Estimating a dynamic labour demand equation using small, unbalanced panels: An application to Italian manufacturing sectors
|
|
- Θέκλα Φραγκούδης
- 8 χρόνια πριν
- Προβολές:
Transcript
1 Estimating a dynamic labour demand equation using small, unbalanced panels: An application to Italian manufacturing sectors Giovanni S.F. Bruno +, Anna M. Falzoni + and Rodolfo Helg *+ + Università Bocconi, Milano Università degli Studi di Bergamo * LIUC - Università CarloCattaneo This version: July, Abstract We estimate a dynamic labour demand equation using a small unbalanced panel data-set of italian manufacturing sectors.there are 31 sectors with an average group size of 24 time observations. The estimator adopted is the Least Squares Dummy Variable estimator corrected for the finite-sample bias (LSDVC) using the bias approximations derived in Bruno (2005a), which extend Bun and Kiviet s (2003) to unbalanced panels. It is implemented in Stata using Bruno s (2005b) code XTLSDVC (available from the SSC archive at The estimated long-run and short-run labour demand elasticities are in line with the ranges indicated in Hamermesh (2000). In addition, their magnitudes are not positively affected by measures of sectoral international exposure, which rejects the Rodrick s (1997) conjecture for Italy. This confirms the results in Bruno, Falzoni, Helg (2004) obtained using a balanced data set. JEL classification: F16, J23. Keywords: within estimator; bias approximations; international exposure; dynamic labor demand equation; labour demand elasticities.
2 1. Introduction This paper estimates a dynamic labour demand equation for Italy using an unbalanced panel data of manufacturing sectors, in an attempt to test for the joint presence of sectoral international exposure (globalization) effects and output generated external economies. Following Bruno, Falzoni and Helg (2004), the model specification accommodates the presence of employment adjustment costs and allows for two types of globalization effects. First, a possible direct effect of globalization on labour productivity may emerge as formulated in Greenaway et al. (1999). Secondly, as emphasizedbydanirodrikinhisbook Has globalization gone too far? (1997), the role played by international exposure in the labour market is not (or not only) that of a labour demand shifter, but rather of a force boosting the responsiveness of labour demand to changes in labour prices regardless of economic structure and the identity of the trade partners (Rodrik, 1997, 26). Our specification will permit to test both effects in a unique estimation run by treating the globalization variable as a shifter for both the labour demand equation and the labour elasticity 1. Also, by conditioning on a measure of sectoral output we can test for the presence of output generated external economies. Three important econometric issues emerge in the empirical analysis, which need a solution. First, as is well known the within (or LSDV) estimator for dynamic panel data models is not consistent for T fixed and N large (Nickell (1981)). Second, the cross-sectional dimension of our panel is small (there are 31 manufacturing sectors with an average group size of 24 years), so that N- consistent GMM estimators -a by now standard alternative to the within estimator for dynamic panel data models- may be affected by a potentially severe small sample bias (Kiviet (1995)). Finally, the unbalanced nature of our panel does not permit to correct the within estimator by applying the bias approximation formulae derived in Kiviet (1995), (1999) and Bun and Kiviet (2003), only valid for balanced panels. The adoption of those formulae as they are would in fact require discarding the cross-sections (or time-series) causing unbalancedness with a potentially high loss of information. This has been the strategy followed in Bruno, Falzoni and Helg (2004), which has led to the sacrifice of the sector Radio, TV & Communication Equipment. 1 As opposed to the two-stage approach followed by Slaughter (2001), who first estimates labour demand elasticities and then regress the estimated elasticities on a set of globalization measures. 2
3 In the view of the above considerations, our estimation strategy will employ a bias corrected LSDV estimator using the recent LSDV bias approximation formulae derived in Bruno (2005a), which extends Kiviet s (1999) and Bun and Kiviet s (2003) to (possibly) unbalanced panels. The received empirical literature on the labour market effects of globalization is not conclusive. Bruno, Falzoni and Helg (2004) carry out a comparative study on OECD countries, including Italy, using a specification similar to that adopted in this paper, but on a balanced version of the data and with a restricted choice of bias approximations, to find support for the Rodrik s conjecture only in the cases of France and the UK. Slaughter (2001), adopting a two-stage approach on an industry-year panel from 1961 through 1991 for the United States, provides mixed support to the view that trade contributed to increased elasticities. In the first stage, Slaughter finds that demand for production labour has become more elastic in manufacturing overall and in five of eight industries within manufacturing; the same is not true for non-production labour. In the second stage, when estimated elasticities are regressed on a set of trade variables and industry dummies are included, Slaughter finds many significant coefficients, with the expected sign. However, in a number of cases, these predicted effects disappear when time dummies are introduced. For production workers as well as for non production workers, time results to be a very strong predictor of elasticity pattern. In sum, there appears to be a large unexplained residual for changing factor demand elasticities 2. The experience of dramatic changes in trade regimes in a number of developing countries might be thought as the appropriate context to investigate the theoretical link between openness and labour demand elasticities. This approach is in fact been followed by Krishna et al. (2001) and Fajnzylber and Maloney (2001), finding however no support to the conjecture of more-elastic labour demand in response to trade liberalization. Using Turkish plant-level data, Krishna et al. (2001) estimates a labour demand equation in which the wage variable is interacted with a liberalization dummy, capturing the effect of changes in trade policy. Overall, the results show that labour demand elasticities seem to be unresponsive to openness. Only very mixed support and no consistent patterns for the idea that trade liberalization has an impact on own wage elasticities also emerges in the study by Fajnzylber and Maloney (2001). They use dynamic panel techniques to estimate labour demand functions for manufacturing establishments in Chile, 2 Applying a similar methodology, Faini et al. (1999) find some support to the hypothesis that greater globalisation is associated with larger elasticities for Italy during the period
4 Colombia and Mexico. Finally, Greenaway et al. (1999) evaluate the impact of trade volumes on employment through induced productivity changes. Adopting a dynamic labour demand framework for the UK, they find that increases in trade volumes, both in terms of imports and exports, cause reductions in the level of derived labour demand, consistently with the view that increased openness serves to increase the efficiency with which labour is utilized in the firm. Greenaway et al. also analyses the impact of trade changes on the slope of the derived labour demand introducing a term corresponding to interactions between the wage rate and import and export volumes. They find a positive effect of trade volumes on the labour demand elasticity but this impact is not significant 3. Our emprical results are as follows. First, all testable regularity conditions implied by cost minimising behaviour are always satisfied, with the estimated labour demand elasticities, both short-run and long-run, being always significantly negative and within the empirical ranges documented in Hamermesh (2000). Second, results for the bias-corrected LSDV estimators are robust to changes in the order of the bias approximations and to different choices of the N-consistent estimator used to initialize the bias correction. Third, the Rodrik s conjecture is decidedly rejected for all estimators used (bias-corrected and GMM), which confirms the results for Italy in Bruno, Falzoni and Helg (2004). Fourth, the direct effect of globalization on labour demand is never found significant. Finally, we find robust evidence in favour of output generated external economies. The structure of the paper is as follow. The next section explains the bias correction strategy. Section 3 set up the theoretical framework. Section 4 describes the data. Estimation results are contained in Section Bias corrected LSDV estimators In this section we review the existing results on the LSDV bias approximations for dynamic panels with N and T small, or only moderately large, and and their use to implement bias-corrected LSDV estimators. Consider the standard dynamic panel data model y it = γy i,t 1 + x 0 itβ + η i + it ; γ < 1; i =1,..., N and t =1,..., T, (2.1) 3 Adopting a different methodology and focusing on the intersectoral dimension of the scale effect, Jean (2000) finds, for France, that trade openness can indeed have a significant effect on labour demand elasticities. 4
