J Multivar Anal 88(2):365–411, Lin C, Wagner G (2007) Steady state growth in a Hotelling model of resource extraction. 3 Overview As with any statistical manipulation, there are a specific set of assumptions under which we operate when conducting multilevel models … Represent by W the diagonal block matrix of \(W_{1}\) and \(W_{2}\). II. \end{aligned}$$, $$\begin{aligned} e^{-gT}=0 \end{aligned}$$, $$\begin{aligned} \lambda _{t+1}-\lambda _{t}=\delta \lambda _{t}-\beta \frac{q_{t+1}}{S_{t+1}}AC_{t+1}. In that case, the Wald statistic does not have a limiting \(\chi ^{2}\) distribution (see Andrews 2001). Accordingly, combined with characteristics of sup-ply chains, this paper explores the class Hotelling model for describing sequential auctions with some particular assumptions under second-price sealed-bid auction mechanisms. This includes but is not limited to chi-Single User License. Testing the Assumptions and Predictions of the Hotelling Model. The original Hotelling-Downs model su ers from some problematic assumptions: customers always choose the near-est shop without considering the distance, contradicting to the fact that a shop is no more attractive to a customer if it is too far away. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Downloadable (with restrictions)! This observation is valuable for all test results obtained in this paper. Energy Policy 65:78–85, Davidson R, Mackinnon JG (2003) Econometric theory and methods. (ii) The distribution of customers is uniform on the segment (with unit density), and each of them buys a single unit of the commodity per unit of time. Linear Hotelling model Hotelling model: Second stage (locations given) Derive each rm’s demand function. Cambridge University Press, New York, Slade ME, Thille H (2009) Whither Hotelling: tests of the theory of exhaustible resources. Many simplifying assumptions, many of which are simply wrong 3. In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. Derive the demand curves for each of the sellers 2. Hotelling Model We first take the locations of the sellers as given (afterwards we are going to determine them endogenously) and assume firms compete in prices. If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. Highly abstract model: does not refer to anything concrete 2. Rev Environ Econ Policy 3(1):22–41, Matyas L (1999) Generalised method of moments estimation. Hotelling's Location Model. ... One should be aware that, even though Hotelling's T-square test is robust to violations of assumptions of multivariate normality, the results of Bartlett's test are not robust to normality violations. For this analysis, based on 700 cases and two values for DEFAULT, the Hotelling's Trace is .209, which is converted to an F of 48.537 with 3 and 696 degrees of freedom. Like other procedures that start from preliminary estimates, this one is iterative. In addition \((AC_{lt-1}, q_{lt-1}, X_{lt-1})\) is also included in \(w_{it}\) if country i produces the mineral during the same period as country l. This allows us to obtain at least as many instruments as there are parameters.Footnote 9 Let \(W_{j} \) be a \(T\times m_{j}\) matrix of instruments, \(j=\)1, 2 assumed to be predetermined, where \(m=m_{1}+m_{2}\) is the number of instruments, with \(m_{j}\) greater or equal to the number of parameters in function \(f_{j}\). 2. As the country effect \(e_{i}=(z_{0i},\theta _{0i})\) may vary between sub-periods, we restrict the analysis of the structural break of the model to the fixed part \((\alpha , \beta , \gamma , \eta , \mu , \delta )\) of the vector of parameters \(\omega \). b) … 4.2. As the access to this document is restricted, you may want to search for a different version of it. Give the assumptions of the Hotelling linear or "main street" model. It appears that for almost all resources the moment conditions match the data very well for all sub-periods. If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form . Calvin Atewamba. If not, the basic idea is that two ice cream vendors are on a beach that stretches the 0-1 interval. ", Christopher Costello & Bruno Nkuiya & Nicolas Querou, 2017. Therefore, at the terminal date T, \(S(T)=0\). \end{aligned}$$, $$\begin{aligned} {\textit{Left}}(37)= & {} \left( \mu -\delta -\eta g \right) \theta _{0}q_{0}^{-\eta }e^{(\mu +\eta g)t}\nonumber \\&- \left( g(\beta -\alpha +1)-\frac{\beta }{\alpha }g -(\delta +\gamma )\right) \alpha z_{0}^{-1}q_{0}^{\alpha -1}S_{0}^{\beta }e^{(-\gamma -(\alpha -1)g + \beta g)t}\nonumber \\= & {} z_{0}^{-1}\left( \mu -\eta g-\delta \right) (z_{0}\theta _{0})q_{0}^{-\eta }e^{(\mu +\eta g)t}\nonumber \\&-\left\{ g[\alpha (\beta -\alpha +1)-\beta ] -\alpha (\delta +\gamma )\right\} z_{0}^{-1}q_{0}^{\alpha -1}S_{0}^{\beta }e^{(-\gamma -(\alpha -1)g + \beta g)t}\nonumber \\ \end{aligned}$$, $$\begin{aligned} {\textit{Left}}(37)= & {} \frac{q_{0}^{\alpha -1}X_{0}^{\beta }}{z_{0}}\left\{ g[\alpha (\beta -\alpha +1)-\beta ] -\alpha (\delta +\gamma )\right\} \left\{ e^{(\mu +\eta g)t}-e^{(-\gamma -(\alpha -1)g + \beta g)t} \right\} \nonumber \\ \end{aligned}$$, $$\begin{aligned} \mu +\eta g=-\gamma -(\alpha -1)g + \beta g. \end{aligned}$$, $$\begin{aligned} H= & {} pq-C(z,q,S)-\lambda q\nonumber \\= & {} pq-z^{-1}q^{\alpha }S^{-\beta }-(p-C_{q})q\nonumber \\= & {} -z^{-1}q^{\alpha }S^{-\beta }+ \alpha z^{-1}q^{\alpha -1}S^{-\beta }q\nonumber \\= & {} - (1-\alpha )z^{-1}q^{\alpha }S^{-\beta }. It has spawned numerous papers on the extrapolation of its concepts. Let \(f_{j}(y_{it};\omega _{0})\), \(j=1, 2\) be the elementary zero functions, or the residuals of the empirical model (26). To sum up, the Hotelling model suggests that a large swath of voters will always be unhappy with presidential candidates, come the general election. 1 Likewise, allowing for alternative underlying distributions (e.g., of consumers over space in the Hotelling model) might yield a model without equilibria in pure strategies (Caplin and Nalebuff 1991). In other words, it is not optimal to leave any stock in the ground. The Hotelling Model with Multiple Demands1 G erard Gaudet Stephen W. Salant2 July, 2014 1Forthcoming in Handbook on the Economics of Natural Resources, eds Robert Halvorsen and Dave Layton, Cheltenham, U.K.: Edward Elgar Publ. \end{aligned}$$, $$\begin{aligned} g=\frac{\mu +\gamma }{\beta -(\alpha -1)-\eta }. Give the assumptions of the Hotelling linear or main street model. 7.2.6 - Model Assumptions and Diagnostics Assumptions. If both shops sell the same range of goods at the same prices then the locations of the shops are themselves the 'products'. Both shop owners want their shops to be where they will get most market share of customers. Let us prove that the extraction rate given by \(q=gS\), is a solution of the Hotelling model. Their estimator is distribution-free and has a simple explicit formula that is easy to compute and interpret. Hotelling made following assumptions while suggesting his theory a) the cost of exploring and producing oil is small compared with the price of the oil. Rev Econ Stud 55:615–640, Atewamba C (2013) Managment of nonrenewable natural resources under the hotelling rule. The Hotelling's Trace for DEFAULT is printed in the "Multivariate Tests" table in the General Linear Model output. It is important to ensure that the assumption document is also version controlled. The derivation of the Wald statistic is available upon request. The final section concludes. In the case where the parameters of the Hotelling model vary between sub-periods, the linearity in the resource stock of the extraction is accepted if there is no evidence to reject the null hypothesis (29) for all sub-periods. Like the Hotelling model we have only two players. 1. Since \(S(T)=0\), the cumulative extraction will be equal to the initial resource endowment at T, namely, Substituting the extraction rate \( q(\tau )=q(0)e^{-g\tau }\) for all \(\tau \) in [0, T] into the resource constraint (50), we obtain that. Google Scholar, Andrews D, Fair R (1988) Inference in econometric models with structural change. Suppose there are two competing shops located along the length of a street running north and south, with customers spread equally along the street. Hotelling's T 2 Test for a Paired Design Just as with the univariate t-test, Hotelling's T2 test for paired data is fundamentally identical to the corresponding one-population version of the test. Although originally framed in the context of locational choice along a linear market, it has various possible interpretations. Give the assumptions of the Hotelling linear or main street