New Economic Geography and Regional Price Level

1. New Economic Geography and Regional Price Level Verein für Socialpolitik, Ausschuss für Regionaltheorie und -politik Jahrestreffen 2008, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg October 17-19, 2008 Reinhold Kosfeld • Contents: • Introduction • Price Indices and Helpman Model • ESDA and Spatial-Econometric Price Level Models • 3.1 Tools of Explanatory Data Analysis (ESDA) • 3.2 NEG-Based Spatial-Econometric Price Level Models • 4. Data • 5. Explanatory Spatial Data Analysis of Regional Price Indices • 6. Spatial Price Level Models: Estimation and Testing Results • 7. Conclusion

2. 1. Introduction Regional economic theory demonstrates that the law of one price does not hold across regions. From some price surveys it is clear that substantial price differentials do occur at a regional level. Newer regional economic theories point out that spatial price differentials are ex- pected to play a crucial role in shaping the economic landscape. The price index effect highlighted in New Economic Geography (NEG) models gives reason for the existence of forward linkages that operate towards agglomeration (Krugman, 1991; Fujta et al., 1999). While low commodity prices may most notably be observed in big cities, prices of non-tradable goods tend to fall with distance from centres (Tabuchi, 2001). Due to congestion effects, land scarcity and other urban costs, prices of non-tradables tend to be high in agglomerated areas.

3. National statistical offices do not gather price data area-wide. Hence, price levels • are generally not known at a regional level of districts or provinces. • Econometric techniques have recently been employed for estimating regional • price levels. Aten and Heston (2005) estimate regional price levels using spatial- • econometric models calibrated with national consumer price indices. • The breakdown of country estimations to a regional level is not easily justified: • The econometric models built from international studies are primarily demand- • orientated and not by grounded in regional economic theory. • The calibration with national consumer price index does not necessarily imply • an adequate explanation of regional price levels. • There is no a priori gua rantee that responses of explanatory variables and • spatial effects at the national and regional level are identical.

4. Present paper: • deals with developing regional price level models on the groundwork of NEG • theory • We particularly rely on the Helpman model (Helpman, 1998) in building spatial • econometric models for consumer price index and its major components. • Spatial price effects are analyzed by means of exploratory spatial data analysis • (ESDA) and spatial Langrange multiplier (LM) tests) • Spatial price effects are also analyzed by means by trend surface and spatial • expansion models • First empirical evidence on the significance of NEG theory in explaining regio- • nal price level is provided from the southern German sample.

5. 2. Regional price indices and Helpman model Forward linkages between firms and consumers act as centripetal forces that are strongly based on the price index effect (Robert-Nicoud, 2005). (Sub-)Price indices in the Krugman-Helpman model Price index for tradables in region r : (1) : uniform price of manufactures in region s Ns: number of varietiesproduced in region s Tsr (Tsr>1): transport costs incurred by shipping a variety form s to r : elasticity of substitution between any two varieties PNT: fixed price of the non-traded good (“agriculture”) Overall price index of Cobb-Douglas type: (2) μ: share of expenditures spent on manufactures

6. Potential centrifugal forces that might arise from congestion or housing costs. (3) Hr: stock of housing fixed in all regions (4) Equilibrium relation for the price index of tradables: (5) λ: share of region’s share of total manufacturing labour force Transport costs: function of distance dsr: (6) Tsr = T(dsr), f’(dsr) > 0

7. Equilibrium condition that real wages: (7) for all rs Price index for tradable goods of region rrestated in terms of the funda-mental economic variables Yr, Hr and wr: (8) Region r’s total income: (9) Price index of tradable goods (simplification): (10) : constant Equations (4) and (10): Major components of NEG-based econometric models for compound prices for tradable and non-tradable goods

8. 3. ESDA and spatial-econometric price level models3.1 Tools of exploratory spatial data analysis (ESDA) Exploratory spatial data analysis (ESDA) aims at identifying spatial properties of data for detecting spatial patterns, formulating hypotheses for geo-referenced variables and assessing spatial models. Locational tools for spatial data analysis: Detecting spatial instationarities by identifying atypical areal units Moran’s I: global measure of spatial autocorrelation (15) Cliff-Ord weight weights: , b > 0 Row-standardized weights:

9. Spatial price lag: (16) Local indicator of spatial association (LISA):Local Moran coefficient (17) Table 1: Types of local spatial association

10. 3.2 NEG-based spatial-econometric price level models Log price indices for tradables and housing: (10’) (4’) NEG-based econometric model for the consumer price level: (18) Xk: control variables Parameter restrictions (Helpman model): (19) for ln PT,r: b1 > 0, b2 > 0, (20) for ln PNT,r: b1 > 0, b2 < 0, (21) for ln Pr: b1 > 0, b2 = 0.

11. Second order trend surface model: (22) xr and yr: coordinates of a representative point in region r Linear spatial expansion of the income parameter b1: (23) ß1r = b0 + b1x×xr + b1y×yr Spatial price lag with ln Pr: (24) Mixed regressive spatial autoregressive model: (25) Spatially autocorrelated errors: (26)

12. 4. Data Regional price level models are estimated and tested for a southern German sample of districts. Survey data for 21 Bavarian municipalities: ● the consumer price index, and three sub-price indices on ● tradable goods, non-tradable goods and housing Table 2: Size classes of municipalities

13. 5. Exploratory spatial data analysis of regional price indices Figure 1: Global Moran tests for regional price indices Notes: *: Consumer price index, o: Price index of tradables, x: Price index of non-tradables, +: Price index of housing Moran test [E(I) = -0.05]: Permutation approach: 10000 permutations

14. Table 3: Local Moran coefficients for regional price indices Notes: MU: Munich, BR: Bad Reichenhall, RO: Rosenheim, NU: Nuremberg, AU: Augsburg, WU: Würzburg, BA: Bamberg, RE: Regensburg, NS: Neuburg-Schrobenhausen, SF: Schweinfurt O: Outlier according to the two-sigma rule

15. Figure 2: Moran scatterplots of price indices

16. 6. Spatial price level models: estimation and testing results Table 4: Estimation und testing results: spatial models for consumer price index

17. Table 5: Estimation und testing results: spatial models for PT, PNT and PM

18. 7. Conclusion Investigation of the contribution of NEG theory in explaining observed regional price indices: ● Spatial-econometric price level models are based on price equations derived from the Helpman model ● Spatial effects of regional (sub-)price indices are revealed with the aid of spatial exploratory data analysis (ESDA) and spatial LM tests ● While spatial dependence and spatial heterogeneity matter for explaining the overall price level and the sub-price index for tradables, spatial interaction in the sub-price indices of non-tradables and housing is captured quite well by trend surface models. Both sub-price indices are strongly linked with income and housing. ● After controlling for human capital, overall regional price level and price index of tradables are as well to a great deal determined by income.In these regional price level models, spatial price dependence does not vanish when controlling for spatial heterogeneity. Such behaviour is expected if spatial interaction is mediated by trade. ● In contrast to the prediction of the Helpman model, housing stock seems to be not neutral with respect to overall price level. The strength of the centripetal force represented by housing seems to be underrated in the Helpman model.