5 where y it is the dependent variable; x it is the ((k 1) 1) vector of strictly exogenous explanatory variables; η i is an unobserved individual effect; and it is an unobserved white noise disturbance. Collecting observations over time and across individuals gives y = Dη + Wδ+, where y and W = y 1.X are the (NT 1) and (NT k) matrices of stacked observations; D = I N ι T is the (NT N) matrix of individual dummies, (ι T is the (T 1) vector of all unity elements); η is the (N 1) vector of individual effects; is the (NT 1) vector of disturbances; and δ = γ.β 0 0 is the (k 1) vector of coefficients. It has been long recognized that the LSDV estimator for model (2.1) is not consistent for finite T. Nickell (1981) derives an expression for the inconsistency for N +, whichiso (T 1 ). Kiviet (1995) obtains a bias approximation that contains terms of higher order than T 1. In Kiviet (1999) a more accurate bias approximation is derived. Bun and Kiviet (2003) reformulate the approximation in Kiviet (1999) with simpler formulae for each term. All foregoing bias approximations are derived for balanced panels. As such they are useless in our case, unless we balance our panel at the cost of time or sector observations. This waste of information can be avoided, however, by using the bias approximations in Bruno (2005a) extending Bun and Kiviet s (2003) formulae to unbalanced panels with a strictly exogenous selection rule. Bruno (2005a) defines the static selection indicator z it such that z it =1if(y it,x it )is observed and z it = 0 otherwise. From this he also defines the dynamic selection rule s (r it,r i,t 1 ) selecting only the observations that are usable for the dynamic model, namely those for which both current values and one-time lagged values are observable: s it = ½ 1 if (zi,t,z i,t 1 )=(1, 1) 0 otherwise i =1,..., N and t =1,..., T. Thus, for any i the number of usable observations is given by T i = P T t=1 s it. The total number of usable observations is given by n = P N i=1 T i;andt = n/n denotes the average group size. For each i define the (T 1)-vector s i =[s i1..., s it ] 0 and the (T T ) diagonal matrix S i having the vector s i on its diagonal. Define also the (NT NT) block-diagonal matrix S = diag (S i ). The (possibly) unbalanced 5
6 dynamic model can then be written as Sy = SDη + SWδ + S. (2.2) The LSDV estimator is given by δ LSDV =(W 0 M s W ) 1 W 0 M s y, where M s = S ³I D (D 0 SD) 1 D 0 S is the symmetric and idempotent (NT NT) matrix wiping out individual means and selecting usable observations. Bruno s (2005a) bias approximation terms for unbalanced panels are then the following c 1 ³ T 1 = σ 2 tr (Π) q 1; (2.3) c 2 ³ N 1 T 1 h ³ = σ 2 QW 0 ΠM s W + tr QW 0 ΠM s W I k+1 + 2σ 2 q 11tr (Π 0 ΠΠ) I k+1 q1 ; c 3 ³ N 1 T 2 n = σ 4 tr (Π) 2q 11 QW 0 ΠΠ 0 Wq 1 + h³q 01W 0 ΠΠ 0 Wq 1 + ³ i o q 11 tr QW 0 ΠΠ 0 W +2tr (Π 0 ΠΠ 0 Π) q11 2 q 1 ; h 1; where Q =[E (W 0 M s W )] 1 = W 0 M s W + σ 2 tr (Π 0 Π) e 1 e1i 0 W = E (W ); e1 = (1, 0,..., 0) 0 is a (k 1) vector; q 1 = Qe 1 ; q 11 = e 0 1q 1 ; L T is the (T T ) matrix with unit first lower subdiagonal and all other elements equal to zero; L = I N L T ; Γ T =(I T γl T ) 1 ; Γ = I N Γ T ;andπ = M s LΓ. Clearly, in any balanced design S I NT,soM s = I D (D 0 D) 1 D 0, and the above terms reduce to Bun and Kiviet s (2003). With an increasing level of accuracy, the following three possible bias approximations emerge ³ 1 ³ 1 ³ 2 B 1 = c 1 T ; B 2 = B 1 + c 2 N 1 T ; B 3 = B 2 + c 3 N 1 T. (2.4) Approximations (2.4) depend upon the unknown parameters σ 2 and γ, sothey are unfeasible for bias correction. The bias corrected LSDV estimator is then 6
7 implemented using the two-step procedure suggested by Kiviet (1995) and Bruno (2005b). The first step obtains estimates for σ 2 and γ from some N consistent estimator. The second step performs bias correction by depuring the LSDV estimator from the bias approximation of choice evaluated at the estimated σ 2 and γ, b B i, as follows: LSDV C i = LSDV b B i,i=1, 2and3. (2.5) Possible consistent estimators for γ are Anderson and Hsiao (AH) and Arellano and Bond (AB). Depending on the estimator of choice for γ, say h, aconsistent estimator for σ 2 is then given by bσ 2 h = e0 h M se h (N k T ), (2.6) where e h = y Wδ h,andh = AH, AB. Monte Carlo analysis in Bruno (2005b) demonstrates that for sample sizes comparable to ours all possible forms of LSDVC outperforms LSDV and GMM estimators. 3. The Model The theoretical model on which we base our empirical analysis has the feature of producing labour demand elasticities in one stage. We consider a sector in the economy with a large number of firms using the same technology. There are two domestic production inputs, domestic labour l and capital k producing output q, with w and r being the compensations for l and k, respectively. The market for production factors is perfectly competitive, whereas no assumption is made on the form of the output market. We allow for two distinct sources of external economies at the firm level. Those generated by the sectoral production ; and those generated by the sectoral international exposure. Sectoral international exposure may foster technology advancement and productivity growth through several channels, such as technology advancement embodied in imported capital goods and intermediate inputs, technology transfers accompanying foreign direct investment, learning-by-exporting effects, etc. The empirical literature on these issues is vast. A number of empirical works have resorted to firm and plant-level panel data to see whether the predicted gains from trade liberalization have materialized in some recent episodes of drastic trade reform in the developing world and/or to see whether productivity 7
8 growth has been a result of increasing international integration and exposure in developed countries. Most of these studies find that trade reform in developing countries was indeed accompanied by productivity growth, technology advancement, falling mark-ups and a reshuffling of resources toward the more efficient firms, although in some cases the evidence may fail to convince because of the hurdles involved in the methodology used in these studies (see, among others, Tybout (2003) which reviews the plant-level evidence in the light of the new trade theory, Bernard and Jensen (1999), Clerides, Lach and Tybout (1998), Pavcnik (2002)). With this in mind, we suppose that the firm technology exhibits constant returns to scale with external economies generated by sectoral international exposure g and also by sectoral output y. We also allow for exogenous technical change captured by a time trend t : q = f (k,l; y, g, t), (3.1) Given the property of constant returns to scale at the firm level, the sectoral production function is just the firm production function f with the aggregate sectoral variables as arguments and it is implicitely defined by y = f (k,l; y, g, t) (3.2) (see Bruno (2004) and the references threin). We suppose that f is invertible in y so that an equivalent form of the sectoral production function in (3.2) is the following y = F (k, l; g, t). We also suppose F homothetic. For given g and y the optimal aggregate input demands l and k must satisfy the following cost minimisation problem: min [wl + rk : y = F (k, l; g, t)] (3.3) l,k We assume that the following labour demand equation emerges as a solution of problem (3.3). ln l = β w + β wg ln g + β wt ln t ln (w/r)+β y ln y + β g ln g + u +, (3.4) 8
9 where β y, β w, β wg, β wt,β g and β x are constant parameters. The parameter β g measures the impact of g as a demand shifter, whereas β wg and β wt measure the impact of g and the time trend t on the relative wage elasticity of the labour demand function, which is given by ε lw ln l ln w = β w + β wg ln g + β wt ln t. (3.5) In equilibrium, sectoral international exposure g may influence labour s own price elasticity, as well as bring about a direct effectonlabourdemandactingas a demand shifter. To correctly interpret parameter estimates it is important to establish the exact relationship between the parameters of the labour demand equation (3.4) and those of the underlying production function. Details on the recovering of the production function from (3.4) are shown in appendix. Basically, we first retrieve the underlying cost function by integrating (3.4), and then we obtain the following production function from the cost function by duality: µ 1 y = e u+ g β g 1 β y µ εlw 1+ε lw ε lw βy (k) ε lw βy (l) 1+ε lw β y. (3.6) From (3.6) it is clear that for equation (3.4) to be theoretically consistent with both cost minimizing behaviour (requiring a downward sloping labour demand curve) and a regular production function (requiring a non negative labour marginal productivity) the regularity condition ε lw [ 1, 0] must hold. Function (3.6) is homothetic of degree 1/β y and has a restricted translog form, with a variable technical efficiency given by µ 1 A = e u+ g β g 1 β y µ εlw ε lw βy. (3.7) 1+ε lw A depends on international exposure g, the stochastic shock, and labour demand elasticity ε lw.ifβ wg =0,thenA reduces to the expression for technical efficiency in Greenaway et al. (1999). Implementing this model empirically we can test for the presence of globalization effectsinthelabourdemandequationasbrokendowninto1)therodrik s conjecture that β wg < 0, that is international exposure has a positive impact on ε lw ; and 2) a globalization s direct effectonlabourdemandasmeasuredbyβ g (Greenaway et al., 1999). We can also test for the presence of output generated scale economies, which implies 0 <β y < 1. 9
