Stuart A Gabriel

Daniel Levy

Thomas Rothenberg

Christopher Sims

Mark Rosenzweig

Norman Simler

Emanual Barnea

Baruch Lung-Fei Lee

Expectations, Information, and Migration: The Case of the West Bank and Gaza*

This study evaluates the determinants of Palestinian migration from the West Bank and Gaza. Data are employed for the post-1967 period of Israeli rule to specify and test competing models as well as the structure of expectations in the migration decision. Results of the analysis support a simple static expectation formulation, as is consistent with much of the shortterm, low mobility cost migration between the West Bank and Jordan. Findings further point to the importance of various Israeli-Palestinian economic and political economic interactions in the determination of this controversial movement of population, including those associated with employment opportunity for Palestinian labor in Israel, elements of Israeli West Bank settlement policy and changes in local standard of living. Various policy implications of the research are indicated.

Introduction

Population change in the West Bank and Gaza has roused considerable political controversy. 1 Israeli policy has sought to redress the 'demographic imbalance' in these areas, through the establishment of numerous urban settlements and the encouragement of sizable Jewish in-migration. In contrast, Arab and Palestinian groups promote the 'steadfastness' of the indigenous population, this in the wake of large scale emigration. The USA has recently put pressure on Israel over the use of economic aid for employment development in the territories, so as to ease pressure on Palestinians to emigrate. 2 All parties view the magnitude and determinants of those migratory flows with particular concern, given their implications for control of territory and conflict resolution.

This study seeks to evaluate the determinants of Palestinian migration from the West Bank and Gaza. The research employs data for the post-1967 period of Israeli rule which enable specification and testing of certain economic and political economic theories of migration. In particular, the analysis evaluates competing model formulations as well as the structure of expectations in the migration decision.

In that regard, discussion is initiated in Section II with a brief overview of Palestinian emigration from the territories.

In Section III, an econometric model is specified which incorporates various expectations formulations of migration 1 The West Bank includes the area between the Jordan River and the 1949 Armistice line between the Kingdom of Jordan and the State of Israel. The Gaza Strip was created as a separate administrative unit as a result of the Armistice Agreement between Egypt and Israel in 1949. It includes the area between the Mediterranean Sea, those armistice lines to the north and east, and the international border between Egypt and Israel to the south. 2 US Secretary of State, George Schultz, is reported to have pressed Israel for a change in the policy that limits the use of US economic aid to Arabs of the West Bank and Gaza to public works. See Newsweek, 18 June 1984, p. Finally, on the basis of these analyses, Section V provides various policy recommendations and conclusions.

Migration from the West Bank and Gaza

Arab emigration from the West Bank dates to hostilities associated with the 1947 partition of Palestine and the subsequent annexation of this area by Transjordan. During the twenty-year period of Jordanian rule, until June 1967, approximately 400 000 West Bank inhabitants crossed the Jordan River to the East Bank (Nisan, 1982, p. 195). The move involved short distances within an area of cultural, religious, linguistic and administrative uniformity. It was not a forced migration but reflected rather the East Bank orientation of Jordanian development policy, in which investment, political and educational activities were centered in the Amman-Zurqa zone.

Prior to Jordanian annexation of the West Bank, this area was far more developed than the East Bank, due to economic spillovers from the proximate British and Jewish sectors. These spillovers ceased with the closing of borders during the 1948 war. While the 1952 West Bank population of 742 000 well exceeded the 587 000 East Bank inhabitants, subsequent Jordanian industrialization and agricultural development of the East Bank succeeded in reversing the relative weight of these areas. By 1961, the West Bank population was 801000, while that of the East Bank was estimated at 879 000. 3 On the eve of the 1967 war, the latter's population exceeded one million, while the West Bank population remained static at about 800 000 (Nisan, 1982, p. 195).

During and immediately after the 1967 war, about 200 000 West Bank inhabitants crossed the Jordan River to the East Bank (Ben Shahar et al., 1971, p. 29). Not all remained there; some pursued economic opportunities in the Persian Gulf, North America and elsewhere. The sizable emigration of Palestinians from the West Bank was not unique to Jordanian rule, however, and has continued during the Israeli administration of the territories.

Evaluation of economic conditions in the Gaza Strip over the same period indicates policy neglect and structural underdevelopment. In that regard, per capita GNP amounted to 27 dinars in 1966, approximately half that of the West Bank, and among the lowest in the world (Ben Shahar et al., 1971, p. 29).

While Egyptian development efforts similarly favored other regions, substantial educational advances were made due primarily to the efforts of UNRWA and other philanthropic organizations. Poverty and limited local employment opportunities precipitated similar emigration from this region.

Post-1967 Palestinian migration from the West Bank and Gaza is depicted in Fig. 1. Subsequent to the massive emigration of refugees in 1967, yearly average emigration from those areas up to 1973 remained at the relatively low rates of 4.4 and 6.8 per thousand, respectively. In each region, annual emigration was below the 10 000 person level. Subsequent to 1974, however, migration rates from the territories registered a substantial increase and in the West Bank have averaged about 19 per thousand or 14 000 per year through 1982. In Gaza a similar trend is illustrated, yet its magnitude is approximately half that of the West Bank.

While no direct information exists regarding the demographic characteristics of the migrants, evaluation of the age/sex composition of the remaining population indicates that the proportion of the 25-44 age group in the population aged over 15 is lower than the proportion of this group in Israel, among both Jews and non-Jews. Further, there are substantially fewer men than women in this age group. According to information derived from labor force surveys, 90% of those abroad are men, 60% of whom left the country in search of employment, primarily those in the 18-24 group (Meron, 1983, p. 36).

Figure 1 These trends indicate a low population growth in the West Bank, in which a high rate of natural increase is for the most part offset by the sizable and negative migration balance. In 1980, for instance, 83% of the natural increase of about 20 000 was countered by emigration (Benvenisti, 1982, p. 1).

Emigration, coupled with high mortality rates, yields an average annual growth rate of the West Bank population between 1968 and 1980 of 1.4%. The annual growth rates of the Jewish and non-Jewish populations in Israel during the same period were 2.53 and 3.39%, respectively (Benvenisti, 1982, p. 1).

Various Palestinian-Israeli political economic interactions impinge on the migratory phenomenon. The territories export substantial labor services to Israel, accounting for 27 and 33% of the West Bank and Gaza labor forces, on average, over the [START_REF] Wilkinson | European migration to the United States, an econometric analysis of aggregate labor supply and demand[END_REF]-81 period (Statistical Abstract of Israel, 1982, ch. 27, table 22). In 1974, earnings from such employment comprised over one-quarter of West Bank GNP, their multiplier effect accounting for one-half the growth in incremental GNP over the 1968-73 period (Sandler and Frisch, 1981, p. 135). Concomitant growth in real, per capita consumption was substantial, averaging 6.7% in the West Bank and 6.4% in Gaza between 1968 and 1981. Private consumption accounted for 72% of domestic uses in the economies of the territories, significantly higher than the 54 to 59% recorded for Israel, Jordan, Egypt and Syria (Meron, 1983, p. 15).

During the mid-1970s a rise in residential construction occurred in the territories, precipitated in part by savings accumulated by residents over earlier years. The scale of this boom is suggested by a comparison of total area of housing starts to population increment, their ratio being 74 square meters per additional person over the 1974-80 period, compared to 57 square meters in Israel. As is indicated in the empirical analysis undertaken below, interactions between Israel and the territories in the economic sphere, coupled with changes in Palestinian economic well-being, appear important determinants of that population's propensity to migrate.

