for by children aged 0-11 years; (c) proportion of household accounted for by children aged 12-17 years: and (d) education level of the household, measured as the proportion of household labour educated to at least junior middle school level. Incorporation of these characteristics within the modelling framework is explained below.

  list the following advantages: (a) it gives an arbitrary first-order approximation to any demand system; (b) it satisfies the axioms of choice exactly; (c) it aggregates perfectly over consumers; (d) it has a functional form which is consistent with previous household budget data; (e) it is simple to estimate in its linear approximate form (thus avoiding the substantial estimation problems of the non-linear pure AIDS model); and (f) it can be used to test for the restrictions of homogeneity and symmetry through linear restrictions on fixed parameters. In addition, the system is indirectly non-additive, allowing consumption of one good to affect the marginal utility of another good, whereas, the linear for example, is directly additive, implying independent marginal utilities[START_REF] Blanciforti | The Almost Ideal Demand System: A Comparison and Application to Food Groups[END_REF].

  can influence the value and sign of the β i , they can, therefore, influence the elasticity values.

  and the inherent quality and suitability of the data sets; (b) the majority of previous studies excluded own-price effects which tended to lead to underestimates of the expenditure elasticity; (c) unlike some previous work this study explicitly takes account of the demand interdependencies of food items within a rigorous framework; and (d) studies before the mid 1980s tended to encounter the effects of central planning, particularly inadequate variation in price and income data. In this study, however, we have used a theoretically plausible AIDS model on high quality pooled household data and thus we feel confident that our results are less susceptible to the above sources of error.

  Stage II but hardly at all in Stage III. We concluded that the theoretical assumptions of homogeneity and symmetry were rejected in Stage II but not rejected in Stage III (Animal Products group). Rejection of these assumptions in Stage II is not entirely surprising in the light of similar results from previous studies, see for example Deaton

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  In general we can say that the inclusion of household characteristics did not have a big impact on the elasticity values in either Stage I or Stage II. The most noticeable

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Page 12 of 20 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  State Statistical Bureau. This is the first detailed household food demand study conducted in rural Jilin province. Of course the results apply only to this particular rural region. However, the "middle" position of Jilin in relation to nationwide rural development indices means that, arguably, the results provide a closer approximation to the national rural position than previous studies on, for example, Guangdong and Jiangshu Provinces or Beijing City.

	allocation of expenditure on Animal Products to three sub-groups: Meat (Pork, Beef,
	Mutton, Chicken); Eggs; Aquatic Products. In this way a complete demand system
	for food was estimated-in a theoretically and econometrically plausible way-using
	the LA-AIDS modelling framework.	We also incorporated four household
	characteristics in our specification. We used a high quality, highly disaggregated,
	household data set obtained from the Rural Jilin Provincial Statistical Bureau-a
	branch of the
	F o r
	P e e
	r
	R e v
		i e
		w
	Grain; Vegetables; Animal Products; Other Foods. In Stage III we focused on the
	15

Table 1 Conditional and Total Household Expenditure Elasticities

 1

	Further work might incorporate different variables such as household location, gender
	and occupation of household members. Unfortunately these variables were not
	available to us in the secondary data set. And of course it would be informative to
	analyse demand within the Meat category in more detail if sufficiently disaggregated
	data were available.