10 4. Data Description Our panel data set comes from the STAN database, a data set compiled by the OECD and containing internationally comparable data. The industries are grouped using the standard ISIC Revision 2 classification 4. The data set originally covered a panel of 40 manufacturing industries in the period across countries. Missing observations for some of the regression variables along with the loss of the first observation when taking lags, however, make the estimation sample unbalanced, reducing to N = 31 sectors (we lose Drugs; Chemicals; Office & Computing Machinery; Machinery & Equipment; Electrical Apparatus; Railroad Equipment; Motorcycles & Bicycles; Transport Equipment) with an average group size of T = 24. Unbalancedness is not severe, as evidenced from the computation of the Ahrens and Pincus index of unbalancedness ω = 0.99, where " # NX ω = N/ T (1/T i ), i=1 with 0 < ω 1 and ω = 1 when the panel is balanced (see Bruno (2005)). Nevertheless, balancing the data would have caused the loss of one further crosssection, namely Radio, TV & Communication Equipment, which we can avoid by using the appropriate estimation techniques. The variables used in the empirical work are the following 5. Our dependent variable l is measured as number engaged (NE). The output variable y is proxied by Value Added in constant 1990 prices (VA90). Relative wage of domestic labour w is constructed as follows: 1) we obtain average remuneration of labour by taking the ratio of total labour cost to number engaged; 2) we divide this variable by the price of capital p which is proxied by the value added deflator. As a proxy for international integration, g, we utilize the share of import over value added 6. The choice of this proxy to measure international integration is motivated by our focus on the substitution effect s component of the labour demand elasticity. In fact, import penetration might well represent, at the same time, a measure of substitution possibilities in production due to the availability of a larger variety 4 Details concerning the industry description and the ISIC rev.2 code are given in Table 1. 5 Table 2 provides definitions for the variables of the STAN database that have been used in the empirical implementation as given in the OECD STAN database manual, as well as the variable codes used in the regression analysis. 6 Further details regarding the construction of these variables are given in Table 3. 10
11 of inputs and a measure of the competitive pressure coming from the international markets. Figures 1 and 2 taken from Bruno, Falzoni and Helg (2004) provide a first picture of the issue under analysis for some OECD countries. In the last decades a generalised reduction in the demand for labour paralleled the developments in the international openness. Employment in the manufacturing industry has been decreasing, in the face of an increasing integration into the world economy, although the correlation between the two phenomena is not high for Italy. 5. Estimation results Our econometric model is based upon equation(3.4). Let N denote the number of sectors and T the largest group size in the panel. We accommodate sector heterogeneity by allowing u to vary across sectors. Since data on r are not available we proxy it by a complete set of time dummies, based on the assumption that the price of capital does not vary across sectors, as it would happen in the presence of perfect capital markets. The time trend interacted with ln w allows for autonomous variations in labour demand elasticity. Time dummies and the interacted trend should also capture the effect of exogenous technical change. Thus, our empirical baseline equation is as follows z it ln l i,t = z it βw + β wg ln g i,t + β wt ln t i,t ln wi,t + β y ln y i,t (5.1) # XT 1 +β g ln g i,t + β t d t + u i + i,t, t=1 where z it is the static selection rule, t =1,..., T, i =1,..., N. Equation (5.1) is static in nature, so it fails to incorporate labour adjustment cost. This is can be taken into account by including the lagged dependent variable into the right hand side of the baseline equation and replacing the static selection rule z it with the dynamic selection rule s it derived from z it as in Section 2 : s it ln l i,t = s it γ ln li,t 1 + β w + β wg ln g i,t + β wt ln t i,t ln wi,t (5.2) # XT 1 +β y ln y i,t + β g ln g i,t + β t d t + u i + i,t, t =1,..., T, i =1,..., N. t=1 11
12 In the empirical application our focus is on the long-run wage elasticity, which depends on ln g, lnt and the long-run parameters according to the following formula 7 : β j = β j / (1 γ),j = w, wg, wt. (5.3) ε lwi,t β w + β wg ln g + β wt ln t. The simple long-run estimator obtained by using the bias-corrected LSDV estimator for the β s into equation (5.3) is not unbiased to order O(T 1 )aspointed out by Bun (2001). Therefore, to estimate the long-run coefficients we adopt the estimator proposed by Bun (2001), based upon Pesaran and Zhao (1999), which is a more appropriate transformation of the bias-corrected LSDV short run estimator. Finally, since analytic expressions for the standard errors of all corrected estimators typically turns out to be very inaccurate, we estimate them by using parametric bootstrap resampling schemes, as proposed in Bun and Kiviet (2001) and Bun (2001) 8. Tables 4 to 7 present estimation results for equation (5.2). Table 4 reports results for all possible bias-corrected LSDV estimators, based on bias approximations B b 1 B2 b and B b 3 and initial estimators AH and AB, as explained in Section 2. For the sake of comparison, Tables 5 and 6 reports results for two different GMM estimators, respectively with strictly exogenous and predetermined regressors. In either case the number of GMM instruments is taken to a minimum to not exacerbate the small-sample bias 9. Results for the uncorrected LSDV are reported in Table 7. Overall, our estimates are statistically and economically satisfactory with all regularity conditions satisfied. Results for the bias-corrected LSDV estimators are robust to changes in the order of the bias approximations and to different choices 7 To avoid that ε lw become too large in absolute value when g is close to zero, the globalization index g is normalized so that g 1. 8 All estimation work has been carried out in STATA 9 using for the bias-corrected LSDV estimators the user-written code XTLSDVC by Bruno (2005c) downloadable from 9 GMM estimation has been carried out in Stata 9 using the user-written code XTABOND2 by David Roodman (2005). 12
13 of the N-consistent estimator used to initialize the bias correction. In the GMM regressions the null hypothesis of no-second order correlation in the disturbances of the first-differenced equation is never rejected at any conventional level of significance. The estimated coefficient on the one-time lagged employment level is always significantly greater than zero and smaller than unity providing evidence of significant adjustment costs. Our dynamic framework allows estimation of both short and long run constant output labour demand elasticities. Estimates are always plausible. The mean value of the long run elasticity is for all countries within the range estimates of other studies surveyed by Hamermesh (2000) and is relatively robust to changes in estimation method. Moreover, all point estimates for the various sectors are negative. What is the role of increasing international integration? In our framework this effect can work on labour demand through two channels: the direct effect and the effect via elasticity (Rodrik s conjecture). The Rodrik s conjecture is decidedly rejected for all estimators used (bias-corrected and GMM), which confirms the results for Italy in Bruno, Falzoni and Helg (2004) and also those obtained by Slaughter (2001) for the US, by Krishna et al. (2001) for Turkey and Fajnzylber and Maloney (2001) for a group of Latin American less developed countries. Fourth, differently from what found in Bruno, Falzoni and Helg (2004) the direct effect of globalization on labour demand is never found significant. This discrepancy may be due to the neglected sector in Bruno, Falzoni and Helg (2004) where a significantly positive direct effect has been found in the bias corrected regressions. Finally, we find robust evidence in favour of output generated external economies. 6. Conclusions This paper has estimated a dynamic labour demand equation for an unbalanced panel data set of Italian manufacturing sectors. We have used both bias-corrected LSDV estimators and GMM estimators. Our findings are substantially robust to changes in the estimator adopted. While we do not find support for either the Rodrik s conjecture or the presence of a direct globalization effect in the labour demand equation, we can provide robust evidence in favour of output generated external economies. Long run and short run estimated elasticities are always plausible in both an economics and statistics sense. 13