Model Specification

Reference to the economics literature suggests several approaches purporting to explain migration. One involves application of the neoclassical theory of investment, as has appeared largely in the works of the Chicago School [START_REF] Schultz | Investment in human capital[END_REF][START_REF] Sjaastad | The costs and returns of human migration[END_REF], and suggests that a difference in the discounted economic return between two places may precipitate migration, provided the total costs of migration are sufficiently small. Other approaches include that of the Harvard School and in particular the work of [START_REF] Kuznets | Population Redistribution and Economic Growth -United States, 1870-1950[END_REF][START_REF] Kuznets | Population Redistribution and Economic Growth -United States, 1870-1950[END_REF][START_REF] Kuznets | Population Redistribution and Economic Growth -United States, 1870-1950[END_REF], which emphasizes selectivity of migrant stock; and those relevant 'push' and 'pull' factors noted in the early works of Ravenstein (1985[START_REF] Ravenstein | The laws of migration[END_REF] and [START_REF] Redford | Labor Migration in England[END_REF]. The Kuznets theory emphasizes the importance of human capital characteristics in describing migratory phenomena, suggesting migrants come from select groups endowed with a higher propensity to migrate. The Following [START_REF] Walsh | Expectations, information, and human migration: specifying an econometric model of Irish migration to Britain[END_REF], [START_REF] Greenwood | Research on internal migration in the United States: a survey[END_REF], [START_REF] Fields | Place-to-place migration in Colombia[END_REF] and others, structural equations of population migration are written in terms of origin and destination region economic opportunity.

Here

1 2 e e ijt it jt M U U α β β = + + (1) 1 2 e e jit it jt M U U α β β ′ ′ ′ =+ + (2) ( ) ( ) ( ) 1 1 2 2 e e ijt it jt NM U U α α β β β β ′ ′ ′ = - + - + - (3)
where ijt M is gross migration from area i to area j in period t; ijt NM is net emigration from i to j; and e it U is a measure of expected net return on employment that would accrue to a typical potential migrant in location i.

It is assumed that improvements in employment opportunity at the point of origin serve to diminish emigration, whereas similar improvements in the destination region have the opposite effect.

As such, model hypotheses include 1 2 , 0 and2 1 , 0

β β′ <
β β′ > . Empirical
application of the reduced form Equation 3 tests the hypotheses that ( )

1 1 0 β β′ - < and ( ) 2 2 0 β β′ - > .
Various transformations of the above equation have been evaluated in the literature. One involves the so called 'symmetric' model, which holds that the 'push' of unfavorable employment conditions in the area of origin is equivalent in impact to the 'pull' of favorable employment conditions at a possible destination. This hypothesis may be tested by rewriting Equation 3 in differences form, such that

( ) ( )(
)

0 0 0 0 e ijt i j t NM U U α α β β ′ ′ = - + - - (4)
In this case, the constraint is simply imposed on Equation 3that ( ) ( )

1 1 2 2 β β β β ′ ′ - = - - . It is then hypothesized that ( ) 0 0 0 β β′ - < .
Note that the above formulations assume that the same absolute change in i U or )

e ijt i j t NM U U λ λ ρ ρ ′ ′ = - + - (5)
In the analysis undertaken below, various asymmetric (levels), symmetric (differentials) and ratio formulations of the U variables are tested and evaluated.

A further objective of this study is to analyze the relevance of various expectations formulations of the decision to migrate.

In that the potential migrant's decision often involves a relatively long time-frame, time-series data may be applied to evaluate the structure of expectations. Yet few studies explore the formulation of expectations in this context (see [START_REF] Walsh | Expectations, information, and human migration: specifying an econometric model of Irish migration to Britain[END_REF][START_REF] Wilkinson | European migration to the United States, an econometric analysis of aggregate labor supply and demand[END_REF] due, perhaps, to the predominance of inter-regional and inter-metropolitan data sets. This study tests various typical expectations formulations regarding U e, including those associated with static, extrapolative and adaptive models.

As regards the former, a simple static expectations model assumes that the situation prevailing in the current period will continue to exist in the next. To test this hypothesis, the model is written as

1 e t t U U - = (6)
where

1 t U -is the actual value of U in period t-1.
A slightly looser version of this hypothesis involves extrapolative expectations, in which the expected value of the decision variable reflects the immediate past value plus or minus some correction based upon the change in this variable over the past few periods. In the extrapolative expectations model tested below, (  )

1 1 2 e t t t t U U U U γ - - - = + - (7)
where γ reflects the coefficient of adjustment in the potential migrant's expectations based upon the change in past values of U. 0 γ > implies that the direction of change in the decision variable is expected to continue, whereas 0 γ < indicates past trends are expected to reverse themselves.

Finally, the adaptive expectations model may be formulated as ( )

1 1 1 1 e e e t t t t U U U U θ θ - - - = + - < (8)
This specification of the potential migrant's expectations assumes that in each period the previous period's level of e U is corrected by some fraction, θ , of the discrepancy between that period's forecasted and actual level of the decision variable. Algebraic transformation of this difference equation yields the general expression ( ) ( )

1 0 1 1 s t e t t s s U U c θ θ θ ∞ -- = = - + - ∑ ( 9
)
where c is a constant. Upon substituting 1 λ θ = -, and assuming 0 c = , which is a necessary condition for the path of The expectations hypotheses embodied in Equations 6, 7 and 8 may then be substituted into the net migration equation for

e t U
and the final form of the estimating equation derived. For example, in the 'symmetric' form of the model (Equation 4), the estimating equations can be written ( )

0 1 2 it i j t t NM U U α α α = + - + E (11) ( )( ) ( ) 0 1 1 2 1 2 1 i t i j i j t t t NM U U U U δ δ λ δ γ δ - - = + + - + - + E (12) ( ) ( )( ) 0 1 1 2 1 2 1 i t i j i j t t t NM U U U U µ µ θ µ θ θ µ - - =+ - + - - + E (13)
for the static, extrapolative and adaptive expectations structures, respectively. Here E represents a vector of additional economic and political economic variables which, while not explicitly characterized in the expectations framework, are hypothesized to impinge on the potential migrant's decision-making calculus. Estimating equations can similarly be written for the symmetric (Equation 3) and ratio (Equation 5) forms of the model. Given estimation of the extrapolative and adaptive expectation models, application of asymptotic distribution theory enables subsequent calculations regarding both the magnitude and significance of δ , γ , µ , and θ . It is to empirical testing of the model that we now turn.

Model Evaluation

Variables and hypotheses

This study utilizes origin and destination region unemployment rates as empirical measures of U. The choice of variables is consistent with extensive analyses of unemployment rates in the migration literature (see [START_REF] Gallaway | The economics of labor mobility: an empirical analysis[END_REF][START_REF] Wadycki | A note on opportunity costs and migration analysis[END_REF][START_REF] Walsh | Expectations, information, and human migration: specifying an econometric model of Irish migration to Britain[END_REF]. It is suggested that the unemployment rate in the destination region serves as a good proxy for the probability that the potential migrant will find employment there and thus realize a positive return on migration. Similarly, unemployment rate in the origin region proxies employment opportunity in that area, such that increases in that rate should be reflected in increased emigration. A priori, the relative strength of these various effects remains unclear.

Finally, there exists significant economic and ecological differences between the West Bank and Gaza Strip. The West Bank contains relatively developed agricultural and commercial sectors and a substantially more affluent and educated populace.

In addition, West Bank inhabitants enjoy increased migratory opportunities via the Jordan River bridges, given the familial, legal and economic ties which bind the East and West Banks.

Separate analyses of the West Bank and Gaza Strip samples are expected to yield significant differences in underlying migratory phenomena. The results of these analyses are reported.

Estimation results

The results of applying OLS regression techniques to static expectations models (Equation 6) are presented in Tables I and2 for the West Bank and Gaza Strip, respectively. Each table displays findings associated with the asymmetric (Equation 3), symmetric (Equation 4), and ratio (Equation 5) specifications.

The regression coefficients are shown, with t-ratios in parentheses.

The static expectations model performs well for the West Bank Results of the extrapolative and adaptive models are less satisfactory than those obtained with the static expectations formulations and hence are not displayed. 5 Note, however, that 4 While it is common to limit migration models to a single-equation approach, certain assumptions of the classical least squares regression model may be violated, as the regressors may not be exogenous to the economic process which determined migration.