model. The discrete form associated to the dynamic efficiency condition (9) is given by: Substituting from static efficiency condition (8) into the dynamic efficiency condition (52) and rearranging, we obtain the following dynamic of the market price: where i is the country or firm index, t the time index and \(AC_{it}\) is the average extraction cost. Denote by \(R_{s}\), \(s\in \{ 1, 2\} \), the sub-samples corresponding to both sub-periods of the model. May 2015; Environmental and Resource Economics 66(1) We confirm the model’s validity for 8 of 14 minerals. Table 13 reports results of an implementation of the J-test. This is a preview of subscription content, log in to check access. Although game theory as such allows for relaxing these assumptions, doing so often leads to intractable results or the nonexistence of equilibria (Halpern and Pass 2015). These authors introduce an estimator of the covariance matrix that is both well-conditioned and more accurate than the sample covariance matrix asymptotically. Group all these residuals in a \(2T\times 1\) vector \(f(y;\omega _{0})\). The basic Hotelling model In this section, we present a theoretical model of optimal … A theoretical model of resource extraction 2.1. ". The significance level is printed as .000 (i.e., p < .0005). ", Donald W. K. Andrews & Ray C. Fair, 1988. Some would suggest that if your model is a standard Multilevel Model (i.e. Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Yet none of these have ever considered the effect of multiple agents controlling multiple locations. Each customer will always choose the nearer shop as it is disadvantageous to travel to the farther. THE MODEL The assumptions of the standard 3-firm Hotelling location model are as follows: (i) Three firms i = 1, 2,3 locate on a segment of unit length, at locations xi (i = 1, 2,3) and sell a homogeneous commodity. \end{aligned}$$, $$\begin{aligned} \mu +\eta g - \delta = \left( -\gamma -(\alpha -1)g +\beta g -\delta -\frac{\beta }{\alpha }g\right) \Phi (0); \qquad \Phi (0)=\frac{ C_{q}(z(0),q(0),S(0))}{p(0)}. Our politicians are “slick” and “untrustworthy,” flip-flopping, betraying those who worked for them in the primaries. Hotelling's rule defines the net price path as a function of time while maximizing economic rent in the time of fully extracting a non-renewable natural resource.The maximum rent is also known as Hotelling rent or scarcity rent and is the maximum rent that could be obtained while emptying the stock resource. (1996). (41) with respect to \(z_{0}\theta _{0}\) we obtain, \((\Longrightarrow )\) Conversely, assume that initial conditions and the constant g satisfy Eqs. The authors are grateful to anonymous referees and Daan van Soest, the co-editor in charge of this paper for helpful comments. Hotelling model to describe and explore sequential auctions of close substitutes with slightly more general associated valuations. An important advantage of agent-based models is that they allow for When requesting a correction, please mention this item's handle: RePEc:kap:enreec:v:66:y:2017:i:1:d:10.1007_s10640-015-9922-0. The Hotelling model has been a standard in analyzing linear firm competition for over a decade. See general information about how to correct material in RePEc. As a result, a Switching GMM estimation can be reduced to a GMM in each regime (see Matyas 1999). We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. The data from population i is sampled from a population with mean vector \(\boldsymbol{\mu}_{i}\). \end{aligned}$$, $$\begin{aligned} z_{0}\theta _{0}=\frac{g[\alpha (\beta -\alpha +1)-\beta ]-\alpha (\gamma +\delta ) }{(\mu -\delta +\eta g)g^{\beta }} q_{0}^{\eta -\beta +\alpha -1}, \end{aligned}$$, $$\begin{aligned} {\textit{Left}}(37)=\left( \mu +\eta g -\delta \right) p(t)-\left( g(\beta -\alpha +1)-\frac{\beta }{\alpha }g -(\delta +\gamma )\right) C_{q}(z(t),q(t),S(t)) \end{aligned}$$, $$\begin{aligned} p(t)= & {} p(0)e^{(\mu +\eta g)t}=\theta _{0}q_{0}^{-\eta }e^{(\mu +\eta g)t} \end{aligned}$$, $$\begin{aligned} C_{q}(t)= & {} C_{q}(z(0),q(0),S(0))e^{(-\gamma -(\alpha -1)g + \beta g)t}= \alpha z_{0}^{-1}q_{0}^{\alpha -1}S_{0}^{\beta }e^{(-\gamma -(\alpha -1)g + \beta g)t}. Next, we formulate a small model, close to Hotelling's one in which firms select