14 References [1] Ahn, S.C. and P. Schimdt, (1995), Efficient Estimation of Models for Dynamic Panel Data, Journal of Econometrics, 68, [2] Arellano, M. and S. Bond, (1991), Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations, Review of Economic Studies, 58, [3] Blundell, R.W. and S.R. Bond, (1998), Initial Conditions and Moment Restrictions in Dynamic Panel Data Models, Journal of Econometrics, 87, [4] Bruno, G.S.F. (2005a). Approximating the bias of the LSDV estimator for dynamic unbalanced panel data models. Economics Letters, 87, [5] Bruno, G.S.F. (2005b) Estimation and inference in dynamic unbalanced panel data models with a small number of individuals. CESPRI WP n.165,università Bocconi-CESPRI, Milan. [6] Bruno, G.S.F. (2005c) XTLSDVC: Stata module to estimate bias corrected LSDV dynamic panel data models, Statistical Software Components S450101, Boston College Department of Economics. [7] Bruno, G.S.F. (2004). On the Equivalence of Two Concepts of Returns to Scale. Bulletin of Economic Research, 56, [8] Bruno, G.S.F., Falzoni A.M. and R. Helg (2004), Measuring the effect of globalization on labor demand elasticity: An empirical application to some OECD countries, w.p. CESPRI n. 153, Università Bocconi-CESPRI, Milano. [9] Bun, M.J.G. (2001) Bias Correction in the Dynamic Panel Data Model with a Nonscalar Disturbance Covariance Matrix Tinbergen Institute Discussion Paper TI /4. [10] Bun, M.J.G. and J.F. Kiviet, (2001), The accuracy of inference in small samples of dynamic data models, Tinbergen Institute D.P. 006/4. [11] Bun, M.J.G. and J.F Kiviet (2003) On the diminishing returns of higher order terms in asymptotic expansions of bias Economics Letters, 79,
15 [12] Coe, D. and E. Helpman, (1995), International R&D spillovers, European Economic Review, 39, [13] Faini, R., A.M. Falzoni, M. Galeotti, R. Helg and A. Turrini, (1999), Importing jobs and exporting firms? On the wage and employment implications of Italian trade and foreign direct investment flows, Giornale degli Economisti ed Annali di Economia, 58 (1), [14] Fajnzylber, P. and W. Maloney, (2001), Labour demand and trade reform in Latin America, World Bank Working Paper No. 2491, January. [15] Feenstra, R. and G. Hanson, (2001), Global production sharing and rising inequality: A survey of trade and wages, NBER W.P. 8372, July. [16] Greenaway, D., R.C. Hine and P.Wright, (1999), An empirical assessment of the impact of trade on employment in the United Kingdom, European Journal of Political Economy, 15, [17] Hamermesh, D.S., (1993), Labor Demand, Princeton University Press, Princeton. [18] Hamermesh, D.S., (2000), Demand for labor, in International Encyclopaedia of the Social & Behavioural Sciences [19] Harris, M.N., and L. Matyas, (2000), A comparative analysis of different estimators for dynamic panel data models, mimeo. [20] Jean, S., (2000), The effect of international trade on labour-demand elasticities: intersectoral matters, Review of International Economics, 8(3), [21] Kiviet, J.F., (1995), On bias, inconsistency and efficiency of various estimators in dynamic panel data models, Journal of Econometrics, 68, [22] Kiviet, J.F. (1999), Expectation of Expansions for Estimators in a Dynamic Panel Data Model; Some Results for Weakly Exogenous Regressors in C. Hsiao, K. Lahiri, L-F Lee and M.H. Pesaran (eds.), Analysis of Panel Data and Limited Dependent Variables, Cambridge University Press, Cambridge. [23] Krishna, P., D. Mitra and S. Chinoy, (2001), Trade liberalization and labour demand elasticities: evidence from Turkey, Journal of International Economics, 55,
16 [24] Nickell, S.J., (1981), Biases in Dynamic Models with Fixed Effects, Econometrica, 49, [25] Panagariya, A., (1999), Trade openness: consequences for the elasticity of demand for labor and wage outcomes, mimeo. [26] Pesaran, M.H. and Z. Zhao (1999), Bias Reduction in Estimating Long-run Relationships from Dynamic Heterogeneous Panels in C. Hsiao, K. Lahiri, L-F Lee and M.H. Pesaran (eds.), Analysis of Panel Data and Limited Dependent Variables, Cambridge University Press, Cambridge. [27] Rauch, J.E. and V. Trindade, (2003), Information, International Substitutability and Globalisation, American Economic Review, 93, [28] Rodrik, D., (1997), Has globalisation gone too far?, Institute for International Economics, Washington DC. [29] Roodman, D. (2003). XTABOND2: Stata module to extend xtabond dynamic panel data estimator, Statistical Software Components S435901, Boston College Department of Economics, revised 22 Apr [30] Slaughter, M.J., (2001), International trade and labor-demand elasticities, Journal of International Economics, 54,
17 Appendix A Basically, we first retrieve the underlying cost function by integrating (3.4), and then we obtain the production function from the cost function by duality. For simplicity, we limit to a specification with no time trend in the labour demand equation and let r =1. The first step of the derivation is straightforward. From Shephard s Lemma and (3.4) we have C w = l = eu+ y β y x β xg β gw β w +β wg ln g, and so the (normalized) cost function must have the following restricted translog form: C = Z w 0 e u+ y β y x β xg β gω β w +β wg ln g dω = eu+ y β y x β xg β g β w + β wg ln g +1 wβ w +β wg ln g+1. (6.1) It is a restricted form in that the interaction term between output and wage and the squared wage do not enter the cost function specification. The second step goes as follows. Singling out w in l = e u+ y β y x β xg β gw β w +β wg ln g. yields µ l w = e u+ y β y x β x g β g Since C is a normalized cost function, we can write 1/(βw +β wg ln g). (6.2) C = wl + k. (6.3) Thus, substituting for C from (6.1) and for w from (6.2) into (6.3) gives µ 1/(βw +β l wg ln g) µ l+k = eu+ y β y x β xg β g 1+ 1 l β w +β wg ln g e u+ y β y x β x g β g β w + β wg ln g +1 e u+ y β y x β, x g β g (6.4) which, after rearrangement and substituting for β w +β wg ln g from (3.5), gives the desired production function. µ 1 y = e u+ x β xg β g 1 β y µ εlw 1+ε lw 17 ε lw βy (k) ε lw βy (l) 1+ε lw β y.
18 By taking equation (3.7) in logarithms and then differentiating it with respect to ln g, we obtain the elasticity of A with respect to g ε Ag = β g + β µ wg εlw 1 ln +. (6.5) β y β y ε lw +1 ε lw +1 In Greenaway s case of β wg =0,ε Ag reduces to the constant parameter β g /β y, with g acting on the isoquant mapping as Hicks-neutral technical change. Thus, in our formulation (6.5) ε Ag must be thought of as generalized technical efficiency effect. Unlike β y and ε lw, there are no theoretical restrictions on the sign of ε Ag, whichinturndependsonthesignofβ g and β wg andthesizeandsignofε lw. Notice that the presence of β g ensures enough flexibility to cover all possible relevant economic instances. For example, should we restrict ourselves to β g =0, then in the presence of a negative impact of g on ε lw (β wg 0), a positive impact of g on technical efficiency (ε Ag 0) would be possible only for ε lw [0, 1/2]. On the other hand, if β g is free to assume any value, then β wg 0andε Ag 0, as well as any other combination of signs, can be compatible with any plausible ε lw. Theeconomicinterpretationofβ g parallels that of β w,inthatβ g is the intercept of the labour elasticity with respect to g. In fact ε lg ln l ln g = β g + β wg ln w. As such, β g measures the responsiveness of labour demand to g at w =1,thatis when the economic rate of substitution (w) is 1. 18
19 Table 1 - Industry Codes, Definitions and Labels ISIC Revision 2 Industry Description Industry Labels* 311/2 Food fod 3130 Beverages bev 3140 Tobacco tob 3210 Textiles tex 3220 Wearing Apparel wear 3230 Leather & Products leather 3240 Footwear foot 3310 Wood Products wood 3320 Furniture & Fixtures furn 3410 Paper & Products pap 3420 Printing & Publishing print 3510 Industrial Chemicals indche 3520 Other Chemicals DRUGS&CHE 3522 Drugs & Medicines drugs 3520 less 3522 Chemical Products n.e.c.** che 3530 Petroleum Refineries petref 3540 Petroleum & Coal Products petcoal 3530 and 3540 Petroleum Refineries & Products REF&COAL 3550 Rubber Products rub 3560 Plastic Products, n.e.c. plas 3610 Pottery, China etc. pot 3620 Glass & Products glass 3690 Non-Metallic Products, n.e.c. nmetp 3710 Iron & Steel festeel 3720 Non-Ferrous Metals nferm 3810 Metal Products met 3820 Non-Electrical Machinery OECOMP&MAEQUIP 3825 Office & Computing Machinery ocomp 3820 less 3825 Machinery & Equipment, n.e.c. maequi 3830 Electrical Machinery COMM&ELEC 3832 Radio, TV & Communication comm Equipment 3830 less 3832 Electrical Apparatus, n.e.c. elec 3841 Ship-Building & Repairing ship 3842 Railroad Equipment rail 3843 Motor Vehicles moto 3844 Motorcycles & Bicycles mcycles 3845 Aircraft air 3849 Transport Equipment, n.e.c. transp 3842 and 3844 and 3849 Railroad Equipment, Motorcycles & Bicycles, Transport Equipment, n.e.c Professional Goods prof 3900 Other Manufacturing, n.e.c. other RAIL&MCYCLES& TRANS * These regression codes refer to the labels that have been attributed to the different industries in the empirical work. ** n.e.c. stands for not elsewhere classified. 19