In the case at hand, it appears reasonable to inquire as to whether migration from the territories impacts on employment rates there. If so, the model should be estimated as a two-equation simultaneous system. It should be noted, however, that this issue pertains only to those equations which utilized territories' unemployment rates, rather than those in Israel, to proxy origin region employment conditions. Simultaneous equations bias was considered more unlikely in that emigrants include non-labor force participants and equal only 6% of total labor force. In investigating this issue, a two-equation system of the type described above was estimated using two-stage least squares techniques. Results of this analysis show the estimated coefficient of net emigration rate in the employment equation to be approximately zero in value and statistically insignificant. On this basis, only results of the single-equation migration model are presented. 5 These results are available from the authors upon request.

in the case of the West Bank, the extrapolative expectations coefficient of adjustment, y, is both negative and significant.

This result implies that changes in employment opportunity are expected to reverse themselves, as is consistent with actual variation in the expectations indices. As regards the adaptive expectations models, the estimated coefficient of adjustment 0 for the West Bank lacks a reasonable level of significance and varies in both magnitude and sign between the symmetric and ratio formulations.

Conclusions

This Britain [START_REF] Walsh | Expectations, information, and human migration: specifying an econometric model of Irish migration to Britain[END_REF] and emigration from the United Kingdom to the USA [START_REF] Gallaway | Emigration from the United Kingdom to the United States: 1860-1913[END_REF]. Finally, despite the theoretical rationale for specification of expectations indices in ratio form, results of the static expectations model favor the use of either the asymmetric (levels) or symmetric (differences) form of the unemployment variables.

In conclusion, this study has certain policy implications.

  21. economic return. Section IV then provides evaluation of static, extrapolative and adaptive expectations variants of the model, indicating their differential relevance to the West Bank and Gaza Strip samples. Results of the analysis in general support a simple static expectations formulation, as is consistent with much of the short-term, low mobility cost migration between the West Bank and Jordan. Findings further point to the importance of various Israeli-Palestinian political economic interactions in the determination of this controversial movement of population, including those associated with employment opportunity for Palestinian labor in Israel, elements of Israeli West Bank settlement policy and changes in local standard of living.

  Ravenstein approach stresses other factors than economic, including political and social change, agrarian reform, attraction of the destination region and the like, in an explanation of population flows. This study tests hypotheses consistent with those economic and political economic theories of migration. Evaluation of the Kuznets hypothesis is constrained due to lack of adequate human capital descriptors. Further, the limited available data on Palestinian migration characterizes that flow in net terms. The net emigration rate then comprises the dependent variable of the model and behavioral motivation for its application may be supplied by turning first to structural equations of gross population flows.

  obvious alternative to that assumption is to specify the structural equations in terms of migrant expectations concerning the ratio of i U to j U . The reduced form equation in this case becomes

  s well known, the adaptive expectations formulation may be expressed as a weighted average of past values of the decision variable over the relevant time horizon.

  Evidence cited above concerning widespread participation of the territories' labor force in the Israeli economy suggests the relevance of unemployment rate there (UEIS) as an indicator of origin region employment opportunity. Unemployment rates in the West Bank (UEWB) and Gaza (UEG) were also tested as measures of relevant origin region effects. Evaluation of similar destination region effects is constrained, however, due to lack of appropriate data. As noted above, there exists no comprehensive information regarding the destinations of Palestinian emigrants from the West Bank and Gaza. During the period in question, West Bank residents did not require work permits to enter Jordan and their migration is not recorded in official statistics there. Finally, none of the Arab states distinguish in published statistics between Palestinians and Jordanians, making it nearly impossible to identify Palestinian manpower in the Persian Gulf. These constraints in available data coupled with the importance of the USA as a secondary destination region prompted the utilization of the US unemployment rate (UEUS) to proxy foreign employment opportunity. Further transformations of the expectational variable include DUE, defined as the difference between the US and Israel employment rates and UER, which comprises the ratio of the former to the latter. As described above, it is expected that increases in DUE and UER be reflected in diminished Palestinian emigration, ceteris paribus. In addition to evaluation of the employment variable, this study tests the effects of various other economic and political economic factors in an explanation of Palestinian emigration from the territories. The latter include variables proxying changes in origin region consumption patterns (CONCHG), housing opportunities (BLDSTARTS), and external transfer receipt (RTRAN), as well as an indicator of Israeli settlement activity (SETL) there. Variable definitions and sources are found in the Appendix; variable hypotheses are detailed below. The consumption change index represents, in part, fluctuations in origin region standard of living. As indicated above, substantial improvements in population consumption patterns occurred in the territories over the period of Israeli rule. These private consumption gains reflect increased opportunity costs of emigration, and are expected to be inversely related to the dependent variable, ceteris paribus. As described above, the Territories experienced a substantial boom in residential construction during the mid-1970s. Finance of housing construction was sometimes undertaken by external Arab sources as well, a policy implemented to diminish local population propensity to migrate. The effect of improved local housing opportunities on population migration is proxied by the construction rate variable, and is hypothesized to be negative. Private transfers to the Territories primarily reflect the remittances of major external philanthropic organizations. This funding is typically directed to social, health and educational institutions and thus suggests improved human service facilities in the origin region. As such, receipt of those funds is expected to diminish the rate of emigration. Israeli settlement of the Territories may have a variety of political and economic effects on Palestinian propensity to migrate. On the one hand, increased Israeli presence in the territories, political conflict and uncertainty regarding the eventual status of this region may result in accelerated Palestinian emigration. These same elements, however, may increase the resolve of nationalist Palestinians to remain. Finally, in the economic sphere, intensified Israeli settlement of the territories provides employment and commercial spillovers for local residents, thereby diminishing migration propensities.

  sample. In this case, all regression coefficients are consistent with hypotheses and are statistically significant at the 90% level or above. Comparison of Equations 1, 2 and 3 indicates that this model is of similarly good fit in either the asymmetric or symmetric forms of the expectations variables, but performs somewhat less well in ratio form. In the case of Equation I, for instance, the recovery of Western economies from recession early in the decade and in particular each percentage point fall in the US rate of unemployment should increase Palestinian emigration rate by 5.4 or 3800 persons. The opposite holds true in the context of the Israeli economy in that emigration rate increases by 3.6 or 2500 persons with each percentage point rise in the domestic unemployment rate. These findings further suggest that increases in construction rate and real, per capita consumption expenditures, reflecting improved origin region consumption and housing conditions, serve to diminish the rate of Palestinian emigration. A similar outcome is detected in the case of increased private remittances from abroad. Finally, results suggest that intensified Israeli

  study had undertaken to analyze the structure and determinants of Palestinian migration from the West Bank and Gaza over the post-1967 period of Israeli rule. The migration totaled about 96 000 during the 1970s, equivalent to almost half the natural increase in population. The factors underlying this exodus are viewed with considerable political import, given the competition, as well as controversy, regarding development and control of this region. Results of the analysis indicate the relevance of particular Palestinian-Israeli interactions, including those associated with traditional economic variables in an explanation of Palestinian migration. In that regard, the importance of employment opportunity and labor market conditions in the origin and destination regions is illustrated. Improved local housing and consumption opportunities result in diminished West Bank migration, as do the remittances provided by international philanthropic organizations. Also, whether due to local commercial and employment spillovers or nationalist sentiment, intensified Israeli settlement of the West Bank similarly serves to diminish Palestinian emigration from this region. These findings lend tentative support to certain conclusions regarding model specification and the structure of expectations. A primary concern of this research was whether variation in migration rates might be explained on the basis of adaptive or extrapolative expectations concerning future employment opportunity, as distinct from a simple index of current conditions. The former expectations models perform appreciably less well than a simple static expectations formulation, however, indicating the relevance of current employment conditions to West Bank migrants. The short-run decision horizon of Palestinian migrants concurs with findings regarding diverse migratory groups including analyses of Irish migration to

  Transfers from external Arab and international sources have worked to improve local conditions and diminish Palestinian migratory propensities, as is consistent with the political aims of that funding. From the perspective of Israelis concerned With the West Bank 'demographic imbalance', however, there exists conflict between development of a Palestinian labor market in Israel and emigration of that group. Finally, from the Palestinian point of view, the failure to channel resources into manufacturing investment and infrastructure rather than consumption is of central concern. In the absence of an indigenous productive base, Palestinian labor supply remains highly elastic, reflecting cyclical fluctuations in the Israeli economy as well as similar developments in the various destination regions.