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

Basic indicators of rural households in Jilin, 1991-1995

	Item	Unit	1991 1992 1993 1994 1995
	General information
	Permanent residents in the households	person	7090 6926 6742 6612 6436
	surveyed
	Average permanent residents per	person	4.43	4.33	4.21	4.13	4.02
	household
	Average full-time and part-time	person	2.67	2.61	2.67	2.74	2.64
	labourers per households
	Numbers of labourers illiterate and	person	7.84	7.06	6.97	6.65	5.02
	semi-illiterate per 100 labourers
	Number of labourers at primary school	person	40.07 38.77 39.5 37.77 37.06
	level per 100 labourers
	Number of labourers at junior middle	person	42.65 44.68 44.02 46.1 49.21
	school level per 100 labourers
	Number of labourers at senior middle	person	8.45	8.47	8.6	8.52	7.6
	school level per 100 labourers
	Number of labourers at polytechnic	person	0.83	0.91	0.75	0.8	0.73
	second school level per 100 labourers
	Number of labourers at college level	person	0.16	0.12	0.16	0.16	0.38
	per 100 labourers
	Household annual per capita net	yuan	748.33 807.41 891.61 1271.6 1609.6
	income
	Household annual per capita living	yuan	648.41 643.13 670.02 853.73 1494.6
	expenditures
	Per capita food consumption
	Coarse Grain	kg	304.04 304.11 324.16 331.54 348.6
	Rice	kg	133.98 138.32 134.95 133 143.46
	Vegetables	kg	151.08 148.6 142.91 168.67 159.83
	Edible vegetable oil	kg	4.34	4.45	4.08	4.97	5.48
	Edible animal fat	kg	1.74	1.73	1.43	1.19	2.09
	Pork	kg	9.3	8.56	8.7	7.49 10.61
	Beef and mutton	kg	0.37	0.45	0.35	0.31	0.49
	Poultry	kg	0.61	0.88	0.88	1.31	1.97
	Eggs and its products	kg	4.81	3.45	4.05	5.14	6.9
	Fish and shrimp	kg	1.92	1.72	1.98	2.27	3.54
	Sugar	kg	0.57	0.7	0.45	0.48	0.63
	Fruit	kg	5.06	6.11	8.66	9.49	9.23
	Cake	kg	1.14	1.05	1.22	1.35	1.92
	Tobacco	box	16.65 15.5 15.05 15.55 21.9
	Liquor	kg	7.01	6.61	7.65	8.21	8.08

Source: Statistical Yearbook of Jilin,

(1996)

. Page 20 of 20 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

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


C23 -Models with Panel Data < C2 -Econometric Methods: Single Equation Models <

Keywords: Earnings dynamics, Minimum distance estimation, Panel data

This paper decomposes the rise in the cross-sectional variance of male annual earnings in Sweden between 1991 and 1999 into its persistent and transitory components. The results show that the persistent component accounts for basically all of the increase in earnings dispersion. This implies that the answer to the 1990s trend reversal in Swedish earnings inequality is to be found in explanations that focus on persistent changes in the labour market, such as changes in the price of skills

Introduction

Sweden has an interesting history of marked changes in earnings and wage inequality. There was precipitous pay compression among all dimensions from the late 1960s through the 1970s which resulted in one of the most compressed wage structures visible among advanced countries. 1 Whilst several countries also experienced pay compression during the 1970s, few, if any, match the magnitude and rapidness of that in Sweden. In the 1990s, however, there was a noticeable trend reversal in Sweden as cross-sectional inequality began increase rapidly; see for instance [START_REF] Edin | LINDA -Longitudinal Individual Data for Sweden[END_REF], [START_REF] Gustavsson | The Evolution of the Swedish Wage Structure: New Evidence for 1992-2001[END_REF], and Lindquist (2005).

What are the causes and consequences of the 1990s move toward increased earnings dispersion in Sweden? Before one tries to answer questions along these lines it is crucial to recognize that the rise can be decomposed into a persistent and a transitory component, with very different ramifications for the duration of inequality. An increase in the persistent component increases both short-and long-term inequality. An increase in the transitory component, on the other hand, only increases short-term inequality. Consequently, if the cross-sectional increase stems from the persistent component, one should try to explain the trend reversal by focusing on factors that affect earnings differentials in a systematic and persistent way, such as increases in the price of skills. An increase in the transitory component, on the other hand, implies that one should focus on factors that can explain increased transitory earnings fluctuations, such as for instance larger job-instability or a closer connection between firm profits and earnings.

Using a large register-based longitudinal database, this paper offers a decomposition of the rise in cross-sectional inequality in Sweden between 1991 and 1999 into its persistent and transitory components. The paper starts with a description of the parametric model of earnings dynamics used in the analysis and section 3 describes the data. Section 4 presents the results, with the main conclusion being that the increased dispersion in persistent earnings accounts for basically all of the increase in cross-sectional inequality. The paper ends with concluding remarks.