20 Table 2 - STAN Variables: Definitions Variable Regression STAN Definition Code Value Added VA This represents the contribution of each industry to national GDP in current prices Value Added 1990 VA90 This represents the contribution of each industry to national GDP in constant 1990 prices Number Engaged NE This includes the number of employees as well as self-employed, owner proprietors, and unpaid family workers Labour Compensation COMP Current price national accounts compatible labour costs which include wages as well as the costs of supplements such as employer s compulsory pension or medical payments Imports, Exports IMP, EXP These represent imports and exports in current prices. Table 3 - Variables Variable Description P90, value added deflator VA/VA90 Wnom, average remuneration of COMP/NE labour W90, average remuneration price Wnom/value taken by Wnom in 1990 index w, relative remuneration of labour W90/P90 g IMP/VA 20
21 Figure 1 - MANUFACTURING EMPLOYMENT IN OECD COUNTRIES (Logarithms) Japan France Italy United states Spain Sweden United Kingdom Source: OECD, STAN Database. 21
22 Figure 2 - IMPORT PENETRATION IN OECD COUNTRIES (Logarithms) Japan France Italy United States Spain Sweden United Kingdom Source: OECD, STAN Database. 22
23 tm / / / table1.txt / / / / / / / / / Statistics/Data Analysis - TABLE 4: BIAS CORRECTED LSDV ESTIMATORS Bias correction initialized by Anderson and Hsiao estimator Bias correction up to order O(1/T) LSDVC dynamic regression (bootstrapped SE) short_run LnNE L Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Pagina 1
24 table1.txt Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ long_run Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Pagina 2
25 table1.txt Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ long_run_el short_run_el Bias correction up to order O(1/NT) LSDVC dynamic regression (bootstrapped SE) short_run LnNE L Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Pagina 3
26 table1.txt Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ long_run Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Pagina 4
27 table1.txt Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ long_run_el short_run_el Pagina 5
28 table1.txt Bias correction up to order O(1/NT^2) LSDVC dynamic regression (bootstrapped SE) short_run LnNE L Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Pagina 6
29 table1.txt Iyear_ Iyear_ Iyear_ long_run Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Pagina 7
30 table1.txt long_run_el short_run_el Bias correction initialized by Arellano and Bond estimator Bias correction up to order O(1/T) LSDVC dynamic regression (bootstrapped SE) short_run LnNE L Lnw Lng Lng2w LnGDP Lnyearw Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Iyear_ Pagina 8
HOMEWORK 4 = G. In order to plot the stress versus the stretch we define a normalized stretch:
HOMEWORK 4 Problem a For the fast loading case, we want to derive the relationship between P zz and λ z. We know that the nominal stress is expressed as: P zz = ψ λ z where λ z = λ λ z. Therefore, applying
Διαβάστε περισσότερα2 Composition. Invertible Mappings
Arkansas Tech University MATH 4033: Elementary Modern Algebra Dr. Marcel B. Finan Composition. Invertible Mappings In this section we discuss two procedures for creating new mappings from old ones, namely,
Διαβάστε περισσότεραCHAPTER 25 SOLVING EQUATIONS BY ITERATIVE METHODS
CHAPTER 5 SOLVING EQUATIONS BY ITERATIVE METHODS EXERCISE 104 Page 8 1. Find the positive root of the equation x + 3x 5 = 0, correct to 3 significant figures, using the method of bisection. Let f(x) =
Διαβάστε περισσότεραEE512: Error Control Coding
EE512: Error Control Coding Solution for Assignment on Finite Fields February 16, 2007 1. (a) Addition and Multiplication tables for GF (5) and GF (7) are shown in Tables 1 and 2. + 0 1 2 3 4 0 0 1 2 3
Διαβάστε περισσότεραΧρηματοοικονομική Ανάπτυξη, Θεσμοί και
ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ, ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ Τομέας Ανάπτυξης και Προγραμματισμού Χρηματοοικονομική Ανάπτυξη, Θεσμοί και Οικονομική
Διαβάστε περισσότεραOther Test Constructions: Likelihood Ratio & Bayes Tests
Other Test Constructions: Likelihood Ratio & Bayes Tests Side-Note: So far we have seen a few approaches for creating tests such as Neyman-Pearson Lemma ( most powerful tests of H 0 : θ = θ 0 vs H 1 :
Διαβάστε περισσότεραStatistical Inference I Locally most powerful tests
Statistical Inference I Locally most powerful tests Shirsendu Mukherjee Department of Statistics, Asutosh College, Kolkata, India. shirsendu st@yahoo.co.in So far we have treated the testing of one-sided
Διαβάστε περισσότεραHomework 3 Solutions
Homework 3 Solutions Igor Yanovsky (Math 151A TA) Problem 1: Compute the absolute error and relative error in approximations of p by p. (Use calculator!) a) p π, p 22/7; b) p π, p 3.141. Solution: For
Διαβάστε περισσότεραderivation of the Laplacian from rectangular to spherical coordinates
derivation of the Laplacian from rectangular to spherical coordinates swapnizzle 03-03- :5:43 We begin by recognizing the familiar conversion from rectangular to spherical coordinates (note that φ is used
Διαβάστε περισσότεραST5224: Advanced Statistical Theory II
ST5224: Advanced Statistical Theory II 2014/2015: Semester II Tutorial 7 1. Let X be a sample from a population P and consider testing hypotheses H 0 : P = P 0 versus H 1 : P = P 1, where P j is a known
Διαβάστε περισσότεραΑπόκριση σε Μοναδιαία Ωστική Δύναμη (Unit Impulse) Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο. Απόστολος Σ.
Απόκριση σε Δυνάμεις Αυθαίρετα Μεταβαλλόμενες με το Χρόνο The time integral of a force is referred to as impulse, is determined by and is obtained from: Newton s 2 nd Law of motion states that the action
Διαβάστε περισσότεραEvery set of first-order formulas is equivalent to an independent set
Every set of first-order formulas is equivalent to an independent set May 6, 2008 Abstract A set of first-order formulas, whatever the cardinality of the set of symbols, is equivalent to an independent
Διαβάστε περισσότεραSection 8.3 Trigonometric Equations
99 Section 8. Trigonometric Equations Objective 1: Solve Equations Involving One Trigonometric Function. In this section and the next, we will exple how to solving equations involving trigonometric functions.
Διαβάστε περισσότεραLecture 34 Bootstrap confidence intervals
Lecture 34 Bootstrap confidence intervals Confidence Intervals θ: an unknown parameter of interest We want to find limits θ and θ such that Gt = P nˆθ θ t If G 1 1 α is known, then P θ θ = P θ θ = 1 α
Διαβάστε περισσότεραCite as: Pol Antras, course materials for International Economics I, Spring MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts
/ / σ/σ σ/σ θ θ θ θ y 1 0.75 0.5 0.25 0 0 0.5 1 1.5 2 θ θ θ x θ θ Φ θ Φ θ Φ π θ /Φ γφ /θ σ θ π θ Φ θ θ Φ θ θ θ θ σ θ / Φ θ θ / Φ / θ / θ Normalized import share: (Xni / Xn) / (XII / XI) 1 0.1 0.01 0.001
Διαβάστε περισσότεραSupplementary Appendix
Supplementary Appendix Measuring crisis risk using conditional copulas: An empirical analysis of the 2008 shipping crisis Sebastian Opitz, Henry Seidel and Alexander Szimayer Model specification Table
Διαβάστε περισσότεραMath221: HW# 1 solutions
Math: HW# solutions Andy Royston October, 5 7.5.7, 3 rd Ed. We have a n = b n = a = fxdx = xdx =, x cos nxdx = x sin nx n sin nxdx n = cos nx n = n n, x sin nxdx = x cos nx n + cos nxdx n cos n = + sin
Διαβάστε περισσότεραMath 6 SL Probability Distributions Practice Test Mark Scheme
Math 6 SL Probability Distributions Practice Test Mark Scheme. (a) Note: Award A for vertical line to right of mean, A for shading to right of their vertical line. AA N (b) evidence of recognizing symmetry
Διαβάστε περισσότερα4.6 Autoregressive Moving Average Model ARMA(1,1)
84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραJesse Maassen and Mark Lundstrom Purdue University November 25, 2013
Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering
Διαβάστε περισσότεραNotes on the Open Economy
Notes on the Open Econom Ben J. Heijdra Universit of Groningen April 24 Introduction In this note we stud the two-countr model of Table.4 in more detail. restated here for convenience. The model is Table.4.
Διαβάστε περισσότεραRisk! " #$%&'() *!'+,'''## -. / # $
Risk! " #$%&'(!'+,'''## -. / 0! " # $ +/ #%&''&(+(( &'',$ #-&''&$ #(./0&'',$( ( (! #( &''/$ #$ 3 #4&'',$ #- &'',$ #5&''6(&''&7&'',$ / ( /8 9 :&' " 4; < # $ 3 " ( #$ = = #$ #$ ( 3 - > # $ 3 = = " 3 3, 6?3
Διαβάστε περισσότεραApproximation of distance between locations on earth given by latitude and longitude
Approximation of distance between locations on earth given by latitude and longitude Jan Behrens 2012-12-31 In this paper we shall provide a method to approximate distances between two points on earth
Διαβάστε περισσότεραCSAE WPS/2009-06 Figure 1: Cut Flower Exports from Kenya, 1995-2007 Table 1: Firms in Areas with and w/out Conflict Panel A - Export Records Variable Observations Mean in No-Conflict
Διαβάστε περισσότεραPartial Differential Equations in Biology The boundary element method. March 26, 2013
The boundary element method March 26, 203 Introduction and notation The problem: u = f in D R d u = ϕ in Γ D u n = g on Γ N, where D = Γ D Γ N, Γ D Γ N = (possibly, Γ D = [Neumann problem] or Γ N = [Dirichlet
Διαβάστε περισσότεραC.S. 430 Assignment 6, Sample Solutions
C.S. 430 Assignment 6, Sample Solutions Paul Liu November 15, 2007 Note that these are sample solutions only; in many cases there were many acceptable answers. 1 Reynolds Problem 10.1 1.1 Normal-order
Διαβάστε περισσότεραAssalamu `alaikum wr. wb.