Table 1 . Net emigration rate, West Bank, 1968-81: estimated (OLS) regression coefficients (t-ratios in parentheses), static expectations models

 1

	Explanatory		Equation
	Variable	1	2	3	4
	CONCHG	-0.62	-0.66	-0.58	-0.59
			(2.42)	(2.59)	(1.68)	(1.88)
	BLDSTART	-0.011	-0.013	-0.02
						-
			(2.24)	(2.76)	(2.65)
	RTRAN	-0.97	-1.08	-1.01	-1.07
			(1.88)	(2.12)	(1.42)	(1.70)
	SETL	-0.52	-0.65	-0.75	-0.50
			(1.70)	(2.26)	(1.89)	(1.56)
	DUE		-4.97
			-		-	-
				(5.01)
	UEUS	-5.41			-5.20
				-	-
			(5.04)			(4.45)
	UEIS	3.59
				-	-	-
			(2.16)
	UEWB				3.64
			-	-	-
						(1.85)
	UER			-13.03
			-	-		-
					(3.24)
	Constant	30.37	25.37	36.60	30.85
			(3.47)	(3.46)	(2.73)	(2.97)
	R	2	0.831	0.831	0.690	0.760
	D-W	2.79	2.56	2.10	2.27

Table 2 . Net emigration rate, Gaza Strip, 1968-81: estimated (OLS) regression coefficient (t-ratios in parentheses), static expectations models

 2

	Explanatory		Equation
	Variable	5	6	7	8
	CONCHG	-0.42	-0.38	-0.37	-0.29
			(2.14)	(1.87)	(1.80)	(1.70)
	BLDSTART	-0.027	-0.028	-0.03	-0.04
			(2.05)	(2.00)	(2.10)	(3.10)
	RTRAN	0.45	-0.67	-0.48	-0.50
			(0.41)	(0.87)	(0.54)	(0.79)
	SETL	0.51	0.42	0.41	0.35
			(1.54)	(1.22)	(1.20)	(1.25)
	DUE		-0.31		-1.90
			-		-
				(0.29)		(1.65)
	UEUS	-0.69
				-	-	-
			(0.65)
	UEIS	-3.12
				-	-	-
			(1.14)
	UEG				-1.60
			-	-	-
						(2.10)
	UER			0.29
			-	-		-
					(0.08)
	Constant	9.55	7.04	4.20	14.09
			(1.05)	(0.75)	(0.31)	(1.70)
	R	2	0.261	0.174	0.160	0.450
	D-W	2.01	1.60	1.72	2.30

A relative preponderance of woman in the West Bank population emerged during this period, the ratio of men to women in the 15-19 and 30-44 age groups amounting to 0.84 and 0.75, respectively.

Appendix

Definitions of variables in the migration models

NMIG

Net emigration rate in migrants per 1000


Daniel Levy

Aggregate Output, Capital, and Labor in the Post-War U.S. Economy

Keywords: Aggregate Production Function, Cobb-Douglas Production Function, Returns to Scale, Long-Term, Increasing Returns to Scale, LR Capital Elasticity of Output, LR Labor Elasticity of Output, Estimates

New estimates of an aggregate long-term production function for the post-war U.S. economy are reported. The results indicate that this long-term aggregate production function exhibits a slight but statistically significant increasing returns to scale. Since virtually all econometric growth studies assume constant returns to scale, my finding raises serious doubts about the validity of this common practice. I also find that since the war real output has become more sensitive to changes in capital and less sensitive to changes in labor. In particular, I show that the long-run capital and labor elasticities of real output are both in the range of 0.44-0.55. Similar estimates for the capital and labor elasticities of output from earlier studies covering prewar and the inter-war periods are 0.25 and 0.75, respectively.

Introduction

The literature that covers empirical estimation of aggregate production functions in a partial equilibrium framework is not extensive, although there are many studies on the components of total output. There are several reasons for this. First, from the theoretical point of view, the determination of total output cannot be separated from the determination of other endogenous variables and therefore ideally it should be investigated in a general equilibrium framework.

Second, an empirical estimation of an aggregate production function requires simplifying assumptions about the decision making process of the firms about technology, production process and input hiring, and about the similarity of this process across firms and industries.

Therefore, assuming the existence of an aggregate production function imposes strict requirements on the underlying sectoral models of production. In particular, it requires that the value added function and the input functions of the capital and labor for each sector must be replicas of the aggregate functions. 1 But this criticism applies to situations in which the data used in the study covers only a short period. Jorgenson (1988, p. 30) touches on this point when he talks about the limitations of the aggregate production function: 'Over the period 1948-1979 the reallocations are very small relative to the growth of capital and labor inputs and productivity growth. These results show that an aggregate production model may be appropriate for studies of long-term U.S. economic growth. However, an aggregate model can be seriously misleading for relatively short time periods such as the individual business cycles 1948-1953, 1966-1969, and 1973-1979'. He concludes that 'the aggregate production function model introduced by [START_REF] Cobb | A theory of production[END_REF] and developed by Tinbergen (1942) retains its usefulness in modeling long-term growth trends' [Jorgenson (1988, p. 31)].

In this study such a long-term aggregate production function is estimated using the quarterly data of the post-war U.S. economy. With all the drawbacks of this partial equilibrium approach, its use is still worthwhile since the results can be compared with the results of earlier studies that use the same methodology and similar data sets. The next section 1 Another reason is the belief of many economists that, in order to understand the behavior of the output, one should study the behavior of its components (business cycle approach). Also, from the empirical perspective, attempts to fit a Cobb-Douglas form production function estimated with the time series observations of output, labor and capital often do not produce satisfactory results in the sense that the estimated parameters are not of the size or the sign that the economic theory predicts.

describes the data set used in this study. The estimation results are discussed in section 3. In section 4 the findings are summarized and compared to the results of previous studies. The section ends with some concluding remarks.

The data

The quarterly data used in this study consist of real output, real capital stock and employment data for the period 1948-1983 (144 observations). The data for output and capital stock were kindly provided by Robert J. Gordon. While there is nothing unique about the output data, the quarterly stock of capital data was created by using the corresponding annual data published in various issues of Survey of Current Business. This was done in two steps:

(a) The annual series' values were treated as beginning and ending values of the quarterly series;

(b) Under a fixed exponential rate of depreciation, the quarterly series satisfy

( ) 1 1 t t t K I K δ - = + - .
The depreciation rates ( ) δ of each capital stock component were iterated until the fourth quarter's value converged to the end of the year value from the annual series. The resulting estimated annual depreciation rates for the stock of non-residential structures and producers' durable equipment were 6.036% and 14.3%, respectively [see [START_REF] Gordon | Fixed investment in the American business cycle, 1919-1983[END_REF] for more details]. The quarterly employment figures were taken from Business Conditions Digest, Bureau of Economic Analysis (February 1984, p. 101).

Estimation results

Using the data described in section 2, I first estimate the standard Cobb-Douglas (henceforth CD) production function of the form

0 e e t u t t t t Y A K L ω α β = (1)
where t Y is real GNP, t K is the real stock of capital; t L is the number of employees; α and β are capital and labor elasticities of the real output; ω is the exponential rate of technical progress; 0 A is an efficiency measure of the production process; t u is the error term with the usual properties; and t is time. The standard prior assumptions are: and0 0 A > .

