Working with Cross-Section Time-Series Data Sometimes data has cross-section and time-series dimensions For example, consider following a group of firms, workers, states, or countries over time The extra dimension allows us to examine issues that cannot be studied with cross-section data or time series data alone: 1.If x% of people are poor, the policy implications depend on whether this is the same group over time or different people 2.If we want to measure inflation when we know the quality of goods changes over time (computers, for example), we need to use quality- adjusted price indexes; estimating these requires cross-section time- series data on products, prices, and qualities 3.How has the diffusion of computers affected wages of different types of workers? Follow wages and computer use over time

Econometric Advantages of Cross-Section Time-Series Data Cross-Section Time-Series data (sometimes referred to as “panel” data) allows us to control for several characteristics we cannot control for effectively in cross section or time series data alone For example, suppose we want to determine how firm-specific product quality affects firm performance; a simple approach would be to regress performance on quality If we have cross-section time-series data, we can control for two very general effects and get a much more accurate estimate of the effect of quality: 1.Any other firm-specific variable that does not change over time (reputation, general ability, brand-name recognition, etc.) 2.Any macro-level effects that vary by time period (aggregate shocks to demand or costs that affect performance)

The Main Specification

Additional Structure

Quality-Adjusted Price Indexes Quality-adjusted price indexes are becoming increasingly popular as inputs into computing inflation measures Traditionally, one of the most important problems with inflation measures such as the CPI is that they ignore changes in the characteristics of particular goods over time The CPI holds the basket of goods constant over time and considers how the price of the basket changes over time; this method is accurate only if the characteristics of the goods in the basket do not change over time Many goods (particularly expensive durables) experience quality improvements over time: cars, computers, CD players, DVD players, TVs, refrigerators, laundry equipment, air conditioners, furnaces, hot water heaters, microwave ovens, batteries, mattresses, mops,…

Implications of Poor Price Indexes Inflation measures are often used in contracts and in social security systems to adjust payments to reflect changes in the “cost of living” To the extent that inflation measures ignore the fact that the quality of the goods in the basket is rising over time, the reported measures are upward biased measures of change in the cost of living This problem itself contributes to inflation and causes real resource transfers: 1.If many income-related payments (wages, social security) are indexed above the true rate of change in the cost of living, then prices in the economy will rise to reflect the upward adjustment 2.Those whose income is indexed in this way experience a benefit relative to those whose income is adjusted according to a less upward biased measure

Bureau of Labor Statistics Response The BLS (The U.S. government agency responsible for computing price indexes) has recognized this problem for some time In the mid-1980s, the BLS began computing quality-adjusted price indexes for computers Later they added quality-adjusted price indexes for related peripherals: monitors, printers, disk drives Currently there are BLS working papers that consider quality-adjusted price indexes for refrigerators and other goods

Methods for Computing Quality-Adjusted Price Indexes The simplest method computes a “matched-model” index: Out of all the models of a particular good produced in 2003 and 2004, select only those produced in both years that did not experience any quality changes Then compute the average prices of these “matched models” in each year, and divide the 2004 average by the 2003 average The resulting price index holds quality constant by construction However, the process of finding matched models may involve discarding far too many models, and there may be particular reasons why some models did not change (firm reputation, particularly high quality, aimed at niche markets, end-of-life strategy) that make them poor representatives of quality and price changes in the market

Regression Analysis Regressions can be used to compute quality adjusted price indexes without discarding any observations The technique builds on the characteristics theory of demand: consumers buy goods because they value the various characteristics of the good We can decompose the price of a good into the implicit price associated with each characteristic Any systematic price change from year to year that cannot be explained by changing characteristics must be a pure price effect; this pure price effect can be used to estimate a quality-adjusted price index The index is “quality-adjusted” because we have controlled for changes in the characteristics of the goods

Equations

The Price Index

Alternative Methods In the above analysis, we assumed that the implicit price on a unit of x (as measured by  ), remained the same across the two years Other methods for computing quality-adjusted price indexes abandon this assumption One alternative method runs a regression using 2003 data, and then uses those estimated coefficients to forecast what the product prices would be with the 2004 characteristics; Dividing the average actual 2004 prices by the average predicted 2004 prices yields a price index For various other methods, see my paper and the sources cited there (particularly the work by Berndt, Griliches, and Rappoport)