1 See Edin and Holmlund (1995) and [START_REF] Palme | Changes in the Rate of Return to Education in Sweden: 1968-1991[END_REF] for an account of changes in Swedish pay differentials between 1968 and 1991. See for instance [START_REF] Katz | Changes in the Wage Structure and Earnings Inequality[END_REF] for an international comparison of pay differentials.

Parametric models of earnings dynamics

This section describes the parametric model that I use to decompose changes in crosssectional inequality into persistent and transitory components. The model in equation ( 2), although intuitive, is likely to be too restrictive to adequately capture changes in persistent and transitory inequality. In particular, persistent and transitory inequality should be allowed to vary with age and transitory shocks should be allowed to last for several periods; see for instance the discussion in [START_REF] Baker | [END_REF].

The model employed in this paper is as follows:

(5)

ibt ia t ibt u p y + = ,
where and(8) 4 4 3 3 2

F o r P e e r R e v i e w (6) ia a i ia r u u + = 1 , , (7) ibt t t ib ibt + = 1 , ,
2 1 0 ) ( a a a a Var ibt + + + + = .
where 27

= b t a
, that is, years since age 27 (the lowest defined age in my sample).

Equations ( 5) and ( 6) model the persistent component as a random walk in age where the innovation at each age is ) iid(0, ~2a , , r ai r

. 2 The innovation variance 2 a , r is allowed to differ between individuals aged 28-37 and 38-56 but is restricted to be the same within these two age intervals.3 I also estimate the variance of an initial persistent shock, as of age 27, denoted 2 u . Equation ( 7) models the transitory component as a first order autoregressive process with year-specific factor loadings on the innovation ibt . Furthermore, equation ( 8) allows the variance of ibt to be a quartic function of age; a quartic function, rather than for example a quadratic function, is used since Wald tests indicate that this specification is required.

The parameters of the model in equations ( 5)-( 8) are estimated by applying the minimum distance estimator of [START_REF] Chamberlain | Panel Data[END_REF]. Basically, the implied variances and auto-covariances of the model are fitted to the corresponding empirical moments in the data by non-linear least squares; the Appendix contains a description of the estimation procedure.

Last, deriving the expressions for the variances and auto-covariances of the model in equations ( 5)-(8) shows that cohort b 's transitory variance in year t depends on its transitory variance in year 1 t , which in turn depends on the transitory variance in 2 t

, and so forth (see the Appendix for details). This raises the question of what the cohort's transitory variance is in its first sample year. As pointed out by [START_REF] Macurdy | The Use of Time Series Processes to Model the Error Structure of Earnings in Longitudinal Data Analysis[END_REF], a time series approach to this problem is problematic since the assumption of infinite history is untenable. I therefore follow the approach of [START_REF] Baker | Earnings Dynamics and Inequality among Canadian Men, 1976-1992: Evidence from Longitudinal Tax Records[END_REF] and treat the initial transitory variance for each cohort as an additional parameter to be estimated. This approach recognizes that earnings volatility varies across cohorts because they are at different stages of the life cycle and have lived through different times.

Data

The analysis is based on Statistics Sweden's register-based longitudinal database LINDA (SCB, 1999). Each year contains a representative sample of 3.35 percent of the Swedish population; see [START_REF] Edin | LINDA -Longitudinal Individual Data for Sweden[END_REF] for details. An attractive feature of the database is that attrition from the sample can be due only to death or migration.

The definition of an individual's earnings used in the analysis is total earnings from all jobs during a year. Information about earnings comes from tax reports, so the earnings variable is free of the measurement errors that are common in survey data such as recall errors and rounding errors.

