Quantile regression koenker pdf download

Though separate methodological literature exists for each subject, the authors seek to explore the natural connections between this increasingly sought-after tool and research topics in the social sciences. Quantile regression as a method does not rely on assumptions as restrictive as those for the classical linear regression; though more traditional models such as least squares linear regression are more widely utilized, Hao and Naiman show, in their application of quantile regression to empirical research, how this model yields a more complete understanding of inequality.

Inequality is a perennial concern in the social sciences, and recently there has been much research in health inequality as well. Major software packages have also gradually implemented quantile regression. Quantile Regression will be of interest not only to the traditional social science market but other markets such as the health and public health related disciplines. Key Features: Establishes a natural link between quantile regression and inequality studies in the social sciences Contains clearly defined terms, simplified empirical equations, illustrative graphs, empirical tables and graphs from examples Includes computational codes using statistical software popular among social scientists Oriented to empirical research.

The text explores topics including robustness, expectiles, m-quantile, decomposition, time series, elemental sets and linear programming. Graphical representations are widely used to visually introduce several issues, and to illustrate each method.

All the topics are treated theoretically and using real data examples. Designed as a practical resource, the book is thorough without getting too technical about the statistical background. The authors cover a wide range of QR models useful in several fields. The software commands in R and Stata are available in the appendixes and featured on the accompanying website.

The text: Provides an overview of several technical topics such as robustness of quantile regressions, bootstrap and elemental sets, treatment effect estimators Compares quantile regression with alternative estimators like expectiles, M-estimators and M-quantiles Offers a general introduction to linear programming focusing on the simplex method as solving method for the quantile regression problem Considers time-series issues like non-stationarity, spurious regressions, cointegration, conditional heteroskedasticity via quantile regression Offers an analysis that is both theoretically and practical Presents real data examples and graphical representations to explain the technical issues Written for researchers and students in the fields of statistics, economics, econometrics, social and environmental science, this text offers guide to the theory and application of quantile regression models.

Complementing classical least squares regression methods which are designed to estimate conditional mean models, quantile regression provides an ensemble of techniques for estimating families of conditional quantile models, thus offering a more complete view of the stochastic relationship among variables.

This volume collects 12 outstanding empirical contributions in economics and offers an indispensable introduction to interpretation, implementation, and inference aspects of quantile regression. Quantile Regression Author : I. QR is an important analytical tool in many disciplines such as statistics, econometrics, ecology, healthcare, and engineering. Quantile Regression: Applications on Experimental and Cross Section Data Using EViews provides examples of statistical results of various QR analyses based on experimental and cross section data of a variety of regression models.

Throughout the text, readers learn how to develop the best possible quantile regressions and how to conduct more advanced analysis using methods such as the quantile process, the Wald test, the redundant variables test, residual analysis, the stability test, and the omitted variables test. This rigorous volume: Describes how QR can provide a more detailed picture of the relationships between independent variables and the quantiles of the criterion variable, by using the least-square regression Presents the applications of the test for any quantile of any numerical response or criterion variable Explores relationship of QR with heterogeneity:.

It will also benefit students using the methodology for the first time, and practitioners at private or public organizations who are interested in modeling different fragments of the conditional distribution of a given variable. The book pursues a practical approach with reference to energy markets, helping readers learn the main features of the technique more quickly. Emphasis is placed on the implementation details and the correct interpretation of the quantile regression coefficients rather than on the technicalities of the method, unlike the approach used in the majority of the literature.

All applications are illustrated with R. The book gives an overview of the field and it shows progress made in recent years and remaining problems. Score: 5. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis.

The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet.

All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately numerical and empirical examples, graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Therefore extending the present estimator to non-parametric setting is relatively straightforward.

The inferential apparatus for non-parametric endogenous quantile regression however will require some attention and up to our knowledge no one has so far proposed reliable inference procedures in this setting.

Data We use a dataset consisting of agricultural land sales in Northern Ireland. This data is analysed in Patton and McErlean , The data were collected by a mail survey from buyers of agricultural land.

The names and addresses of buyers of agricultural land were obtained from the Valuation and Lands Agency. Such a dataset could be considered relatively small to allow an efficient non-parametric estimation, but it is nevertheless large enough to apply the proposed methodology.

