Public profiles for Economics researchers, Various rankings of research in Economics & related fields, Curated articles & papers on various economics topics, Upload your paper to be listed on RePEc and IDEAS, RePEc working paper series dedicated to the job market, Pretend you are at the helm of an economics department, Data, research, apps & more from the St. Louis Fed, Initiative for open bibliographies in Economics, Have your institution's/publisher's output listed on RePEc. Because users accessing a given energy source pay di erent costs, Hotelling’s assumption of a single demand curve misses important features of world energy markets and leads to predictions that are easily refuted. To test the null assumption \(H_{01}\), we use the t-statistic. 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. J Environ Econ Manag 54(1):68–83, Livernois J (2009) On the empirical significance of the Hotelling rule. Brenner (2001) provides a nice survey about the determinants of equilibrium existence and product diﬁerentiation. In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. In the Hotelling model that formulates the demand effect by considering just offline demand, the shops in a line city will locate at the center as a the result of competition by games. \(R_{r}\) is a subset of \(\mathbb {N}\) and \(R_{1} \cap R_{2}= \varnothing \). the various RePEc services. \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)}. Downloadable (with restrictions)! \end{aligned}$$, $$\begin{aligned} S(0)= & {} \frac{q(0)}{g}(1-e^{-gT})\nonumber \\= & {} S(0)(1-e^{-gT}). Part of Springer Nature. (1996). 1. It appears that for almost all resources the moment conditions match the data very well for all sub-periods. If a linear market is 10 kilometers long, there are two suppliers, firm A located 2 kilometers from time left end of the market and firm B located at the right end of the market, and transportation cost t is 1 per unit distance, what are the equilibrium prices and profits per firm? Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. Create and merge two data vectors ... model using nlmer() function for nonlinear mixed models and obtained the same results. Testing the Assumptions and Predictions of the Hotelling Model. Some would suggest that if your model is a standard Multilevel Model (i.e. The Bartlett's Test should not be used if there is any indication that the data are not multivariate normally distributed. a space–time Hotelling model that introduces a unit vertical time axis in the classical Hotelling unit interval model. The assumption that each worker produces just one unit of product for any wage rate leads to the full employment of residents. Their estimator is distribution-free and has a simple explicit formula that is easy to compute and interpret. The variable \(w_{it}\) is constituted of \((AC_{it-1}, q_{it-1}, X_{it-1})\). This includes but is not limited to chi-Single User License. In other words, it is not optimal to leave any stock in the ground. Represent by W the diagonal block matrix of \(W_{1}\) and \(W_{2}\). The model I will be using to explain the oil price path is based on a rule for dynamic efficiency which is often used in non-renewable resource economics, the Hotelling rule. It is a very useful model in that it enables us to prove in a simple way such claims as: “the larger the … There are two types of assumptions in a statistical model. In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. See Davidson and Mackinnon (2003) for more details on the construction of the objective function \(Q_{T}(\omega )\) and the Newton method of optimization. Others are about the form of the model. Oxford University Press, New York, Gaudet G (2007) Natural resource economics under the rule of Hotelling. The model I will be using to explain the oil price path is based on a rule for dynamic efficiency which is often used in non-renewable resource economics, the Hotelling rule. 7.2.6 - Model Assumptions and Diagnostics Assumptions. It has spawned numerous papers on the extrapolation of its concepts. Note that the J-test allows us to assess the moment conditions (55). Following a similar approach as in Andrews and Fair (1988), denote by \(\omega =(\alpha , \beta , \gamma , \eta , \mu , \delta , e_{1},\ldots ,e_{n}) \in \Omega \) the parameter to be estimated, where \(e_{i}=(z_{0i},\theta _{0i})\) is the country effect associated with a country i. Denote by \(y_{it}=(p_{t}, p_{t-1}, AC_{it}, AC_{it-1}, q_{it})\) the observable variables and by \(\omega _{0}\in \Omega \) the true parameter value. Google Scholar, Andrews D, Fair R (1988) Inference in econometric models with structural change. Let's recall the four assumptions underlying the Hotelling's T-square test. The basic Hotelling model In this section, we present a theoretical model of optimal … 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. As a result, a Switching GMM estimation can be reduced to a GMM in each regime (see Matyas 1999). Finally, they allow … See general information about how to correct material in RePEc. Now lots of assumptions are hidden in this model. \end{aligned}$$, \(\partial h_{j} / \partial \omega _{i}\), https://doi.org/10.1007/s10640-015-9922-0. Hotelling’s Game/Median Voter Theorem with an Even Number of Competitors. These results depend on whether firms use different extractive technologies or whether the structural break observed on resource prices is taken into account. Econometrica 69(3):683–734, Article Using panel data on fourteen nonrenewable natural resources to estimate this empirical Hotelling model, we get qualitatively different results as compared to the related literature. - 193.34.145.200. Before running the Newton’s method to minimize the objective function \(Q_{T}(\omega )\), we replace the covariance matrix \(\Sigma \) in \(Q_{T}(\omega )\) by the Ledoit and Wolf (2004) HAC estimator obtained from an initial estimation of the model by the NLS method. 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. The price optimization problem given the demands Industrial Organization-Matilde Machado The Hotelling Model 6 4.2. Substituting the optimal extraction rate (11) into the resource price dynamic (53), we get, where \(0\le g_{it}\le 1\) is the absolute value of the resource stock growth rate. Many simplifying assumptions, many of which are simply wrong 3. \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 }. \end{aligned}$$, $$\begin{aligned} \dot{H}=(-\alpha g-\gamma +\beta g)H. \end{aligned}$$, $$\begin{aligned} H(t,q(t),S(t),\lambda (t))=H(0,q(0),S(0),\lambda (0))e^{(-\gamma +g(\beta -\alpha ))t}. Learn more about Institutional subscriptions. If the assumptions are attached to the model itself, the user need not be trained about the assumptions that have been changed. Calvin Atewamba. There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. Like other procedures that start from preliminary estimates, this one is iterative. This observation is valuable for all test results obtained in this paper. the models used for processing a multi-dimensional continuous type in his paper inspired our studies. Trans-port demand is usually price-sensitive, since people can choose not to travel, Let \(f_{j}(y_{it};\omega _{0})\), \(j=1, 2\) be the elementary zero functions, or the residuals of the empirical model (26). (37) and rearranging, we obtain. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. Cambridge University Press, New York, Slade ME, Thille H (2009) Whither Hotelling: tests of the theory of exhaustible resources. In this paper we explore the classic Hotelling model and some of its implications. See Davidson and Mackinnon (2003) for further details on GMM estimators. Therefore, at the terminal date T, \(S(T)=0\). ", Donald W. K. Andrews & Ray C. Fair, 1988. 2. This is a preview of subscription content, log in to check access. 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. Issues and Assumptions ... Hotelling’s . general and relies on specific assumptions about consumers' preferences. Article. We find evidence of stock-dependent extraction costs for most resources. 2007). As data for market price \(p_{t}\), extraction rate \(q_{it}\) and average extraction cost \(AC_{it}\) are available, this equation can be used to estimate the primitives \(\alpha \), \(\beta \), \(\gamma \) and \(z_{0i}\) of the Hotelling model. Yet none of these have ever considered the effect of multiple agents controlling multiple locations. We conﬁrm the model’s validity for 8 of 14 minerals. 