LUMP SUM Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. Assalamu `alaikum wr. wb. LUMP SUM Wassalamu alaikum wr. wb. LUMP SUM Lump sum lump sum lump sum. lump sum fixed price lump sum lump
Διαβάστε περισσότεραPhys460.nb Solution for the t-dependent Schrodinger s equation How did we find the solution? (not required)
Phys460.nb 81 ψ n (t) is still the (same) eigenstate of H But for tdependent H. The answer is NO. 5.5.5. Solution for the tdependent Schrodinger s equation If we assume that at time t 0, the electron starts
Διαβάστε περισσότεραThe Simply Typed Lambda Calculus
Type Inference Instead of writing type annotations, can we use an algorithm to infer what the type annotations should be? That depends on the type system. For simple type systems the answer is yes, and
Διαβάστε περισσότεραΜηχανική Μάθηση Hypothesis Testing
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Μηχανική Μάθηση Hypothesis Testing Γιώργος Μπορμπουδάκης Τμήμα Επιστήμης Υπολογιστών Procedure 1. Form the null (H 0 ) and alternative (H 1 ) hypothesis 2. Consider
Διαβάστε περισσότεραHomework 8 Model Solution Section
MATH 004 Homework Solution Homework 8 Model Solution Section 14.5 14.6. 14.5. Use the Chain Rule to find dz where z cosx + 4y), x 5t 4, y 1 t. dz dx + dy y sinx + 4y)0t + 4) sinx + 4y) 1t ) 0t + 4t ) sinx
Διαβάστε περισσότεραSection 7.6 Double and Half Angle Formulas
09 Section 7. Double and Half Angle Fmulas To derive the double-angles fmulas, we will use the sum of two angles fmulas that we developed in the last section. We will let α θ and β θ: cos(θ) cos(θ + θ)
Διαβάστε περισσότεραMatrices and Determinants
Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z
Διαβάστε περισσότεραLecture 2. Soundness and completeness of propositional logic
Lecture 2 Soundness and completeness of propositional logic February 9, 2004 1 Overview Review of natural deduction. Soundness and completeness. Semantics of propositional formulas. Soundness proof. Completeness
Διαβάστε περισσότεραQueensland University of Technology Transport Data Analysis and Modeling Methodologies
Queensland University of Technology Transport Data Analysis and Modeling Methodologies Lab Session #7 Example 5.2 (with 3SLS Extensions) Seemingly Unrelated Regression Estimation and 3SLS A survey of 206
Διαβάστε περισσότερα6.1. Dirac Equation. Hamiltonian. Dirac Eq.
6.1. Dirac Equation Ref: M.Kaku, Quantum Field Theory, Oxford Univ Press (1993) η μν = η μν = diag(1, -1, -1, -1) p 0 = p 0 p = p i = -p i p μ p μ = p 0 p 0 + p i p i = E c 2 - p 2 = (m c) 2 H = c p 2
Διαβάστε περισσότεραAreas and Lengths in Polar Coordinates
Kiryl Tsishchanka Areas and Lengths in Polar Coordinates In this section we develop the formula for the area of a region whose boundary is given by a polar equation. We need to use the formula for the
Διαβάστε περισσότεραFigure A.2: MPC and MPCP Age Profiles (estimating ρ, ρ = 2, φ = 0.03)..
Supplemental Material (not for publication) Persistent vs. Permanent Income Shocks in the Buffer-Stock Model Jeppe Druedahl Thomas H. Jørgensen May, A Additional Figures and Tables Figure A.: Wealth and
Διαβάστε περισσότεραConcrete Mathematics Exercises from 30 September 2016
Concrete Mathematics Exercises from 30 September 2016 Silvio Capobianco Exercise 1.7 Let H(n) = J(n + 1) J(n). Equation (1.8) tells us that H(2n) = 2, and H(2n+1) = J(2n+2) J(2n+1) = (2J(n+1) 1) (2J(n)+1)
Διαβάστε περισσότεραΔΘΝΗΚΖ ΥΟΛΖ ΓΖΜΟΗΑ ΓΗΟΗΚΖΖ
Ε ΔΘΝΗΚΖ ΥΟΛΖ ΓΖΜΟΗΑ ΓΗΟΗΚΖΖ Κ ΔΚΠΑΗΓΔΤΣΗΚΖ ΔΗΡΑ ΣΜΖΜΑ : Σνπξηζηηθήο Οηθνλνκίαο θαη Αλάπηπμεο (ΣΟΑ) ΣΔΛΗΚΖ ΔΡΓΑΗΑ Θέκα: Σνπξηζκφο θαη Οηθνλνκηθή Κξίζε Δπηβιέπσλ : Νηνχβαο Λνπθάο πνπδάζηξηα : Σζαγθαξάθε
Διαβάστε περισσότεραΚΥΠΡΙΑΚΗ ΕΤΑΙΡΕΙΑ ΠΛΗΡΟΦΟΡΙΚΗΣ CYPRUS COMPUTER SOCIETY ΠΑΓΚΥΠΡΙΟΣ ΜΑΘΗΤΙΚΟΣ ΔΙΑΓΩΝΙΣΜΟΣ ΠΛΗΡΟΦΟΡΙΚΗΣ 19/5/2007
Οδηγίες: Να απαντηθούν όλες οι ερωτήσεις. Αν κάπου κάνετε κάποιες υποθέσεις να αναφερθούν στη σχετική ερώτηση. Όλα τα αρχεία που αναφέρονται στα προβλήματα βρίσκονται στον ίδιο φάκελο με το εκτελέσιμο
Διαβάστε περισσότερα1 1 1 2 1 2 2 1 43 123 5 122 3 1 312 1 1 122 1 1 1 1 6 1 7 1 6 1 7 1 3 4 2 312 43 4 3 3 1 1 4 1 1 52 122 54 124 8 1 3 1 1 1 1 1 152 1 1 1 1 1 1 152 1 5 1 152 152 1 1 3 9 1 159 9 13 4 5 1 122 1 4 122 5
Διαβάστε περισσότεραSecond Order RLC Filters
ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor
Διαβάστε περισσότερα6.3 Forecasting ARMA processes
122 CHAPTER 6. ARMA MODELS 6.3 Forecasting ARMA processes The purpose of forecasting is to predict future values of a TS based on the data collected to the present. In this section we will discuss a linear
Διαβάστε περισσότεραDémographie spatiale/spatial Demography
ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΙΑΣ Démographie spatiale/spatial Demography Session 1: Introduction to spatial demography Basic concepts Michail Agorastakis Department of Planning & Regional Development Άδειες Χρήσης
Διαβάστε περισσότεραChapter 6: Systems of Linear Differential. be continuous functions on the interval
Chapter 6: Systems of Linear Differential Equations Let a (t), a 2 (t),..., a nn (t), b (t), b 2 (t),..., b n (t) be continuous functions on the interval I. The system of n first-order differential equations
Διαβάστε περισσότεραExample Sheet 3 Solutions
Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note
Διαβάστε περισσότεραTMA4115 Matematikk 3
TMA4115 Matematikk 3 Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet Trondheim Spring 2010 Lecture 12: Mathematics Marvellous Matrices Andrew Stacey Norges Teknisk-Naturvitenskapelige Universitet
Διαβάστε περισσότεραDERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C
DERIVATION OF MILES EQUATION FOR AN APPLIED FORCE Revision C By Tom Irvine Email: tomirvine@aol.com August 6, 8 Introduction The obective is to derive a Miles equation which gives the overall response
Διαβάστε περισσότεραΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 7η: Consumer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Τέλος Ενότητας Χρηματοδότηση Το παρόν εκπαιδευτικό υλικό έχει αναπτυχθεί
Διαβάστε περισσότεραSCHOOL OF MATHEMATICAL SCIENCES G11LMA Linear Mathematics Examination Solutions
SCHOOL OF MATHEMATICAL SCIENCES GLMA Linear Mathematics 00- Examination Solutions. (a) i. ( + 5i)( i) = (6 + 5) + (5 )i = + i. Real part is, imaginary part is. (b) ii. + 5i i ( + 5i)( + i) = ( i)( + i)
Διαβάστε περισσότεραAppendix to Technology Transfer and Spillovers in International Joint Ventures
Appendix to Technology Transfer and Spillovers in International Joint Ventures Thomas Müller Monika Schnitzer Published in Journal of International Economics, 2006, Volume 68, 456-468 Bundestanstalt für
Διαβάστε περισσότεραPARTIAL NOTES for 6.1 Trigonometric Identities
PARTIAL NOTES for 6.1 Trigonometric Identities tanθ = sinθ cosθ cotθ = cosθ sinθ BASIC IDENTITIES cscθ = 1 sinθ secθ = 1 cosθ cotθ = 1 tanθ PYTHAGOREAN IDENTITIES sin θ + cos θ =1 tan θ +1= sec θ 1 + cot
Διαβάστε περισσότεραIMES DISCUSSION PAPER SERIES
IMES DISCUSSION PAPER SERIES Will a Growth Miracle Reduce Debt in Japan? Selahattin mrohorolu and Nao Sudo Discussion Paper No. 2011-E-1 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN 2-1-1
Διαβάστε περισσότεραInstruction Execution Times
1 C Execution Times InThisAppendix... Introduction DL330 Execution Times DL330P Execution Times DL340 Execution Times C-2 Execution Times Introduction Data Registers This appendix contains several tables
Διαβάστε περισσότεραΚόστος Κεφαλαίου. Estimating Inputs: Discount Rates
Αρτίκης Γ. Παναγιώτης Κόστος Κεφαλαίου Estimating Inputs: Discount Rates Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount
Διαβάστε περισσότερα22 .5 Real consumption.5 Real residential investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.5 Real house prices.5 Real fixed investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.3 Inflation
Διαβάστε περισσότεραSolution Series 9. i=1 x i and i=1 x i.