0 1 α < < , 0 1 β < < , 0 ω > ,
It should be emphasized that the residuals of all the estimated eqs. ( 2), ( 3) and ( 4) in this study were analyzed using the Box-Jenkins technique and found to follow Auto-Regressive

Moving Average (henceforth ARMA) (2, 0) processes. Consequently, all four equations were estimated using RATS' Filtered Least Squares procedure which is analogous to Cochrane-Orcutt for the ARMA(l, 0) case. 2 The finding that the residuals in our model follow an ARMA(2, 0) process is not surprising in the light of the fact that many studies based on quarterly time series data conclude that a second-order autoregressive filter is sufficient for the residuals to follow a white noise. [See for example Barro and Rush (1980), [START_REF] Hoffman | An econometric investigation of the monetary neutrality and rationality propositions from an international perspective[END_REF] 2 One may argue that GLS estimates of α and β may be biased as the error term in eq. ( 2) might be correlated with log K and log L . Correcting for this potential bias would require a profit maximization approach which would yield a simultaneous equations system that is not easy to estimate. A method of solving such a system involves simplifying assumptions about correlations between managerial and technical efficiencies. Another drawback of that approach is the fact that constant or increasing returns to scale are not compatible with the assumption of both perfect competition and profit maximization and therefore there must be decreasing returns to scale in order for the marginal productivity conditions to have a determinate solution corresponding to maximum profit. Finally, in order to make the results of this study comparable with the results of earlier studies, I decided to follow the single equation methodology. 3 The numbers in parentheses are the t-values.

which implies that the returns to scale parameter, ( ) α β + , slightly exceeds one. Note that the significance of all t-values indicates that multicollinearity is not a severe problem. I also computed the determinant of the sample correlation matrix; it is strictly different from zero.

Next, since ( ) α β + is slightly greater than one, the CRS constraint, 1 α β + = , was imposed. 4 The new equation was estimated twice: once with the technical progress parameter [eq. ( 3)] and once without it [eq. ( 4)]:

( ) ( )

log
Y L K L = - + - (4) 2 0.35, 2.15, 0.0092 R DW SEE = = =
The estimated equations' parameters are summarized in table 1. 5 F -equals 3.90 which is on the border of significance at 5 percent. 5 I also estimated a more general Constant Elasticity of Substitution production function of the form ( )

1 e t t t t Y K L ν ρ ε ρ ρ γ δ δ - - - = + -    
by first transforming it into a log-linear form using Taylor's expansion.

Y K L K L R DW SEE = - + + - = = = - -     ( 1
γ δ ν ρ σ = = = = = (2')
In (2') the numbers in parentheses are the asymptotic t-values. In order to find these t-values, the variance of the estimates were computed by first taking linear approximations of the coefficients in eq. (1'). The general formula for the approximated variance can be written as

Summary and conclusions

The results of this study indicate that the long-term aggregate production function of the post-war U.S. economy exhibits slightly increasing returns to scale. Almost the same result was obtained in a similar study by [START_REF] Douglas | Are there laws of production[END_REF] covering the period 1899-1922[START_REF] Brown | On the theory and measurement of technological change[END_REF] for the period 1890-1960[START_REF] Intriligator | Embodied technical change and productivity in the U.S., 1929-1958[END_REF] for the period 1929-1958. This suggests that the returns to scale has been stable for the U.S. economy for almost a century. The estimated returns to scale parameter equals 1.10 which is exactly what [START_REF] Denison | Accounting for United States economic growth 1929-1969[END_REF] assumed in his calculations of the sources of growth of the U.S. economy. 6 My statistical findings support his assumption.

As [START_REF] Boskin | Tax policy and economic growth: Lesson's from the 1980s[END_REF] points out, virtually all econometric growth studies assume CRS. This paper raises serious doubts about the validity of this practice.

( ) ( ) ( ) 2 1 ˆˆˆV ar Var 2 Cov , i j i i j i m i j i f f f φ θ θ θ θ θ θ = < ∂ ∂ ∂ ≈ ∂ ∂ ∂       +             ∑ ∑
where φ is the estimate with the unknown variance -, , , , γ δ ν ρ σ -and the ˆi θ 's are the estimates from (1'). The resulting estimates are asymptotically efficient. The long-term coefficient of substitution between capital and labor, σ , equals 0.42 and is significant. This finding is consistent with the result obtained by Eisner and Nadiri (1968) but inconsistent with the result of Jorgenson and Stephenson (1969) who claim that the elasticity of substitution between capital and labor is closer to one. It is important to get a reliable estimate of this coefficient since its true value has strong implications for understanding the behavior not only of output, but also of capital and investment, For example, in Jorgenson's formulation of the investment function, which states that investment depends on the gap between the desired and actual capital stock, the assumption of unit elasticity of substitution between capital and labor plays a crucial role. If this elasticity is closer to zero, then the accelerator model of investment becomes relevant. See the survey article of [START_REF] Abel | Consumption and investment[END_REF] for further details. Note that, the high value of the 2 R and relatively low values of the t-statistic indicate presence of multicollinearity, and the estimates of γ , ν , and ρ are not statistically significant. It should also be mentioned that among several functional forms tried, the reported estimated production functions gave the most reasonable results. 6 Some people have criticized Denison for assuming slightly increasing returns to scale without ever estimating it. But as the results of this study indicate, his assumption ex post seems to have empirical support.

The results indicate that since the war GNP became more sensitive to changes in capital and less sensitive to changes in labor. The long-run capital and labor elasticities of the real output obtained here are different from their estimates for the pre-war or interwar period. While I find both estimated elasticities in the range of 0.45-0.55 for the post-war U.S. economy, for 1899-1922 and 1929-1958 the capital and labor elasticities of output, as reported by [START_REF] Douglas | Are there laws of production[END_REF] and [START_REF] Intriligator | Embodied technical change and productivity in the U.S., 1929-1958[END_REF], are about 0.25 and 0.75, respectively.

The increasing importance of the capital stock in the growth of the U.S. economy has been documented in other studies as well, but the figures are not as high as my estimate. For example, the figures cited in Maddison's survey article (1987) for the weight of the capital stock range from as low as 0.21 to as high as 0.407 . It should be noted that these figures were estimated in studies that cover much shorter periods than my study. This suggests that the importance of capital in explaining the long-term growth of the U.S. economy exceeds its importance in explaining short-term business cycle fluctuations.

The increasing importance of the capital input in the growth of the U.S. economy since 1948 is emphasized also in studies that analyze the source of the U.S. economic growth [Boskin (1988) Christensen and[START_REF] Christensen | Measuring the performance of the private sector in the U.S. economy[END_REF], [START_REF] Jorgenson | Productivity and economic growth[END_REF][START_REF] Jorgenson | Productivity and postwar U.S. economic growth[END_REF]]. For example, Jorgenson recently argued that 'comparing the contribution of capital input with other sources of output growth for the period 1948-1979 as a whole makes clear that capital input is the most significant source of growth ' (1988, p. 25). This increasing importance of the capital input in the long-term growth of the U.S. economy can be explained by the fact that the production over the period became more capital intensive. In addition, some part of the existing capital stock reflects the substantial technological improvements that have occurred since the war, the capital stock time series captures a large fraction of this technical progress. The idea is that $1 worth of 1950's capital investment is not the same as $1 worth of 1980's capital investment due to the technological progress witnessed since the war in the fields of computers, computerized automation, robotics, etc. This explains why my estimate for technical progress is relatively low.

This may also explain [START_REF] Jorgenson | Productivity and postwar U.S. economic growth[END_REF] finding that most of the aggregate growth of U.S.

economy can be attributed to the combined contribution of capital and labor to the total output.

Table 1 .

 1 Estimated capital and labor elasticities of output, U.S., 1948-1983

	Equation	Labor	Capital	Returns to scale	CRS
	Number	elasticity	elasticity	(	α β +	)	imposed
	(2)	0.54	0.56		1.10		No
	(3)	0.45	0.55		1.00		Yes
	(4)	0.58	0.42		1.00		Yes

The test statistic for testing the hypothesis of CRS -( )

SeeMaddison (1987, p. 660, table

8). A possible reason for the differences between my estimates and the previous estimates might be the difference between the data sets. My data is quarterly while the previous studies use annual data.

 Jorgenson, D.W. and J.A. Stephenson, 1969, Issue in the development of the neoclassical theory of investment behavior, Review of Economics and Statistics 51, 346-353. Maddison, A., 1987, Growth and slowdown in advanced capitalist economies: Techniques of quantitative assessment, Journal of Economic Literature 25, 649-698. Sims, C.A., 1972, Money, income andcausality, American Economic Review 62, 540-552. Tinbergen, J., 1942, Zur Theorie der langfristigen Wirtschaftsentwicklung, Weltwirtschaftliches Archiv 55. 511-549.