Additionally transactions between family members, as well purchases for non-agricultural purpose were excluded in order to make the dataset as close to the assumptions of the pure hedonic model as possible. Price per acre was deflated using a retail price index because of the time span over which it was collected. The variables used are the same as in Patton and McErlean These are listed below. Acreage is measured in number of acres and represents the size of the land plot.

Land quality score is measured using values close to 1 to represent good quality land and values close to 7 to represent poor quality land. The land quality score is the variable most closely representing the productive capacity of agricultural land. It is however not possible to perfectly capture the land quality in a single variable. Another land quality proxy used in the study is the drainage score. Similarly to the land quality score smaller values imply higher drainage capability.

Most of the Northern Ireland agricultural land is actually grazing land. Owing to the significant amount of rainfall in the region, poor drainage would mean the corresponding land plots would be unusable for livestock grazing for prolonged periods of time and hence will be less productive. Similarly the drainage score would affect the productivity of the arable land. Therefore for Northern Ireland lower drainage score implies better land quality. The other land quality variable is the number of dairy cows per hectare.

It reflects the grass growing capacity of grazing land that may not be properly captured by the other two land quality variables. Since such missing variables like temperature would in general be spatially correlated, the inclusion of dairy cows per hectare should contribute to reducing the possibility to find spatial autocorrelation. Access to road is self explanatory indicator variable. The Distance to nearest urban area is measured in metres and is computed using GIS procedures.

Finally the potential site indicates whether, according to the buyer, there is potential building site included within the land parcel. Patton and McErlean , consistently find that this variable is insignificant, which is hardly surprising, since it is designed to capture the influence of non-agricultural factors, while only land to be used for agricultural purposes is included in the sample. Some descriptive statistics are presented in table 1.

Results First, for illustration purposes we present estimation results for the linear model. Table 2 shows the results from several spatial dependence tests. We present these for both a linear and a log-linear model. We use an inverse squared distance spatial weighting matrix. The standard LM tests for both forms of spatial dependence are significant.

Similarly the DLR double length artificial regression tests introduced by Baltagi and Li , which are similar to the LM tests but have better small sample properties, are both significant. When the robust to the presence of the other form of spatial dependence, for more details see Anselin, LM tests are applied however, only the one for spatial lag one is significant.

Thus one could conclude that there is spatial lag dependence but not spatial error dependence. Insert Table 2. The portmanteau test is essentially a joint version of the robust spatial lag LM test and the standard spatial error LM test. It tests whether both forms of spatial autocorrelation are present. Note that it is highly significant thus rejecting the null. This is consistent with the robust LM tests above and suggests that only spatial lag is present. The last test is the spatial Durbin test.

It exploits the fact that the spatial lag representation can nest within itself spatial error dependence the so called spatial Durbin model. It is essentially an LR test on the general spatial Durbin model against the spatial error model and tests whether the restrictions implied by the latter are valid. The spatial Durbin test statistic is insignificant. This is at odds with the previous tests, because it suggests that the spatial error restriction cannot be rejected.

Since the spatial lag autocorrelation can account for spatially correlated omitted variables, one should be inclined to deduce that a likely source of this misspecification is the functional form assumption. Note that we reach the same conclusion about the loglog functional form. A summary of the estimation results for the linear spatial lag model is presented in Table 3. The two stage least squares 2SLS estimation is implemented following Kelejian and Prucha by using spatially lagged independent variables as instruments for the spatially lagged dependent variable.

Insert Table 3. What is remarkable about these results is that the spatial lag parameter is considerably different between the ML and the 2SLS estimators, which also can indicate some problems with the functional representation.

Now we proceed to the results from the IVQR model, presented on figures We estimate the whole quantile process which produces separate coefficients estimates for every observation in the sample. We use an equidistant grid over the interval [- 1. We omit the estimates for the intercept in the model, since it is not readily interpretable. Due to the heteroscedasticity correction, applied in the latter estimates, they should be the linear model estimates most comparable to the quantile regression results.

Additionally we plot both the asymptotic and the finite sample confidence intervals for the IVQR estimates. Note that we view the quantile regression as a semiparametric model and thus use a graphical representation for the results, as it is customary for non and semi-parametric estimation. For example Zietz et al. Here we advocate for the use of the quantile regression models as a semiparametric alternative. This means estimating the whole quantile regression process where possible.

In this case due to the rather small dataset, this involves estimating only separate quantile regressions. When the dataset is large, this may not be practical.