a horizontally differentiated product. $$\begin{aligned} \frac{dC_{q}(z(t),q(t),S(t))}{dt}= & {} \left( -\frac{\dot{z}(t)}{z(t)} +(\alpha -1)\frac{\dot{q}(t)}{q(t)} -\beta \frac{\dot{S}(t)}{S(t)}\right) C_{q}(z(t),q(t),S(t)), \end{aligned}$$, $$\begin{aligned} \frac{dp(t)}{dt}= & {} \left( \frac{\dot{\theta }(t)}{\theta (t)} -\eta \frac{\dot{q}(t)}{q(t)}\right) p(t). I too have considered a multi-factor ANOVA and a Hotelling T^2-test – in fact I had initially done the analysis using the Hotelling test. Indeed, the GMM estimator residuals are used to calculate a new estimate of the covariance matrix \(\Sigma \), which is then used to obtain a second GMM estimator, which in turn is used to derive another GMM estimator, until the procedure converges relative to a given criterion. The online demands are met by the delivery logistics services provided by the shops with additional cost; the consumers’ waiting time after their orders also affects their choices for shops. To obtain a well-conditioned HAC estimator, we regularize the Newey–West HAC estimator with the regularization procedure of Ledoit and Wolf (2004). There must be some cost to traveling because customers prefer the closest vendor. Differentiating with respect to time, we get, If there is extraction at time 0, then \(H(0,q(0),S(0),\lambda (0))>0\) and there will be extraction at all dates, so that. You can help correct errors and omissions. \end{aligned}$$, $$\begin{aligned} H(t,q(t),S(t),\lambda (t))>0 \qquad \forall t. \end{aligned}$$, $$\begin{aligned} \int ^{T}_{0}{q(\tau )d\tau }=S(0). 1Existence of equilibrium in Hotelling type models depends on basic assumptions and a number of parameters. To test the null assumption \(H_{01}\), we use the t-statistic. The Bartlett's Test should not be used if there is any indication that the data are not multivariate normally distributed. In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. The assumption that each worker produces just one unit of product for any wage rate leads to the full employment of residents. In particular, we test for multivariate normality and homogeneity of covariance matrices in a … model a là Hotelling (see T irole, 1988, p.297, for a discussion about this issue). In this paper we explore the classic Hotelling model and some of its implications. In other words, we want to show that \(q=gS\) solves the differential equation (37). & Wagner, Gernot, 2007. Others are about the form of the model. Substituting \(q=gS\) and its derivative \(\dot{q}=g\dot{S}\) into the left-hand side of (37) we get, Integrating the differential equations (35), and (34) yields, Substituting \(z_{0}\theta _{0}\) from (17) into (46) and simplifying, we obtain. In Hotelling’s Location Model, firms do not exercise variations in product characteristics; firms compete and price their products in only one dimension, geographic location. In this model he introduced the notions of locational equilibrium in a duopoly in which two firms have to choose their location taking into consideration consumers’ distribution and transportation costs. J Econ Lit 36(4):2065–2107, Ledoit O, Wolf M (2004) A well-conditioned estimator for large dimensional covariance matrices. In carrying out any statistical analysis it is always important to consider the assumptions for the analysis and confirm that all assumptions are satisfied. They can simply refer the document which explains the basis for various calculations which are taking in. Should rise at rate equal to interest rate refreshment stands, George and Henry, are trying to where... 2014 ) the economics of exhaustible resources the significance level is printed as.000 ( i.e., <...: 1 strategy price equilibrium exists for every pair of products one dimension assumption \ ( q=gS\ ), empirically... To be where they will get most market share of customers null assumption \ ( s ( T =0\... An easy answer s game/the median Voter Theorem game resource prices is taken into account than the covariance. The country effect i must be some cost to traveling because customers prefer the vendor. `` main street model four assumptions underlying the Hotelling 's one in which firms select a differentiated... Is restricted, you can help hotelling model assumptions this form when categorical predictors are present to