The target group in the sample selection is males born in Sweden aged 26 to 56. As in previous studies, the focus upon males is due to their relatively steady labour market participation. Comparatively irregular female labour market participation, e.g. due to parental leave, would complicate the interpretation of results regarding transitory and persistent earnings. 4 The chosen age range is to ensure that included individuals are old enough to have completed their education and too young to be considered for early retirement. [START_REF] Moffitt | Trends in the Transitory Variance of Earnings in the United States[END_REF]. The variance of log earnings for the pooled revolving balanced panel is depicted in Figure 1. To estimate the parameters of the model in equations ( 5)-( 8), I take each cohort separately and estimate the variances and auto-covariances of log annual earnings. Each autocovariance matrix for the 11 cohorts observed for the whole 1991-99 period contains 45=(9x10)/2 distinct elements; the matrices for the other cohorts have fewer elements.

Computing auto-covariance matrices for each cohort results in a total of 605 distinct variance and auto-covariance elements -these are the data to which the implied variances and autocovariances of the model in equations ( 5)-( 8) are fitted.

Results

Table 2 presents the parameter estimates and associated standard errors of the model in equations ( 5)-( 8). Starting with the factor loadings for the persistent component, the value for 1991 is normalized to unity in order to obtain identification. The estimated factor loading for 1992 is significantly larger than unity and the estimates for the following years are all significantly larger than that for 1992. 5 The estimates thus indicate a rise in persistent earnings inequality in the beginning of the 1990s.

Moving next to the estimated year-specific factor loadings on the transitory innovation, the value for 1992 is normalized to unity because the innovation variance in 1991 must be left unrestricted to identify the initial variances of the cohorts, i.e. the transitory variance in a cohort's first sample year is estimated solely by their initial variance. Of the estimates, only those for 1995 and 1996 are significantly different (smaller) than unity. Hence, there is no rise in the dispersion of transitory shocks. The other parameter estimates in Table 2 reveal some interesting information about individuals' earnings dynamics. For the persistent component, the variances of the innovation in the random walk are significantly larger than zero. As the variance of a variable that 5 Wald tests are used throughout the analysis. , indicating that persistent inequality increases faster at younger ages. The presence of larger persistent shocks at younger ages is consistent with matching models in which information about a worker's ability is revealed over time, as for instance in [START_REF] Jovanovic | Job Matching and the Theory of Turnover[END_REF].

For the transitory component, the ˆ0.555 = implies that more than 80 percent of a transitory shock has disappeared after 3 years. The estimated parameters in the variance of transitory shocks imply the U-shaped age profile displayed in Figure 2. As can be seen, the initial decline in the variance is quite sharp as it falls with over 60 percent to the mid 30's.

Overall, the results of for how transitory earnings fluctuations vary with age are similar to those obtained by [START_REF] Baker | Earnings Dynamics and Inequality among Canadian Men, 1976-1992: Evidence from Longitudinal Tax Records[END_REF] based on Canadian data. factor loadings on the two components change, but also the cohort specific initial variances that are used to generate the transitory variances up to these ages vary.6

The persistent variances in Figure 3

Concluding remarks

This paper decomposes the rise in the cross-sectional variance of male annual earnings in Sweden between 1991 and 1999 into its persistent and transitory components. The results

show that the persistent component accounts for basically all of the increase in earnings dispersion. This indicates that future research trying to explain the reversal in Swedish inequality should focus on factors that can explain systematic and persistent changes in earnings differentials, such as increases in the price of skills.

A natural question, and where the answer may provide more clues to the Swedish evolution, is how the changes in Sweden during the 1990s compare to changes in other industrialized countries. This is however to a large extent a question for future research as knowledge about the international evolution during the 1990s is still sparse, but the work of [START_REF] Ramos | The Covariance Structure of Earnings in Great Britain, 1991-1999[END_REF] permits comparison with the U.K. between 1991 and 1999. His results indicate increased persistent earnings inequality in the U.K., whilst transitory inequality has been constant. Thus, there appears to have been a similar evolution in Sweden and the U.K..

Results for two countries are of course not enough to be able to say that increased persistent earnings inequality during the 1990s is an international trend. Studies that examine persistent and transitory inequality for other countries during this period are therefore warranted.