Lecturer: Prof. Dr. Mete SONER Coordinator: Yilin WANG Solution Series 9 Q1. Let α, β >, the p.d.f. of a beta distribution with parameters α and β is { Γ(α+β) Γ(α)Γ(β) f(x α, β) xα 1 (1 x) β 1 for < x
Διαβάστε περισσότεραTridiagonal matrices. Gérard MEURANT. October, 2008
Tridiagonal matrices Gérard MEURANT October, 2008 1 Similarity 2 Cholesy factorizations 3 Eigenvalues 4 Inverse Similarity Let α 1 ω 1 β 1 α 2 ω 2 T =......... β 2 α 1 ω 1 β 1 α and β i ω i, i = 1,...,
Διαβάστε περισσότερα3.4 SUM AND DIFFERENCE FORMULAS. NOTE: cos(α+β) cos α + cos β cos(α-β) cos α -cos β
3.4 SUM AND DIFFERENCE FORMULAS Page Theorem cos(αβ cos α cos β -sin α cos(α-β cos α cos β sin α NOTE: cos(αβ cos α cos β cos(α-β cos α -cos β Proof of cos(α-β cos α cos β sin α Let s use a unit circle
Διαβάστε περισσότεραPolicy Coherence. JEL Classification : J12, J13, J21 Key words :
** 80%1.89 2005 7 35 Policy Coherence JEL Classification : J12, J13, J21 Key words : ** Family Life and Family Policy in France and Germany: Implications for Japan By Tomoko Hayashi and Rieko Tamefuji
Διαβάστε περισσότεραEcon 2110: Fall 2008 Suggested Solutions to Problem Set 8 questions or comments to Dan Fetter 1
Eon : Fall 8 Suggested Solutions to Problem Set 8 Email questions or omments to Dan Fetter Problem. Let X be a salar with density f(x, θ) (θx + θ) [ x ] with θ. (a) Find the most powerful level α test
Διαβάστε περισσότεραPotential Dividers. 46 minutes. 46 marks. Page 1 of 11
Potential Dividers 46 minutes 46 marks Page 1 of 11 Q1. In the circuit shown in the figure below, the battery, of negligible internal resistance, has an emf of 30 V. The pd across the lamp is 6.0 V and
Διαβάστε περισσότεραSrednicki Chapter 55
Srednicki Chapter 55 QFT Problems & Solutions A. George August 3, 03 Srednicki 55.. Use equations 55.3-55.0 and A i, A j ] = Π i, Π j ] = 0 (at equal times) to verify equations 55.-55.3. This is our third
Διαβάστε περισσότεραInverse trigonometric functions & General Solution of Trigonometric Equations. ------------------ ----------------------------- -----------------
Inverse trigonometric functions & General Solution of Trigonometric Equations. 1. Sin ( ) = a) b) c) d) Ans b. Solution : Method 1. Ans a: 17 > 1 a) is rejected. w.k.t Sin ( sin ) = d is rejected. If sin
Διαβάστε περισσότεραProblem Set 3: Solutions
CMPSCI 69GG Applied Information Theory Fall 006 Problem Set 3: Solutions. [Cover and Thomas 7.] a Define the following notation, C I p xx; Y max X; Y C I p xx; Ỹ max I X; Ỹ We would like to show that C
Διαβάστε περισσότεραResearch on Economics and Management
36 5 2015 5 Research on Economics and Management Vol. 36 No. 5 May 2015 490 490 F323. 9 A DOI:10.13502/j.cnki.issn1000-7636.2015.05.007 1000-7636 2015 05-0052 - 10 2008 836 70% 1. 2 2010 1 2 3 2015-03
Διαβάστε περισσότεραCSAE Working Paper WPS/
CSAE Working Paper WPS/2016-04 China sexpansionofhighereducation:thelabourmarket ConsequencesofaSupplyShock JohnKnight 1,DengQuheng 2 andlishi 3 March2016 Centre for the Study of African Economies Department
Διαβάστε περισσότεραOn a four-dimensional hyperbolic manifold with finite volume
BULETINUL ACADEMIEI DE ŞTIINŢE A REPUBLICII MOLDOVA. MATEMATICA Numbers 2(72) 3(73), 2013, Pages 80 89 ISSN 1024 7696 On a four-dimensional hyperbolic manifold with finite volume I.S.Gutsul Abstract. In
Διαβάστε περισσότεραANSWERSHEET (TOPIC = DIFFERENTIAL CALCULUS) COLLECTION #2. h 0 h h 0 h h 0 ( ) g k = g 0 + g 1 + g g 2009 =?
Teko Classes IITJEE/AIEEE Maths by SUHAAG SIR, Bhopal, Ph (0755) 3 00 000 www.tekoclasses.com ANSWERSHEET (TOPIC DIFFERENTIAL CALCULUS) COLLECTION # Question Type A.Single Correct Type Q. (A) Sol least
Διαβάστε περισσότεραΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 6η: Basics of Industrial Organization Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 6η: Basics of Industrial Organization Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Course Outline Part II: Mathematical Tools Firms - Basics
Διαβάστε περισσότεραProblem Set 9 Solutions. θ + 1. θ 2 + cotθ ( ) sinθ e iφ is an eigenfunction of the ˆ L 2 operator. / θ 2. φ 2. sin 2 θ φ 2. ( ) = e iφ. = e iφ cosθ.
Chemistry 362 Dr Jean M Standard Problem Set 9 Solutions The ˆ L 2 operator is defined as Verify that the angular wavefunction Y θ,φ) Also verify that the eigenvalue is given by 2! 2 & L ˆ 2! 2 2 θ 2 +
Διαβάστε περισσότεραOverview. Transition Semantics. Configurations and the transition relation. Executions and computation
Overview Transition Semantics Configurations and the transition relation Executions and computation Inference rules for small-step structural operational semantics for the simple imperative language Transition
Διαβάστε περισσότεραSecond Order Partial Differential Equations
Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y
Διαβάστε περισσότεραΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ. Ψηφιακή Οικονομία. Διάλεξη 8η: Producer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών
ΕΛΛΗΝΙΚΗ ΔΗΜΟΚΡΑΤΙΑ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ Ψηφιακή Οικονομία Διάλεξη 8η: Producer Behavior Mαρίνα Μπιτσάκη Τμήμα Επιστήμης Υπολογιστών Firm Behavior GOAL: Firms choose the maximum possible output (technological
Διαβάστε περισσότεραStrain gauge and rosettes
Strain gauge and rosettes Introduction A strain gauge is a device which is used to measure strain (deformation) on an object subjected to forces. Strain can be measured using various types of devices classified
Διαβάστε περισσότερα«ΑΓΡΟΤΟΥΡΙΣΜΟΣ ΚΑΙ ΤΟΠΙΚΗ ΑΝΑΠΤΥΞΗ: Ο ΡΟΛΟΣ ΤΩΝ ΝΕΩΝ ΤΕΧΝΟΛΟΓΙΩΝ ΣΤΗΝ ΠΡΟΩΘΗΣΗ ΤΩΝ ΓΥΝΑΙΚΕΙΩΝ ΣΥΝΕΤΑΙΡΙΣΜΩΝ»
I ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΣΧΟΛΗ ΝΟΜΙΚΩΝ ΟΙΚΟΝΟΜΙΚΩΝ ΚΑΙ ΠΟΛΙΤΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΤΜΗΜΑ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ ΠΡΟΓΡΑΜΜΑ ΜΕΤΑΠΤΥΧΙΑΚΩΝ ΣΠΟΥΔΩΝ ΣΤΗΝ «ΔΙΟΙΚΗΣΗ ΚΑΙ ΟΙΚΟΝΟΜΙΑ» ΚΑΤΕΥΘΥΝΣΗ: ΟΙΚΟΝΟΜΙΚΗ
Διαβάστε περισσότεραΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ
ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΤΜΗΜΑ ΝΟΣΗΛΕΥΤΙΚΗΣ ΠΤΥΧΙΑΚΗ ΕΡΓΑΣΙΑ ΨΥΧΟΛΟΓΙΚΕΣ ΕΠΙΠΤΩΣΕΙΣ ΣΕ ΓΥΝΑΙΚΕΣ ΜΕΤΑ ΑΠΟ ΜΑΣΤΕΚΤΟΜΗ ΓΕΩΡΓΙΑ ΤΡΙΣΟΚΚΑ Λευκωσία 2012 ΤΕΧΝΟΛΟΓΙΚΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΥΠΡΟΥ ΣΧΟΛΗ ΕΠΙΣΤΗΜΩΝ
Διαβάστε περισσότεραforms This gives Remark 1. How to remember the above formulas: Substituting these into the equation we obtain with
Week 03: C lassification of S econd- Order L inear Equations In last week s lectures we have illustrated how to obtain the general solutions of first order PDEs using the method of characteristics. We
Διαβάστε περισσότεραthe total number of electrons passing through the lamp.
