paneldatanotesfinal

paneldatanotesfinal - 1 CHAPTER 12: PANEL DATA ANALYSIS...

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Unformatted text preview: 1 CHAPTER 12: PANEL DATA ANALYSIS 12.1 INTRODUCTION Recall that panel (or longitudinal) data is a mixture of cross section data and time series data. For these data, a cross section of households, individuals, municipalities, firms, etc. is repeatedly sampled over two or more points in time. This allows us to study dynamic (time series), as well as cross sectional aspects of the problem under investigation. To see the rationale for using panel data, let us suppose that we wish to determine the price elasticity of water demand for six municipalities in southern Ontario, Canada (St. Catharines, Hamilton, Niagara Falls, Welland, Grimsby, and Thorold). Let us consider the following hypothetical data on per capita water consumption and price for the 6 municipalities and 4 years (1955, 1960, 1965, and 1970). For this problem, we may specify a double-log model , where C and P denote per capita consumption of water and the price of water, respectively; u denotes the error term that captures other determinants of water demand that are not included in the model. For this model, is the price elasticity of water demand (in a double-log model, the slope coefficients represent elasticities). As we shall demonstrate below, the parameters of the above model may be estimated using time series, cross section, or panel data. (a) Estimation using time series data Obtaining the elasticity of water demand using time series data would involve estimating the model municipality by municipality. Hence, there will be only 4 observations for each municipality corresponding to the 4 years (1955, 1960, 1965, and 1970). The model to be estimated would, therefore, be t=1,2,..,4 (the subscript t denotes time period). Since there are only 4 observations for each cross section unit (municipality) corresponding to the 4 years, the number of degrees of freedom is only 2, which is too small for meaningful inference (#degrees of freedom(2)=#observations(4)-#independent variables including the intercept(2)). In this case, it would not be possible to augment the model with many other independent variables representing other determinants of water demand even if we wanted to do so, since the number of independent variables cannot exceed the number of observations. The time series data and the estimation results for each municipality are given below (the subscript t denotes the t-th time period). St. Catharines (SC): Year C t P t 1955 3.154 214 1960 4.271 419 1965 4.584 588 2 1970 5.849 1025 Estimated model: Hamilton (HA): Year C t P t 1955 3.859 696 1960 5.535 811 1965 8.127 1640 1970 10.966 2506 Estimated model: Niagara Falls (NF): Year C t P t 1955 19.035 3202 1960 26.041 4802 1965 32.444 5821 1970 41.180 9275 Estimated model: Welland (WE): Year C t P t 1955 35.229 5668 1960 51.111 7612 1965 61.045 10206 1970 77.885 13702 Estimated model: 3 Grimsby (GR): Year C t P t 1955 33.154 6000 1960 40.044 8222 1965 43.125 8484 1970 57.727 10004 Estimated model: Thorold (TH): Year C t P t 1955 73.05073....
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This note was uploaded on 04/28/2011 for the course ECON 2P91 taught by Professor Ogwang during the Winter '09 term at Brock University.

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paneldatanotesfinal - 1 CHAPTER 12: PANEL DATA ANALYSIS...

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