Figure

  Figure 1: The variance of log earnings in the sample

  and auto-correlation robust standard errors are in parentheses.

  walk is the sum of the variances of the innovation, this implies that persistent inequality increases over the whole studied age-range (with the time-varying factor loadings held constant). The estimate of

Figure

  Figure 2: Age profile of the variance of the transitory innovation

  display an upward trend during the 1990s. Another interesting feature of Figure 3 is the different role played by the transitory variance in the three age groups. Transitory earnings fluctuations dominate earnings dispersion among individuals who are 30 years old, whereas it is much smaller among individuals aged 40 and 50. Figure 3 also shows that the evolution of the transitory variance differs between the age groups. The transitory variance is roughly the same in 1991 and 1999 for 40-and 50-year olds but higher in 1999 for 30-year olds.

  To provide intuition behind this model, I first describe a more basic model of earnings dynamics.

		Let ibt Y denote the log of earnings in year t of the th i individual born in year b . Then
	(1)	ibt Y	= µ	bt	+	y	ibt
	expresses ibt Y as the cohort specific mean bt µ in year t plus an individual specific deviation
	ibt y from that mean. A stripped down model for ibt y is
	(2)	ibt y	=	t ib pu	+		t ibt	.
	In equation (2), the variable ib u and its year-specific factor loading, t p , capture persistent, or
	permanent, earnings. The variable ibt and its factor loading, t , capture stochastic transitory
	deviations from persistent earnings. The transitory component is serially uncorrelated with
	mean zero, and ib u and ibt are uncorrelated with variances 2 u and 2 respectively. With
	these assumptions, the variance of log earnings is
	(3)	( ) ibt Var y	=		2 2 t u p	+	2 2 t	,
	and the auto-covariance between year t and t-s is
	(4)	Cov	(	y	ibt	,	y	ib	,	t	s	)	=	p	t	p	t	s	2 u	.
		Equation (3) shows that an increase in either factor loading generates increased cross-
	sectional earnings dispersion. The character of the change depends crucially, however, on
	which of the factor loadings that changes. A persistent rise in t p increases long-run inequality
	as the relative labour market advantage of workers with chronically high earnings is
	enhanced. An increase in t without any change in t p generates increased cross-sectional
	earnings dispersion by raising year-to-year earnings instability but with no change in long-run
	inequality.

Table 1 : Cohorts included in the revolving balanced panel

 1 1999. I then select all males who have positive earnings in each year that the age requirement is met and who did not received any form of pension. The end result is a balanced earnings panel for each cohort, with the panel length varying across cohorts. Table1describes the included cohorts. It is worth pointing out that the sample sizes for each cohort are similar to the total sample sizes used in the corresponding U.S. studies by[START_REF] Haider | Earnings Instability and Earnings Inequality of Males in the United States: 1967-1991[END_REF] and Moffitt

	Birth year	Sample size	Years observed	Age in initial year
	1939/40	1925	1991-95	52

Table 2 : Minimum distance estimates of the earnings dynamics model in equations (5)-(8)

 2

					Persistent component			Transitory component (cont.)
	Factor loadings		AR-parameter
	91 p		1.000				0.555 (0.011)
	92 p		1.049 (0.013)	Parameters in the variance of transitory shocks
	93 p		1.128 (0.016)	0			0.201 (0.017)
	94 p		1.169 (0.019)	1			-0.034 (0.006)
	95 p		1.122 (0.019)	2			0.003 (0.0008)
	96 p		1.189 (0.021)	3			-1.35E-4 (3.63E-5)
	p	97		1.193 (0.021)	4			2.11E-6 (5.86E-7)
	98 p		1.153 (0.021)	Initial cohort variances
	99 p		1.151 (0.020)	2 1939	/	40	0.069 (0.017)
	Variances of the random walk innovation	2 1941	/	42	0.071 (0.016)
		2 u			0.0469 (0.0035)	2 1943	/	44	0.065 (0.014)
		2 , r	28	37	0.0053 (0.0005)	2 1945	/	46	0.038 (0.011)
		2 , r	38	56	0.00089 (0.00032)	2 1947	/	48	0.065 (0.014)
						2 1949	/	50	0.031 (0.014)
					Transitory component	2 1951	/	52	0.091 (0.016)
	Factor loadings		2 1953	/	54	0.071 (0.017)
	92			1.000	2 1955	/	56	0.077 (0.015)
	93			1.048 (0.038)	2 1957	/	58	0.071 (0.015)
	94			0.937 (0.042)	2 1959	/	60	0.101 (0.017)
	95			0.854 (0.039)	2 1961	/	62	0.142 (0.019)
	96			0.803 (0.044)	2 1963	/	64	0.180 (0.017)
	97			0.945 (0.041)	2 1965	/	66	0.269 (0.018)
	98			0.943 (0.040)	2 1967	/	68	0.325 (0.021)