1. A 12 V 36 W lamp is lit to normal brightness using a 12 V car battery of negligible internal resistance. The lamp is switched on for one hour (3600 s). For the time of 1 hour, calculate (i) the energy
Διαβάστε περισσότεραEcon Spring 2004 Instructor: Prof. Kiefer Solution to Problem set # 5. γ (0)
Cornell University Department of Economics Econ 60 - Spring 004 Instructor: Prof. Kiefer Solution to Problem set # 5. Autocorrelation function is defined as ρ h = γ h γ 0 where γ h =Cov X t,x t h =E[X
Διαβάστε περισσότεραΚόστος Κεφαλαίου. Estimating Inputs: Discount Rates
Αρτίκης Γ. Παναγιώτης Κόστος Κεφαλαίου Estimating Inputs: Discount Rates Critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount
Διαβάστε περισσότερα5.4 The Poisson Distribution.
The worst thing you can do about a situation is nothing. Sr. O Shea Jackson 5.4 The Poisson Distribution. Description of the Poisson Distribution Discrete probability distribution. The random variable
Διαβάστε περισσότεραExercises 10. Find a fundamental matrix of the given system of equations. Also find the fundamental matrix Φ(t) satisfying Φ(0) = I. 1.
Exercises 0 More exercises are available in Elementary Differential Equations. If you have a problem to solve any of them, feel free to come to office hour. Problem Find a fundamental matrix of the given
Διαβάστε περισσότεραLecture 15 - Root System Axiomatics
Lecture 15 - Root System Axiomatics Nov 1, 01 In this lecture we examine root systems from an axiomatic point of view. 1 Reflections If v R n, then it determines a hyperplane, denoted P v, through the
Διαβάστε περισσότεραw o = R 1 p. (1) R = p =. = 1
Πανεπιστήµιο Κρήτης - Τµήµα Επιστήµης Υπολογιστών ΗΥ-570: Στατιστική Επεξεργασία Σήµατος 205 ιδάσκων : Α. Μουχτάρης Τριτη Σειρά Ασκήσεων Λύσεις Ασκηση 3. 5.2 (a) From the Wiener-Hopf equation we have:
Διαβάστε περισσότεραStatistics 104: Quantitative Methods for Economics Formula and Theorem Review
Harvard College Statistics 104: Quantitative Methods for Economics Formula and Theorem Review Tommy MacWilliam, 13 tmacwilliam@college.harvard.edu March 10, 2011 Contents 1 Introduction to Data 5 1.1 Sample
Διαβάστε περισσότερα周建波 孙菊生 经营者股权激励的治理效应研究 内容提要 关键词
: 3 ( ( 330013) 200083) : : (1),,(2), (3), (4),, ; : :, ;,,, 50 %, 100, : 17 %, 11 %, 7 %, 65 % 1999 50, 94. 92 %, (,2002) 1999 5 3, 1999 9,, 2001 12 31 34,,,,??,? 3, 74 2003 5,,?,,,?, 2002 4 30 2001,,34,
Διαβάστε περισσότεραBounding Nonsplitting Enumeration Degrees
Bounding Nonsplitting Enumeration Degrees Thomas F. Kent Andrea Sorbi Università degli Studi di Siena Italia July 18, 2007 Goal: Introduce a form of Σ 0 2-permitting for the enumeration degrees. Till now,
Διαβάστε περισσότεραOLS. University of New South Wales, Australia
1997 2007 5 OLS Abstract An understanding of the macro-level relationship between fertility and female employment is relevant and important to current policy-making. The objective of this study is to empirically
Διαβάστε περισσότεραCongruence Classes of Invertible Matrices of Order 3 over F 2
International Journal of Algebra, Vol. 8, 24, no. 5, 239-246 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ija.24.422 Congruence Classes of Invertible Matrices of Order 3 over F 2 Ligong An and
Διαβάστε περισσότεραΕΘΝΙΚΗ ΣΧΟΛΗ ΔΗΜΟΣΙΑΣ ΔΙΟΙΚΗΣΗΣ ΙΓ' ΕΚΠΑΙΔΕΥΤΙΚΗ ΣΕΙΡΑ
ΕΘΝΙΚΗ ΣΧΟΛΗ ΔΗΜΟΣΙΑΣ ΔΙΟΙΚΗΣΗΣ ΙΓ' ΕΚΠΑΙΔΕΥΤΙΚΗ ΣΕΙΡΑ ΤΜΗΜΑ ΤΟΠΙΚΗΣ ΑΥΤΟΔΙΟΙΚΗΣΗΣ ΚΑΙ ΠΕΡΙΦΕΡΕΙΑΚΗΣ ΑΝΑΠΤΥΞΗΣ ΤΕΛΙΚΗ ΕΡΓΑΣΙΑ: ΠΕΡΙΒΑΛΛΟΝ ΚΑΙ ΑΝΑΠΤΥΞΗ: ΠΡΟΣΕΓΓΙΣΗ ΜΕΣΩ ΔΕΙΚΤΩΝ Επιβλέπων: Αθ.Δελαπάσχος
Διαβάστε περισσότεραHISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? What is the 50 th percentile for the cigarette histogram?
HISTOGRAMS AND PERCENTILES What is the 25 th percentile of a histogram? The point on the horizontal axis such that of the area under the histogram lies to the left of that point (and to the right) What
Διαβάστε περισσότεραOrdinal Arithmetic: Addition, Multiplication, Exponentiation and Limit
Ordinal Arithmetic: Addition, Multiplication, Exponentiation and Limit Ting Zhang Stanford May 11, 2001 Stanford, 5/11/2001 1 Outline Ordinal Classification Ordinal Addition Ordinal Multiplication Ordinal
Διαβάστε περισσότεραSCITECH Volume 13, Issue 2 RESEARCH ORGANISATION Published online: March 29, 2018
Journal of rogressive Research in Mathematics(JRM) ISSN: 2395-028 SCITECH Volume 3, Issue 2 RESEARCH ORGANISATION ublished online: March 29, 208 Journal of rogressive Research in Mathematics www.scitecresearch.com/journals
Διαβάστε περισσότεραDESIGN OF MACHINERY SOLUTION MANUAL h in h 4 0.
DESIGN OF MACHINERY SOLUTION MANUAL -7-1! PROBLEM -7 Statement: Design a double-dwell cam to move a follower from to 25 6, dwell for 12, fall 25 and dwell for the remader The total cycle must take 4 sec
Διαβάστε περισσότεραGlobal energy use: Decoupling or convergence?
Crawford School of Public Policy Centre for Climate Economics & Policy Global energy use: Decoupling or convergence? CCEP Working Paper 1419 December 2014 Zsuzsanna Csereklyei Geschwister Scholl Institute
Διαβάστε περισσότερα1) Formulation of the Problem as a Linear Programming Model
1) Formulation of the Problem as a Linear Programming Model Let xi = the amount of money invested in each of the potential investments in, where (i=1,2, ) x1 = the amount of money invested in Savings Account
Διαβάστε περισσότεραΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ
ΠΑΝΔΠΗΣΖΜΗΟ ΠΑΣΡΩΝ ΣΜΖΜΑ ΖΛΔΚΣΡΟΛΟΓΩΝ ΜΖΥΑΝΗΚΩΝ ΚΑΗ ΣΔΥΝΟΛΟΓΗΑ ΤΠΟΛΟΓΗΣΩΝ ΣΟΜΔΑ ΤΣΖΜΑΣΩΝ ΖΛΔΚΣΡΗΚΖ ΔΝΔΡΓΔΗΑ Γηπισκαηηθή Δξγαζία ηνπ Φνηηεηή ηνπ ηκήκαηνο Ζιεθηξνιόγσλ Μεραληθώλ θαη Σερλνινγίαο Ζιεθηξνληθώλ
Διαβάστε περισσότερα