In such cases a regular grid at e. At first sight one may notice that the confidence intervals for the quantile regression estimates are comparable, in terms of size, to the confidence intervals for the corresponding 2SLS estimates.

The finite sample inference approach of Chernozhukov and Hansen generally produces wider confidence intervals when compared to the asymptotic inference method. Let us first consider the land quality variables. These are land quality score, drainage score and dairy cows per hectare. The land quality score coefficients are negative indicating that better quality land i. Note however that the coefficients for the land quality scores are insignificant for the higher quantiles i.

One may also notice that there is some significant difference between the asymptotic and the finite sample inference results for these higher quantiles. Owing to weaker identification, inverting the corresponding Wald tests at the higher quantiles produces considerably wider confidence intervals. The drainage score coefficients are also negative which conforms to the expectations Figure 2. The coefficient estimates are broadly similar to the parametric specification, except at the lower and the higher quantiles.

Yet again at the higher quantiles the finite sample inference method produces considerably wider confidence intervals.

In this case finite sample IVQR inference yields insignificant coefficient estimates at the higher quantiles, in contrast to the asymptotic one. The coefficients for dairy cows per hectare Figure 3 are all insignificantly different from zero which is also consistent to the mean model. The coefficients for the potential site Figure 4 are also insignificant, as in the mean model. In principle the dataset is constructed based on purely agricultural land sales and this should be expected to exclude the effect of non- agricultural pressures on the price.

This in general makes the coefficients of potential site, which is measured by the responses of the buyers, which may not shared by the sellers, insignificant.

Whenever such pressures are not excluded from the dataset however, one could expect that this variable would have significant positive impact on the price.

Since such non-agricultural opportunities would in general be more profitable that purely agricultural use of this land, they will only be pronounced in the more expensive parcels of land, i. This is exactly the result we obtain. The effect of access to road Figure 5 which is highly significant in the mean regression however is not significant for most observations in the IVQR estimates.

It seems to be significantly positive for the lower according to the asymptotic IVQR confidence intervals only and higher quantiles in our sample.

Distance to urban area has a significant negative effect consistent with expectations and with the mean model Figure 6. The quantile regression coefficients however show considerable variability compared to the linear estimates.

Additionally there is considerable difference between the asymptotic and the finite inference confidence intervals. The nature the effect of distance to urban area on the price of agricultural land is complex. In principle the desirability of land parcels depends on their accessibility.

This feature is proxied here by the indicator Access to road, but it also depends on the nature of the local infrastructure, i. Obviously distance to urban area is a very imprecise proxy for these characteristics. For these reasons it only weakly identifies the endogenous spatial variation.

This results in significant differences between asymptotic and finite sample inference. The coefficients of acreage are not significant except for the extreme low quantiles and for the higher quantiles Figure 7. The result for the extreme low quantiles may be due to the unreliability of the conventional quantile regression estimates at extreme quantiles and for this reason we will not comment on it.

The considerable number of significant negative effects at the higher quantiles however suggests that there is a price discount for higher acreages in the most expensive parcels of land. The difference between asymptotic and finite sample confidence intervals is most pronounced for the spatial lag coefficient.

While the asymptotic inference discovers spatial lag dependence over most of the sample, the finite sample inference only finds evidence for spatial lag dependence in the higher quantiles of the dependent variable Figure 8. At these higher quantiles we had the significant effect of access to road, acreage and potential site and the loss of significance of land quality score.

Remembering that in general spatial lag dependence is inconsistent with the pure hedonic model, our results suggest market segmentation where the higher quantiles, in contrast to the rest of the sample deviate from the pure hedonic model. Note that similarly to the significance of the spatial lag coefficient, the other high quantile effects also suggest some kind of deviation from perfect competition. One may say that the hedonic model essentially breaks down at the higher quantiles, because none of the three land quantity variables is significant.

The reason why the pure hedonic model breaks down for the higher quantiles is also obvious. If we abstract for a moment from the potential site effect, this is likely to be the best agricultural land, which as discussed earlier is in short supply in Northern Ireland.

The latter means that the market for such land will be much thinner with the potential effects of creating distortions and deviations from the purely competitive market. As for the potential site cases, then due to the nature of residential planning, there could be spatial spillovers.