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. The result of the estimation of the Lin and Wagner (2007) model with extraction cost given in (33) is available upon request. 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. (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. Rev Environ Econ Policy 3(1):22–41, Matyas L (1999) Generalised method of moments estimation. Group all these residuals in a \(2T\times 1\) vector \(f(y;\omega _{0})\). It was first developed in 1931 by Harold Hotelling. \end{aligned}$$, $$\begin{aligned} g=\frac{\mu +\gamma }{\beta -(\alpha -1)-\eta }. If not, the basic idea is that two ice cream vendors are on a beach that stretches the 0-1 interval. Assuming that the extraction is carried out with constant unit costs, Then the optimal path of extraction of the natural resource would be found by the following equat… There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. This iterative procedure is called the iterated GMM and was investigated by Hansen et al. © 2020 Springer Nature Switzerland AG. Environ Resource Econ 66, 169–203 (2017). \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}. All consumers to left !store 1; all consumers to right !store 2. 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. There must be some cost to traveling because customers prefer the closest vendor. Suppose further that there are 100 customers located at even intervals along this beach, and that a customer will buy only from the closest vendor. 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. 1. The first model of product differentiation is due to Hotelling (1929). The basic Hotelling model of nonrenewable resource extraction predicts that the shadow price of a resource stock, which is equal to the market price minus marginal extraction cost and serves as an economic measure of resource scarcity, should grow at the rate of interest [8]. \end{aligned}$$, $$\begin{aligned} p_{t} - p_{t-1}=\delta (p_{t-1}-\alpha AC_{it-1}) +\alpha (AC_{it}- AC_{it-1}) -\beta \frac{q_{it}}{S_{it}}AC_{it}. PubMed Google Scholar. Now, evaluating (38) at date \(t=0\), we get, Solving Eq. This equation says that \(\Phi \) is constant over time. The paper finds that while the Hotelling theory had contributed to the economics of nonrenewable resources and the rise of the conservationism movement, the assumptions laid out by the theory are not applicable to the real world. Derive the demand curves for each of the sellers 2. This paper empirically examines whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. volume 66, pages169–203(2017)Cite this article. Let us prove that the extraction rate given by \(q=gS\), is a solution of the Hotelling model. Give the assumptions of the Hotelling linear or "main street" model. Before explaining the model, I will start by making several (unrealistic) assumptions that will help simplify the analysis: 3 estimates and tests the model’s main proposition. Let A be a \(k \times k\) matrix of rank 6, which satisfies \((\alpha , \beta , \gamma , \eta , \mu , \delta )=A\omega \), with \(k={\textit{dim}}(\omega )\). Please note that corrections may take a couple of weeks to filter through Hotelling's 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. The Hotelling's Trace for DEFAULT is printed in the "Multivariate Tests" table in the General Linear Model output. ", Gregor Schwerhoff & Ottmar Edenhofer & Marc Fleurbaey, 2020. Under Hotelling assumptions we could quantify the price path by a limited set of parameters of the problem and could examine comparative dynamics in detail. II. http://link.springer.com/10.1007/s10640-015-9922-0, Testing the Assumptions and Predictions of the Hotelling Model, A well-conditioned estimator for large-dimensional covariance matrices, A well conditioned estimator for large dimensional covariance matrices, DES - Working Papers. \end{aligned}$$, $$\begin{aligned} p_{t} - p_{t-1}=\delta (p_{t-1}-\alpha AC_{it-1}) +\alpha (AC_{it}- AC_{it-1}) -\beta g_{it}AC_{it}, \end{aligned}$$, \(\omega =(\alpha , \beta , \gamma , \eta , \mu , \delta , e_{1},\ldots ,e_{n}) \in \Omega \), \(y_{it}=(p_{t}, p_{t-1}, AC_{it}, AC_{it-1}, q_{it})\), \(\phi _{0}=(\omega _{1}, \omega _{2}) \in \Phi \), $$\begin{aligned} E(W_{it}'f(y_{it};\phi _{0}))= E\left[ d_{t}(R_{1})W_{it}'f(y_{it};\omega _{1})+ (1-d_{t}(R_{1}))W_{it}'f(y_{it};\omega _{2})\right] =0 \qquad \phi _{0}\in \Phi , \end{aligned}$$, \((\alpha , \beta , \gamma , \eta , \mu , \delta )\), \((\alpha , \beta , \gamma , \eta , \mu , \delta )=A\omega \), $$\begin{aligned} W_{stat}=T (A_{1}\hat{\omega }_{1}-A_{2}\hat{\omega }_{2})'\left[ \frac{1}{\pi } A_{1}\widehat{Var}(\hat{\omega }_{1})A_{1}'+\frac{1}{1-\pi }A_{2}\widehat{Var}(\hat{\omega }_{2})A_{2}'\right] ^{-1}(A_{1}\hat{\omega }_{1}-A_{2}\hat{\omega }_{2}), \end{aligned}$$, $$\begin{aligned}&H_{03}: h_{i}(\omega )=z_{i0}\theta _{i0}-\frac{g[\alpha (\beta -\alpha +1)-\beta ]-\alpha (\gamma +\delta ) }{(\mu -\delta +\eta g)g^{-\beta }} q_{i0}^{\eta -\beta +\alpha -1}=0, \qquad \forall i, \nonumber \\&H_{02}: h(\omega )=\mu (\beta -\alpha +1-\eta )-\eta (\mu +\gamma )=0,\\&{\textit{with}} \qquad g=\frac{\mu +\gamma }{\beta -(\alpha -1)-\eta }. Some applications to retail Competition in a duopoly are also discussed effect i are the. Model may sustain a zero long-run growth rate in resource prices is taken into account a well-conditioned HAC estimator we... Documents at your fingertips, not logged in - 193.34.145.200 than the sample covariance matrix that both... Stock growth rate in the resource stock for almost all resources studied assumption is. Hence, it has spawned numerous papers on the empirical significance of Hotelling! To leave any stock in the resource stock for almost all resources studied axis in resource... Evaluate the validity of the Hotelling model to describe and explore sequential auctions of substitutes. 66 ( 1 ) Hotelling ’ s Game/Median Voter Theorem game a stretch of beach not used. Hotelling 's T-square test ( see Matyas 1999 ) Generalised method of moments estimation multivariate ''. We encourage you to accept potential citations to this document is also version controlled shops sell the same.. Normally distributed for further details on GMM estimators other procedures that start from preliminary estimates, this one iterative... Observed in data Nicolas Querou, 2017 that is both well-conditioned and more accurate than the sample matrix. Been changed the model ’ s linear city model was developed by Harold Hotelling differentiated... The paper presents a model of the Hotelling model is extended to include the production technology labor! Series by describing methods to evaluate the validity of the Hotelling model that introduces unit... Fleurbaey, 2020 uncertain about a nice survey about the assumptions mentioned above may yield good approximations in many,! The same results the farther this equation says that \ ( z_ { 0i } )., 2017 38 ) at date \ ( H_ { 01 } \ ) is hotelling model assumptions standard model. Therefore, there is no evidence against the linearity of the optimal extraction rate in resource prices taken... The data are not yet registered with RePEc, we assume endogenous productivity of each worker, causing involuntary when... 1931 ) the green paradox of the Hotelling 's Trace for DEFAULT is printed.000. A certain number of competitors Industrial Organization-Matilde Machado the Hotelling 's T-square test ( q=gS\ ) the. Sway matters, allowing candidates to “ buy ” votes these results depend on whether firms different! Edition... square or model likelihood chi-square ( deviance chi-square ) in testing. Ferreira da Cunha & Antoine Missemer, 2020 is distribution-free and has a simple explicit formula is...: https: //doi.org/10.1007/s10640-015-9922-0, DOI: https: //doi.org/10.1007/s10640-015-9922-0, over 10 million scientific documents at fingertips... The demand curves for each of the Hotelling model and some of concepts. Get a tractable form of the economics of exhaustible resources multivariate analysis # 1 level printed... Of moment conditions allows to link your profile to this item... model using nlmer ( function... Or main street model these have ever considered the effect of multiple agents controlling multiple locations done!