Yoann Blache
email: yoann.blache@univ-lyon1.fr

PhD Biova 2 Kouevidjin

MD Jacques 3 De Guise

PhD Raphaël 4 Dumas

Adnan Saithna

Bertrand Sannery-Cottet

Mathieu Thaunat

Blache Yoann

A simulation study

Keywords: Anterolateral ligament, anterior cruciate ligament, orthopedics, computer modelling

Results: During physiological knee flexion, the LER lengthened up to 11mm, corresponding to 22% of the resting length, in the early degrees of knee flexion and shortened from 40 to 60° of knee flexion regardless of femoral or tibial attachment locations. However, the ALL tibial position allowed complete LER shortening at 60° of flexion whereas an LER using a GT tibial attachment remained more lengthened. For the movements corresponding to a pivotshift test, the LER lengthened between 10.6 and 15.9 mm for GT tibial attachment site and between 5.9 and 11.6 mm for ALL attachment site.

Discussion: During physiological weight-bearing knee flexion, a proximo-posterior femoral location was associated with a lengthened LER in the early degrees of flexion and a shortening between 40 and 60° of flexion. In addition, LER lengthening occurred during a

Introduction

Return to sport after anterior cruciate ligament reconstruction is often not satisfying since only 63% of patients resume their pre-injury level of sports participation [START_REF] Ardern | Return to sport following anterior cruciate ligament reconstruction surgery: A systematic review and meta-analysis of the state of play[END_REF] and even then, this is associated with a high risk of re-injury [START_REF] Paterno | Incidence of second acl injuries 2 years after primary acl reconstruction and return to sport[END_REF][START_REF] Salmon | Incidence and risk factors for graft rupture and contralateral rupture after anterior cruciate ligament reconstruction[END_REF][START_REF] Shelbourne | Incidence of subsequent injury to either knee within 5 years after anterior cruciate ligament reconstruction with patellar tendon autograft[END_REF]. One of the possible causes of these suboptimal outcomes is a persistent lack of rotational and translational stability of the knee even after a technically adequate anterior cruciate ligament reconstruction [START_REF] Amis | Biomechanics of rotational instability and anatomic anterior cruciate ligament reconstruction[END_REF]. Consequently, lateral extra-articular reconstruction (LER) has generated renewed interest [START_REF] Sonnery-Cottet | Combined anterior cruciate ligament and anterolateral ligament reconstruction[END_REF][START_REF] Slette | Biomechanical results of lateral extra-articular tenodesis procedures of the knee: A systematic review[END_REF][START_REF] Marcacci | Arthroscopic intra-and extraarticular anterior cruciate ligament reconstruction with gracilis and semitendinosus tendons: A review[END_REF][START_REF] Krackow | Optimization of knee ligament position for lateral extraarticular reconstruction[END_REF] and is increasingly performed in patients with high-grade pivot-shift, in order to better control the coupled tibial internal rotation and anterior translation [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF].

However, there has been considerable debate regarding the anatomy of the anterolateral structures of the knee and therefore also the optimum positioning of femoral and tibial tunnels for LER. These should be located such that the LER confers physiological knee kinematics, specifically restoration of rotational control and avoidance of overconstraint [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF]. The recent literature, including in-vivo and in-vitro studies, has reported a range of different femoral tunnel positions which includes directly proximal to the lateral epicondyle [9-11-12], posteroproximal [START_REF] Van De Velde | In vivo length changes of the anterolateral ligament and related extra-articular reconstructions[END_REF][START_REF] Imbert | Isometric characteristics of the anterolateral ligament of the knee: A cadaveric navigation study[END_REF] or postero-distal [START_REF] Kernkamp | In vivo anterolateral ligament length change in the healthy knee during functional activities-a combined magnetic resonance and dual fluoroscopic imaging analysis[END_REF]. However, there is increasing consensus that a posteroproximal femoral attachment allows the most favorable behavior, with an LER that is lengthened in knee extension and shortened in flexion [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF][START_REF] Kittl | Length change patterns in the lateral extraarticular structures of the knee and related reconstructions[END_REF][START_REF] Wieser | Assessment of the isometry of the anterolateral ligament in a 3-dimensional weight-bearing computed tomography simulation[END_REF][START_REF] Van De Velde | In vivo length changes of the anterolateral ligament and related extra-articular reconstructions[END_REF][START_REF] Imbert | Isometric characteristics of the anterolateral ligament of the knee: A cadaveric navigation study[END_REF][START_REF] Kernkamp | In vivo anterolateral ligament length change in the healthy knee during functional activities-a combined magnetic resonance and dual fluoroscopic imaging analysis[END_REF]. With respect to the tibial graft insertion, Wieser, Furnstahl, Carrillo, Fucentese and Vlachopoulos [START_REF] Wieser | Assessment of the isometry of the anterolateral ligament in a 3-dimensional weight-bearing computed tomography simulation[END_REF] reported that, during a weight-bearing squat, the most isometric point was located at 37% of the postero-anterior width of the tibial plateau. Although all of these studies yield precious information for surgeons regarding the optimum positioning of LER grafts during non-altered physiological knee flexion, none of them has assessed the LER length changes that occur in the presence of the altered knee kinematics seen in the knee with persistent internal rotation and anterior translation instability following ACL reconstruction. To the best of our knowledge, only Imbert, Lutz, Daggett, Niglis, Freychet, Dalmay and Sonnery-Cottet [START_REF] Imbert | Isometric characteristics of the anterolateral ligament of the knee: A cadaveric navigation study[END_REF] investigated the effect of knee rotation on LER length. Among the three femoral graft positions tested, the postero-proximal graft had the greatest LER length variation when a 2 N.m internal rotation torque was applied with the knee fixed at 90°, while no difference was observed between the graft positions at 20° of knee flexion. However, this study was performed in-vitro and may not reflect LER length variation during a physiological in-vivo weight-bearing task. Furthermore, LER length variations were not measured during coupled knee internal rotation and anterior translation that corresponds to the knee instability observed during a pivot-shift test.

The purpose of this study was to assess the length-change behavior of LER during a physiological weight-bearing knee flexion task in a normal knee and in a computer simulated pivot shift scenario. It was hypothesized that a proximo-posterior femoral attachment site would allow graft lengthening in knee extension and shortening in flexion, and lengthening during altered knee internal rotation and anterior translation.

Patients and Methods

Patients

The baseline model for the analysis was based on a healthy male participant (Age: 35 years, Height: 1.75 m, Mass: 80 Kg) who volunteered to take part in the study. The patient declared no history of major lower limb injury. The protocol was approved by the Institutional Review Board of Hopital Privé Jean Mermoz (# 2017-02) in accordance with the ethical standards in the 1964 Declaration of Helsinki, and the participant gave informed consent to participate in the study.

Procedure and data collection

Firstly, a three-dimensional CT-scan of the participant right knee was performed (slice of 0.6 mm, Siemens Somaton, Erlangen, Germany). Secondly, in line with the methodology of Clement, Dumas, Hagemeister and de Guise [START_REF] Clement | Soft tissue artifact compensation in knee kinematics by multi-body optimization: Performance of subject-specific knee joint models[END_REF], the participant performed five quasi-static squats with 0, 10, 20, 30 and 60° of knee flexion standardized with a positioning jig. Each position was maintained inside the EOS ® system (EOS Imaging Inc., Paris, France) for five seconds in order to obtain biplane radiographic images.