Decompositions of the variance of log earnings Males 30 years old

		0.05 0.1 0.15 0.2 0.25 Figure 3: 0 0.3
			1991		1992	1993	1994	1995	1996	1997	1998	1999
			F o Permanent component F o	Transitory component		Sum
					r r	Males 40 years old
		0.3
	0.25	0.2 0.25 0.15				P e P e e e
	0.15 0.2	0.1 0 0.05	1991		1992	1993	r r R e 1994 1995 1996 R e	1997	1998	1999
	1				Permanent Component	v i Transitory Component v i		Sum
		0.3					Males 50 years old	e w e w
		0.25
	27	29 0.2	31	33	35	37	39	41 Age	43	45	47	49	51	53	55
		0.15
	What do the estimates in Table 2 imply about changes in the persistent and transitory 0.1
	components of earnings inequality for different age groups? To investigate this I use the full 0.05
	model to predict the two components for each year, holding age constant. Figure 3 displays 0
	these predictions for males 30, 40, and 50 years old. In moving from year to year, not only do 1991 1992 1993 1994 1995 1996 1997 1998 1999
					Permanent Component	Transitory Component		Sum

A random walk specification is also used, among others, in[START_REF] Dickens | The Evolution of Individual Male Earnings in Great Britain: 1975-95[END_REF] and[START_REF] Moffitt | Trends in the Transitory Variance of Earnings in the United States[END_REF].

The age intervals are chosen based on graphs of how the longer-lag auto-covariances, which mainly reflect persistent inequality, vary over the life cycle; these graphs are available on request.

In fact, the initial variances change every two years, corresponding to the cohort estimates in Table2. For example, the initial variance for cohort 1951/52 is a direct estimate of the variance of the transitory component for individuals aged 40 in 1991. For 1993 I use the initial variance for cohort 1953/54, whose members are 40 in this year.

Acknowledgements

I am grateful to Per-Anders Edin, Meredith Beechey, Patrik Hesselius, Bertil Holmlund, Stephen Jenkins, Mårten Palme, and an anonymous referee. Financial support from the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.

Appendix: The estimation procedure

The parameters of the model in equations ( 5)-( 8) are estimated by applying the minimum distance estimator of [START_REF] Chamberlain | Panel Data[END_REF]. Specifically, let b C contain the distinct elements of the population auto-covariance matrix of ibt y for cohort b and let C be an aggregate vector stacked with the b C vectors. Let the vector 3 contain all the parameters of the model and

express the model's moment restrictions. The model in equations ( 5)-( 8) then implies that the general variance element in C is

where W is a positive definite weighting matrix.

The asymptotically optimal choice of W is the inverse of a matrix that consistently estimates the covariance matrix of C . However, Altonji and Segall (1996) and [START_REF] Clark | Small-Sample Properties of Estimators of Nonlinear Models of Covariance Structure[END_REF] provide Monte Carlo evidence of potentially serious finite sample bias in the estimate of 3 using this approach. I therefore follow the practice of the most recent literature and use the identity matrix as the weighting matrix. This "equally weighted minimum distance estimation" amounts to using non-linear least squares to fit

As outlined in [START_REF] Chamberlain | Panel Data[END_REF], robust standard errors for 3 ˆare obtained from the formula (A4)

where G is the gradient matrix ( ) f 3 3 evaluated at 3 and V is a block diagonal matrix containing the estimated covariance matrices of each b C ˆvectors.