One can formally test whether the model is different at the higher quantiles. To illustrate this we present in table 4 Wald-type tests for equality of slopes i. Insert Table 4 We are essentially testing whether the model in the upper quantiles, represented here by the 0. Both the joint and the individual for separate quantile regression coefficients tests are presented. The joint tests are highly significant demonstrating the difference in the quantile regression model in the upper quantiles and the rest of the sample.

Note however, that these tests have an auxiliary function. The primary point of interest here is not exactly how different are the estimated quantile regression coefficients, but their statistical significance, which as explained earlier, allows us to effectively split the sample into two qualitatively different segments.

Therefore we are mainly interested in the joint tests as supporting evidence for the discovered market segmentation. A peculiar characteristic of the Northern Ireland and Ireland land market is the conacre system, under which land is only rented on a short-term basis of up to 11 months.

This system effectively creates information about the productive characteristics of agricultural land. The main stakeholders have to some extent directly or indirectly access to this type of information and therefore this contributes to a more efficient land pricing. We can however hypothesise that due to its scarcity the best agricultural land is rarely available for conacre rental.

This means that it is much more difficult for the interested buyers to reliably assess its productive ability. Our results suggest that this is indeed the case, since at the higher quantiles we discover significant deviations from the fully competitive hedonic model. Owing to the small size of the agricultural land market in Northern Ireland, a signaling system, such as the conacre one, is instrumental in facilitating more efficient market pricing.

It helps reduce market inefficiencies. Therefore a transition towards a longer term based rental system, as in Great Britain, can be expected to impact negatively on the land market in Northern Ireland. Conclusions We have applied a spatial lag quantile regression to a hedonic land prices model. In this way we allow for varying effects of the hedonic characteristics and more importantly varying degrees of spatial autocorrelation.

We apply this approach to a sample of agricultural land sales in Northern Ireland. Due to the parametric rate of convergence of the quantile regression estimator the estimated confidence intervals compare favourably to those from a parametric spatial lag model.

Therefore the proposed spatial quantile regression generalizes the linear spatial lag model at a relatively low cost and is applicable to small samples. Finite sample inference, robust to weak identification, is available. Our results suggest that the agricultural land market in Northern Ireland effectively consist of two segments. The larger of these two segments conforms to the conventional hedonic model with no spatial lag dependence, while the smaller much thinner market segment exhibits considerable spatial lag dependence.

Although we use a linear quantile regression that cannot fully overcome the potential pitfalls of a functional misspecification, it is essentially a semi-parametric approach that is much more flexible than the conventional parametric modeling. Additionally the linear quantile regression has been extensively studied and provides tools for a fully parametric inference.

Nevertheless, the approach could, if desired, be potentially extended to a more general non-parametric setting. References: Abadie, A. Angrist and G. Imbens Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings, Econometrica 70, Amemiya, T. Anselin, L. Le Gallo. Baltagi, B. Li Double length artificial regressions for testing spatial dependence, Econometric Reviews, 20 1 , Basile R. Bassett, G. Koenker Blundell, R.

Powell Endogeneity in semiparametric and nonparametric regression models. Chen, L. Portnoy Two-stage regression quantiles and two-stage trimmed least squares estimators for structural equation models, Communications in Statistics, Theory and Methods, 25, Chernozhukov, V. Hansen Instrumental quantile regression inference for structural and treatment effect models, Journal of Econometrics , Hansen and M.

Jansson Inference approaches for instrumental variable quantile regression, Economics Letters 95, — Hansen Instrumental variable quantile regression: A robust inference approach, Journal of Econometrics , — Ekeland, I. Heckman and L. Fotheringham, A. Charlton and C. Bundson and M. Freeman, M. Goodman A. Greene, W. Kelejian, H. Prucha A generalized moments estimator for the autoregressive parameter in a spatial model, International Economic Review 40, Prucha Specification and estimation of spatial autoregressive models with autoregressive and heteroscedasticity disturbances.

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Bassett Regression Quantiles, Econometrica 46, Lee, L. Lancaster, K. Journal of Political Economy, 74, — Lee, L-F. Lee, S. Lin, X. Ma, L. Koenker Quantile regression methods for recursive structural equation models, Journal of Econometrics, 2 , Maddison, D. McMillen D. International Regional Science Review — Nesheim, L. Patton, M. McErlean Spatial effects within the agricultural land market in Northern Ireland, Journal of Agricultural Economics, 54 1 : McErlean Spatial effects within the agricultural land market in Northern Ireland: a reply, Journal of Agricultural Economics, 55 1 : Powell, J.