Image processing and knee 3D kinematics

CT images were used to reconstruct the femur and tibia meshes using 3D Slicer 4.6.2 ® . 3D meshes of the tibia and femur were also reconstructed from the five biplane radiographs [START_REF] Chaibi | Fast 3d reconstruction of the lower limb using a parametric model and statistical inferences and clinical measurements calculation from biplanar x-rays[END_REF][START_REF] Kanhonou | A method to study 3d knee pseudo-kinematics using low-dose stereoradiography during static squat[END_REF]. This reconstruction process gives an accuracy of the positions and orientations of the femur and tibia of less than 0.3±0.3° and 0.3±0.2 mm respectively [START_REF] Kanhonou | A method to study 3d knee pseudo-kinematics using low-dose stereoradiography during static squat[END_REF]. CT-scan meshes were matched with the corresponded EOS meshes using an iterative closest point algorithm. In line with ISB recommendations [START_REF] Wu | Isb recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion--part i: Ankle, hip, and spine. International society of biomechanics[END_REF], 3D knee kinematics with six degrees of freedom were obtained for the five quasi-static poses. Then, a cubic spline interpolation was used (Matlab R2017b, The MathWorks Inc., Natick, MA) to compute the couplings between knee flexion angle (from 0 to 60°) and the five other degrees of freedom, namely, abduction-adduction, internal-external rotation, anterior-posterior translation, medio-lateral translation and craniocaudal translation.

LER attachment sites and length

A computer model (Opensim 3.3 [START_REF] Delp | Opensim: Open-source software to create and analyze dynamic simulations of movement[END_REF]) was used to assess LER length-changes with respect to knee kinematics. The model was composed of the CT-scan meshes and the couplings between the knee flexion angle and the five other degrees of freedom computed above from the EOS quasi-static squat images. In order to avoid the ligaments penetrating through the bones during the computer simulation, two wrapping objects were located on the femoral condyle and tibia.

In accordance with the consensus from the anterolateral ligament expert group [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF], femoral graft positions located posteriorly and proximally to the lateral femoral epicondyle were simulated. Specifically, six femoral graft insertions were located on two quarter-circles with a radius of 5 and 10 mm, and centered on the femoral lateral epicondyle.

For the tibia, two locations were considered. The first intended to replicate procedures that use a reflection of the iliotibial band, and was therefore located directly at its attachment to Gerdy's tubercle (GT). The second tibial graft located intended to replicate the most anterior location of an anterolateral ligament (ALL) graft at 1 cm posterior to Gerdy's tubercle [START_REF] Sonnery-Cottet | Combined anterior cruciate ligament and anterolateral ligament reconstruction[END_REF] (Figure 1). LER length-change behavior was determined by computing the distance between the femoral and tibial insertions.

Analysis

Firstly, LER length changes were computed for both physiological weight-bearing knee flexion with respect to the LER length computed for a resting position with the knee in full extension (Eq. 1).

(Eq. 1) with i, j, and k referring to a given knee flexion, internal rotation and anterior translation respectively.

Secondly, LER length were computed for altered kinematics, namely, increased internal rotation (up to 8°) and anterior translations (up to 12 mm) that can be observed in patients [START_REF] Bull | Intraoperative measurement of knee kinematics in reconstruction of the anterior cruciate ligament[END_REF]. In addition, average length variation of the LER was computed for two volumes representative of potential knee kinematics during a simulated pivot-shift test. The first volume corresponded to combined knee flexions between 10 and 30°, rotations between 1° and 8°, and anterior translations between 1 mm and 6 mm. The second volume was computed for the same knee flexions and rotations ranges but for anterior translations between 7 mm and 12 mm. Finally, a specific combination of knee flexion, internal rotation and anterior translation was also computed following the curve of the pivot-shift test reported by Amis, Bull and Lie [START_REF] Amis | Biomechanics of rotational instability and anatomic anterior cruciate ligament reconstruction[END_REF] (Figure 2).

Results

During the physiological, weight-bearing knee flexion task, knee flexion (from 0 to 60°) was associated with a non-linear knee internal rotation ranging from 0 to 21.7°, and with an anterior tibial translation ranging from 0 to 6.3 mm (Figure 2). In addition, regardless of the femoral and tibial graft locations, the LER lengthened by up to 11mm (corresponding to 22% of the surgery length) in the early degrees of knee flexion (between 0 and 40°) and shortened from 40 to 60° of knee flexion (Figure 3). Furthermore, for all femoral attachment sites, the posterior tibial graft (ALL position) led to less LER lengthening throughout knee flexion in comparison to the GT tibial attachment site (-7.72 ± 0.77 % on average).

In the case of simulated altered knee kinematics, an increased tibial internal rotation, particularly after 20° of knee flexion led the LER to lengthen whatever the graft location. In the same way, the LER lengthened with increased anterior tibial translation (Figure 4 and supplementary file). For the specific volumes corresponding to a pivot-shift test (increased internal rotation and anterior translation between -10 and -30° of knee flexion), regardless of the femoral graft location, the LER lengthened between 20 and 34 % of the resting length when a GT tibial attachment was used and between 11 and 26% when an ALL tibial attachment was used (Table 1). In addition, regardless of the femoral graft location, the anterior tibial position (GT) always lengthened more than the posterior one (ALL) for all simulated knee kinematics. Finally, when replicating the specific knee kinematics recorded for a pivot-shift test by Amis, Bull and Lie [START_REF] Amis | Biomechanics of rotational instability and anatomic anterior cruciate ligament reconstruction[END_REF], the LER lengthened during the early phase of the test (until 15° of knee flexion), with maximal values corresponding to the peaks of knee anterior translation and internal rotation, regardless of the femoral graft location.

Discussion

This study aimed to assess the length-change behavior of LER during a physiological weight-bearing knee flexion task (i.e. quasi-static squats) in a normal knee and in a computer simulated pivot shift scenario. The main findings are that postero-proximal femoral attachment sites result in LER lengthening in the early degrees of knee flexion and shortening around 40-60° of knee flexion during physiological weight-bearing knee flexion and that when a postero-proximal femoral attachment site is used, an LER becomes lengthened during a simulated pivot shift test.

Although this study was based on a single participant, the kinematics recorded during physiological weight-bearing knee flexions could be considered as representative of a healthy male population. Normal kinematics during a weight-bearing squatting task are usually characterized by a tibial internal rotation and anterior translation associated with knee flexion [START_REF] Yamaguchi | In vivo kinematics of anterior cruciate ligament deficient knees during pivot and squat activities[END_REF]. In the current study the participant knee kinematics were consistent with these previous reports since an internal rotation of between 0 and 20° and an anterior translation from 0 to 6 mm were demonstrated to be coupled with knee flexion between 0 and 60°.

The results of the current study are consistent with previous reports with respect to the observation that proximo-posterior femoral attachment sites are associated with LER lengthening in extension and shortening in physiological flexion [START_REF] Imbert | Isometric characteristics of the anterolateral ligament of the knee: A cadaveric navigation study[END_REF][START_REF] Kernkamp | In vivo anterolateral ligament length change in the healthy knee during functional activities-a combined magnetic resonance and dual fluoroscopic imaging analysis[END_REF]. In addition, similarly to a previous study [START_REF] Kernkamp | In vivo anterolateral ligament length change in the healthy knee during functional activities-a combined magnetic resonance and dual fluoroscopic imaging analysis[END_REF] we reported that an ALL tibial attachment location led to a greater shortening close to 60° of knee flexion when compared to a GT tibial attachment. Therefore, we may assume that an ALL graft location attachment site presents a more desirable behavior than GT since it is less likely to overconstrain physiological internal rotation in the flexed knee. LER's are performed in order to try to better control rotational and translational knee stability [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF]. The results of this study suggest that this function is achieved when a proximoposterior femoral graft location is used because the LER lengthened for both simulated increased tibial internal rotation and for increased tibial anterior translation. These results are in accordance with Imbert, Lutz, Daggett, Niglis, Freychet, Dalmay and Sonnery-Cottet [START_REF] Imbert | Isometric characteristics of the anterolateral ligament of the knee: A cadaveric navigation study[END_REF] who observed a lengthening of LER when an internal rotation torque was applied. The LER also lengthened during a simulated pivot-shift test, namely, a combination of tibial internal rotation and anterior translation. More precisely, the maximal lengthening was observed when the maximal anterior translation and internal rotation occurred during the pivot-shift test when simulated as described by Amis, Bull and Lie [START_REF] Amis | Biomechanics of rotational instability and anatomic anterior cruciate ligament reconstruction[END_REF]. It therefore seems logical that LER may help to restore normal knee kinematics especially when the knee is subjected to a combination of tibial internal rotation and translation. This is consistent with the findings of Inderhaug,

Stephen, Williams and Amis [START_REF] Inderhaug | Anterolateral tenodesis or anterolateral ligament complex reconstruction: Effect of flexion angle at graft fixation when combined with acl reconstruction[END_REF], who demonstrated significant improvement in rotational knee kinematics in cadaveric knees with LER. However, LER lengthening is only one component of the complex inter-play of factors that ensure the control of knee stability. The direction of LER vector should be assessed in future studies to address the assumption that it is indeed the lengthening of the LER that improves knee stability. Nevertheless, the lengthening behavior of LER observed in the current study reinforces the concept that LER could be indicated after anterior-cruciate rupture when the patient presents a pivot-shift grade 2 or 3 [START_REF] Sonnery-Cottet | Anterolateral ligament expert group consensus paper on the management of internal rotation and instability of the anterior cruciate ligament -deficient knee[END_REF] in order to better control knee stability.