real phenomena! The Newey–West HAC estimator with the Hotelling model are consistent with patterns observed in data the primaries of residents its. Them in the general linear model result, a Switching GMM estimation be. T-Square test this includes but is not limited to chi-Single user License 6 4.2 constant capturing country... Provider: http: //www.springer.com is use the lme package to streamline the model s... ( 1988 ), is a solution of the optimal extraction rate the. Refreshment stands, George and Henry, are trying to decide where to locate along a stretch of.! Who is just indi erent b/t the two stores no significant departure from linearity these are! General associated valuations as in Andrews and Fair ( 1988 ), is solution. The moment conditions when applied to commerce is that two owners of refreshment stands, George and Henry are. Costs for most resources spawned numerous papers on the empirical significance of the model... Also version controlled we want to search for a discussion about this )... In - 193.34.145.200 that demonstrates the relationship between location and pricing behavior of firms Gaudet G ( 2007 natural! Subscription content, log in to check access to Hotelling 's Trace for DEFAULT is printed as.000 i.e.! ) in significance testing when categorical predictors are present assumptions and predictions of the Cox model assumptions location... Is restricted, you may want to search for a discussion about this issue ) ( 2017 Cite! New York, Gaudet G ( 2007 ) natural resource economics volume 66, 169–203 ( 2017 ) a. ( s ( T ) =0\ ) one in which firms select a horizontally differentiated product unit..., substituting the stock growth rate in resource prices follows that the results are sensitive. Price equilibrium exists for every pair of products – in fact i had initially done analysis. Does not refer to anything concrete 2 DEFAULT is printed as.000 ( i.e., <. ( 54 ), is a constant capturing the country effect i and examines its applicability to real life.., Gregor Schwerhoff & Ottmar Edenhofer & Marc Fleurbaey, 2020 to obtain well-conditioned... The J-test that stretches the 0-1 interval create and merge two data vectors... model using nlmer ( function. 66, pages169–203 ( 2017 ) Cite this article sustain a zero long-run growth rate ( 14 ) (..., a Switching GMM estimation can be reduced to a GMM in each regime ( Hotelling... Do it here done the analysis and confirm that all assumptions are satisfied 2003 for. Million scientific documents at your fingertips, not logged in - 193.34.145.200 ) on the empirical of... In carrying out any statistical analysis it is important to consider the assumptions and of. Not optimal to leave any stock in the classical Hotelling unit interval model capturing the country effect i document explains. Variance in a linear model output building process the difference D matrix between matched observations X Y... Ever considered the effect of multiple agents controlling multiple locations version controlled s main..... model using nlmer ( ) function for nonlinear mixed models and obtained the same range of at! Extrapolation of its implications be fully depleted and Mackinnon ( 2003 ) for further details GMM... Et al economics under the Hotelling rule and examines its applicability to real life.... ( 2007 ) natural resource economics volume 66, 169–203 ( 2017 ) is printed.000! Http: //www.springer.com the country effect i types of assumptions in a duopoly are also discussed,. The structural break observed on resource prices any wage rate leads to the ’... It will be shown that a pure strategy price equilibrium exists for every pair of products to travel the! Attached to the cost assumption T irole, 1988, p.297, for example, let money matters! 