Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model

We find the asymptotics of the OLS estimator of the parameters $\beta$ and $\rho$ in the spatial autoregressive model with exogenous regressors $Y_n = X_n\beta+\rho W_nY_n+V_n$. Only low-level conditions are imposed. Exogenous regressors may be bounded or growing, like polynomial trends. The assumption on the spatial matrix $W_n$ is appropriate for the situation when each economic agent is influenced by many others. The asymptotics contains both linear and quadratic forms in standard normal variables. The conditions and the format of the result are chosen in a way compatible with known results for the model without lags by Anderson (1971) and for the spatial model without exogenous regressors due to Mynbaev and Ullah (2006).mixed regressive spatial autoregressive model; OLS estimator; asymptotic distribution

Regressions with Asymptotically Collinear Regressor

We investigate the asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors. It is shown that the asymptotic distribution is normal one-dimensional and may belong to one of four types depending on the relative rates of growth of the regressors. The analysis establishes, in particular, a new link between slow variation and $L_p$-approximability. A revised version of this paper has been published in Econometrics Journal (2011), volume 14, pp. 304--320.Asymptotically collinear regressors; asymptotic distribution; Lp-approximability; OLS estimator

OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model: Extended Version

We find the asymptotic distribution of the OLS estimator of the parameters $$ and $\rho$ in the mixed spatial model with exogenous regressors $$. The exogenous regressors may be bounded or growing, like polynomial trends. The assumption about the spatial matrix $W_n$ is appropriate for the situation when each economic agent is influenced by many others. The error term is a short-memory linear process. The key finding is that in general the asymptotic distribution contains both linear and quadratic forms in standard normal variables and is not normal.$L_p$-approximability; mixed spatial model; OLS asymptotics

Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends

We propose a general method of modeling deterministic trends for autoregressions. The method relies on the notion of $L_2$-approximable regressors previously developed by the author. Some facts from the theory of functions play an important role in the proof. In its present form, the method encompasses slowly growing regressors, such as logarithmic trends, and leaves open the case of polynomial trends.autoregression; deterministic trend; OLS estimator asymptotics

Profit Maximization and the Threshold Price

If the output market is perfectly competitive and the firm’s production function is not concave, an increase in the output price may lead to an explosive increase in firm’s profits at some point. We explore the properties of this point, called a threshold price. We derive the formula for the threshold price under very general conditions and show how it helps to study correctness of the profit maximization problem, without explicit assumptions about returns to scale or convexity/concavity of the production function.threshold price; profit maximization; production function; cost function; Cobb-Douglas function; returns to scale

Comment on "Regression with slowly varying regressors and nonlinear trends" by P.C.B. Phillips

Standardized slowly varying regressors are shown to be $L_p$-approximable. This fact allows one to relax the assumption on linear processes imposed in central limit results by P.C.B. Phillips, as well as provide alternative proofs for some other statements.slowly varying regressors; central limit theorem; $L_p$-approximability

Housing market of Almaty

The housing market is special in that houses are immobile, costly and durable. In this paper we look at the determinants of prices of the housing market of Almaty. What affects the prices of houses and apartments? How was the housing market developing during the economic boom and after the financial crisis started? The paper starts with a review of the existing models. The theory indicates the size, quality and location as the main determinants. To apply the hedonic model, we collected a random sample of about 2,500 observations on housing units in seven districts of Almaty from newspaper advertisements. Those units were categorized by the number of rooms, quality, district, floor, etc. Some of those characteristics are nonnumerical and require dummy variables. With the data collected, we ran several regressions in Eviews. We have obtained valuation figures for different characteristics of housing units. The data clearly show existence of a bubble during 2006-2007. The regression results revealed the differences between different districts, dependence on the quality and floor. Among unexpected results are the facts that corner apartments and floor level have negative coefficients, perhaps because first-floor apartments are considered as potential commercial property or perhaps lower stories are preferred in general but the first storey is the least preferred. Some questions, such as valuation of luxury apartments or those in the north of the city remain unanswered because of lack of data. It would be also interesting to correlate housing prices with the interest rate on mortgages. A shorter version of this paper has been published as K. T. Mynbaev and S. Ibrayeva, Housing market of Almaty, Herald of the Kazakh-British Technical University, N 2 (17), 2011, 88-93.housing market; hedonic analysis; real estate bubble; multiple regression

Companion for “Statistics for Business and Economics” by Paul Newbold, William L. Carlson and Betty Thorne

This is a mathematical companion for “Statistics for Business and Economics” by Paul Newbold, William L. Carlson and Betty Thorne, London: Prentice-Hall, 2003, 6th edition. It contains derivations of most formulas from the first 12 chapters of that textbook. Most importantly, the companion provides methodological recommendations as to how statistics should be studied and teaches the reader to learn algebra from scratch. There are 21 examples, 57 exercises, 16 figures and 30 tables. Step-by-step instructions for Monte Carlo simulations in Excel are included.statistics; estimation; hypothesis testing; simple regression