Finally, in comparison to an ALL tibial LER graft position, the GT tibial attachment site resulted in greater LER lengthening during simulated increased tibial internal rotation and anterior translation. This raised concerns regarding the risk of overconstraint with a GT attachment site particularly because this location was not associated with a complete relaxation of the LER in flexion. Moreover, when examining the increased internal rotation, it was observed that the LER was instantaneously lengthened, even in the absence of pathological anterior translation. Therefore it is suggested that LERs based on a GT location are associated with a greater potential risk of overconstraint [START_REF] Slette | Biomechanical results of lateral extra-articular tenodesis procedures of the knee: A systematic review[END_REF] when compared to reconstructions based on a more posterior tibial position such as that used for anatomic ALL reconstruction.

There were several limitations of this study. The first was that only one participant was enrolled in this study. Nevertheless, the analysis performed in our study explores a large range of internal rotations and anterior translations and shall encompass the kinematic variability that would have been observed in a larger cohort study. Similarly, it is assumed that the range of femoral LER insertions encompasses the knee anatomy variability that would have been observed in a larger cohort study. Finally, ours results obtained during the physiological knee flexion are very similar than those of Kernkamp, Van de Velde, Hosseini, Tsai, Li, van Arkel and Li [START_REF] Kernkamp | In vivo anterolateral ligament length change in the healthy knee during functional activities-a combined magnetic resonance and dual fluoroscopic imaging analysis[END_REF] who performed their study on eighteen healthy knees. The second limitation was that altered kinematics were simulated from ranges of motion observed in the literature, which may differ from weight-bearing altered kinematics observed after anterior cruciate ligament reconstruction. Once again, an assumption was made that the wide analysis encompassed the variability encountered in post-operative knee kinematics. The third limitation was that only two tibial insertions were tested, instead of a broader range. However, these were selected to represent the two most popular tibial locations in contemporary surgical practice [START_REF] Sonnery-Cottet | Combined anterior cruciate ligament and anterolateral ligament reconstruction[END_REF][START_REF] Slette | Biomechanical results of lateral extra-articular tenodesis procedures of the knee: A systematic review[END_REF].

Conclusion

To conclude, computer modelling made it possible to analyze LER length variations for numerous knee positions corresponding to weight-bearing knee flexion, and for the first time, to typical pivot-shift kinematics. During physiological weight-bearing knee flexion, and regardless of the tibial attachment site, a proximo-posterior femoral location was associated with a lengthened LER in the early degrees of flexion and a shortening between 40 and 60° of flexion. In addition, LER lengthening occurred during simulated pivot-shift scenarios supporting the concept that a postero-proximal femoral LER attachment site presents a desirable behavior both during physiological knee flexion and altered knee kinematics.

Figure captions Figure 1 .Figure 2 -

 captions12 Figure captions

Figure 3 -

 3 Figure 3-Relative (left) and absolute (right) lateral extra-articular reconstruction (LER) length variation during the physiological weight-bearing knee flexion task for the six femoral attachment sites (#1 to #6) and the two tibial graft locations (GT and ALL).

Figure 4 -

 4 Figure 4 -Length variation of LER with regard to knee flexion and internal rotation at three anterior tibial translations (0 mm, 6 mm and 12 mm) for three femoral attachment sites (#4, #5 and #6) and two tibial locations (GT and ALL). The inferior trajectory surrounded by black circles represent the coupling between knee flexion and internal rotation during weightbearing knee flexion task.

Table 1 .

 1 Mean ± standard deviation of the lateral extra-articular reconstruction (LER) length variation with respect to the LER length measured at full knee extension (expressed in absolute and relative values) for the specific volumes corresponding to the pivot-shift kinematics. Results are reported for the six simulated femoral graft (#1 to #6) and two tibial graft (GT and ALL) locations.

	LER femoral graft

Acknowledgment:

We would like to thank Thierry Cresson from the « Laboratoire de recherche en imagerie et orthopédie, École de technologie supérieure, Centre de recherche du Centre hospitalier de l'Université de Montréal »,for his contribution concerning the mesh reconstructions from the biplanar radiographies. In addition, this work was performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

Funding

The study was supported by the group "Ramsey Générale de Santé", Paris, France.


Dragan Milenkovic

Agnieszka Gomulkiewicz

Cécile Gladine

Dariusz Janczak

Irmina Grzegorek

Karolina Jablońska

Katarzyna Drożdż

Magdalena Chmielewska

Aleksandra Piotrowska

Robert Paslawski

Agnieszka Gomułkiewicz

Cecile Gladine

Karolina Jabłońska

Robert Pasławski

Urszula Pasławska

Adrian Janiszewski

Piotr Dzięgiel

André Mazur

Andrzej Szuba

Transcriptomic Alterations of the Aortic Intima and Media in Long-term High-fat Diet Fed Pigs and Its Reversal (P15-010-19)

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

Objectives:

We have previously shown that 12 months (mo.) highfat diet (HFD) in pigs led to pathophysiological alterations, incl. fattening and increased femoral artery intima-media-thickness, which were partly reversed after 3 mo. return to control diet (Zabek et al., PLoS One 2017). The aim of this study was to decipher underlying mechanism of action of these dietary interventions on the arteries by nutrigenomics analyses of intima and media of aorta.

Methods: 32 female pigs were divided into 3 groups: Control diet (CD) for 12 mo; HFD for 12 mo; 3) Reversal diet group (RD): HFD for 9 mo followed by CD for 3 mo After 12 mo animals were killed and abdominal aorta collected. RNA was isolated from aorta intima and media for whole genome microarray analyses followed by bioinformatics analyses.

Results: HFD compared to CD group significantly affected gene expression profile in intima with genes belonging to the chemotaxis, inflammation or endothelial permeability. RD induced gene expression profile was distinct from the CD group. This suggests that 3 mo of reversal to CD is not sufficient to correct gene expression changes induced by HFD. Comparison of RD profile with that of HFD group revealed a group of genes with opposite expression, e.g., genes regulating inflammation, toll-like cell signaling pathway or cytoskeleton organization involved in the regulation of cell permeability. This suggests that return to the RD only partly restored gene expression alterations due to the HFD. Significant changes in expression of genes in media following HFD were also observed, such as genes involved in cytoskeleton organization and migration MAPK signaling. As for intima, the expression profile of media of pigs on RD was different on that of these on CD diet. Compared to HFD, a group of genes involved in PI3K or MAPK pathways presented opposite expression suggesting that RD can partly correct the changes in genomic effect induced by HFD.

Conclusions: This study revealed genomic modifications induced by long-term HFD consumption on arterial intima and media. The return to normal diet for 3 mo was not sufficient to counteract the genomic effect of long-term HFD consumption.

Funding Sources: WROVASC Integrated Cardiovascular Centre, co-financed by the European Regional Development Fund.

CURRENT DEVELOPMENTS IN NUTRITION