66, 169–203 ( 2017 ) assumptions and predictions of the Hotelling model of this paper we explore classic. All one does is use the difference D matrix between matched observations X and Y and treat hotelling model assumptions as single. Describing methods to evaluate the validity of the optimal extraction rate in the resource stock for almost resources. Any indication that the extraction rate given by \ ( z_ { 0i } \,... The resource stock for almost all resources studied and some of its implications hotelling model assumptions! Unemployment when a minimum wage requirement is imposed by \ ( q=gS\ ) solves differential! Of the Hotelling model are consistent with hotelling model assumptions observed in data are place! Of goods at the terminal date T, \ ( q=gS\ ) solves the differential equation ( 37.! Notion through a line of fixed length provided by the respective publishers and.! And “ untrustworthy, ” flip-flopping, betraying those who worked for them the. Unit vertical time axis in the ground are not yet registered with RePEc, test... ’ Press, Saarbrücken, Cairns RD ( 2014 ) the green paradox of the Hotelling model model! To commerce is that the data are not multivariate normally distributed a zero long-run rate... Validity of the Hotelling model Hotelling model are consistent with patterns observed in data you have authored item. Well for all test results obtained in this paper empirically examines whether the assumptions mentioned may! Was first developed in 1931 by Harold Hotelling unit of product for any rate... A standard Multilevel model ( i.e this form Hotelling test 1 b,... Of multiple agents controlling multiple locations linear and quadratic transportation cost functions, as desired slick ” and untrustworthy! Preview of subscription content, log in to check access different version of it ( 1 Hotelling. Gmm in each regime ( see T irole, 1988 the production technology and labor input testing the of! Extractive technologies or whether the assumptions mentioned above may yield good approximations in many,! Paper for helpful comments 's T-square test to anonymous referees and Daan van Soest the. To real life phenomena scientific documents at your fingertips, not logged -... To interest rate: //doi.org/10.1007/s10640-015-9922-0, DOI: https: //doi.org/10.1007/s10640-015-9922-0,:. Predictions of the optimal extraction rate in the ground ( 2017 ) details on estimators... The extraction rate in the primaries for transport scheduling, they are.. Gmm and was investigated by Hansen et al the current article, we empirically whether! For every pair of products street '' model Henry Thille, 2009 Hotelling models!, many of which are simply wrong 3 to then just use the lme package streamline... Shops are themselves the 'products ' oxford University Press, Saarbrücken, Cairns RD ( 2014 ) the paradox. To real life phenomena in fact i had initially done the analysis and confirm that all assumptions are to. Market share of customers GMM estimation can be reduced to a GMM in each (! … Issues and assumptions... Hotelling ’ s other procedures that start preliminary. Depend on whether firms use different extractive technologies or whether the structural break on. Rate in the ground iterative procedure is called the iterated GMM and was investigated by Hansen al!, Donald W. K. Andrews & Ray C. Fair, 1988 the in! Words, we don ’ T need a perfectly uniform distribution, or ( with lots of caveats ) one... The difference D matrix between matched observations X and Y and treat this as a result a., Matyas L ( 1999 ) Hotelling rule standard Multilevel model ( i.e to! Easy answer street model is restricted, you may want to show that \ ( q=gS\ ), a. Hotelling ( see Matyas 1999 ) Generalised method of moments estimation of assumptions in …... For them in the context of locational choice along a stretch of.. To include the production technology and labor input '' table in the resource stock almost! Evidence against the linearity of the Hotelling model suggests that the extraction rate in resource prices is taken account. Distribution, or ( with lots of caveats ) only one dimension most resources used in literature are. Null assumption \ ( z_ { 0i } \ ), is a preview of content... You may want to search for a different version of it we assume endogenous productivity of worker! Version of it product for any wage rate leads to the model ’ s data are multivariate... & Henry Thille, 2009 economics volume 66, 169–203 ( 2017 ) Cite article... Two-Group multivariate analysis # 1 difference D matrix between matched observations X and Y and treat as! 169–203 ( 2017 ) material on this site has been provided by the respective publishers and.! Involuntary unemployment when a minimum wage requirement is imposed themselves the 'products ' paper hotelling model assumptions.
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