Regional inflation dynamics using space–time models

Abstract

This article provides empirical evidence of the role of spatial factors on the determination of inflation dynamics for a representative set of tradable commodities in Chile. We present a simple model that explains inflation divergence across regions in a monetary union with similar preferences as a consequence of the geographical allocation of producers in the different regions. Our results indicate that spatial allocation together with transport costs are important determinants of regional inflation, while macroeconomic common factors do not play an important role in this process. Existing literature had obtained the opposite result for Europe, and the reasons for this difference warrant further investigation. Moreover, we find that geographical distance seems to be a more appropriate measure of neighbourhood than the adjacency of regions. Our results are robust to different specifications, regression methods and product groupings.

This is a preview of subscription content, access via your institution.

Fig. 1

Notes

  1. 1.

    We assume monopolistic competition given that it is realistic to think that most commodities are not perfect substitutes. This could be true even for similar commodities due, for example, to the required time to gather information about new alternative sellers or to some degree of differentiation as a consequence of advertising. This assumption also allows us to compare our framework to that of Obstfeld and Rogoff (1995) and to other relevant contributions in the field. Nevertheless, some of the commodities considered in the article are likely to be homogeneous across producers. If this is the case, then we would have a model a la Hotelling in which firms located in the centre of the market have more power to steal customers compared with its rivals. Under this assumption, it would be possible to observe different prices in different geographical areas, and this difference would be determined by transport costs. However, given the assumption of homogenous commodities in a perfectly competitive market, spatial prices would adjust immediately to exogenous shocks, and it should not be possible to observe persistent differences in the inflation dynamics of the different Chilean cities. As is shown further ahead, the empirical results of the article, by demonstrating the time-lagged adjustment of prices, provide evidence against the assumption of perfect competition and in favour of monopolistic competition.

  2. 2.

    The assumption that all goods can be traded precludes other effects inducing price divergence, such as the Balassa–Samuelson effect. In this way, we are left with transport costs and short run rigidities as the only sources of price divergence. Naturally, in the long run, all persistent divergence is attributable to transport costs.

  3. 3.

    The transport of commodities between Chilean cities is done by road. Therefore, the kilometric distance between locations is taken as the road (driving) distance, and our results apply to road transport.

  4. 4.

    Appendix 2 contains a detailed description of these variables.

  5. 5.

    Regressing separately for each of the 98 commodities in the sample can be seen as assuming independence between the markets. However, note that this approach is in fact less restrictive as it allows for parameters to vary across commodities. In any case, in Sect. 5, we run regressions using product groups to be able to further examine the sign and significance of the coefficients.

  6. 6.

    The factor estimation method is explained in detail by Beck et al. (2009). The model includes the time-lagged dependent variable, which is potentially endogenous. However, using Monte Carlo simulations, Beck and Katz (2004) find that the nickel bias is low (2 % or less) once , and they advise the use of a least-square estimator with a time-lagged dependent variable included if is at least 20. Our sample contains 45 months; hence, we do not correct for endogeneity of the time-lagged dependent variable. Nevertheless, in Sect. 5, we control for endogeneity issues.

  7. 7.

    Due to the large number of commodities used, only a summary of results is presented. The full set of results is available with the authors.

  8. 8.

    See, Anselin (1988) for a definition of the weights matrix in spatial econometric models and for different tests of spatial correlation.

  9. 9.

    This simultaneous equations model may present simultaneity problems. We start by assuming that the prices of neighbour cities can be regarded as exogenous with respect to the prices in each city as they are a weighted average of a set of prices. In Sect. 5, we relax this assumption and conduct some robustness checks of our results under simultaneity.

  10. 10.

    A summary of results is available from the authors.

  11. 11.

    Again these results are omitted but are available from the authors.

  12. 12.

    The instruments used are common factor (contemporaneous and first time-lag); national inflation (contemporaneous and first two time-lags); neighbour inflation (up to the fifth time-lag); dependent variable (second to fifth time-lags). The results are robust to the selected time-lags. We have used the Hansen test to study if instruments are strong and valid. At the 5 % significance level, we can accept that the residuals of the estimation are uncorrelated with all exogenous variables (i.e. the exogenous variables and the instrumental variables) in 98 and 67 % of the cases for the GMM and the General spatial 2SLS estimation respectively. We could also reject the hypothesis of weak instruments in 100 and 99 % of the cases for the GMM and the General spatial 2SLS estimation respectively.

  13. 13.

    We thank an anonymous referee for suggesting this approach.

  14. 14.

    For this estimation, we used the sphet package in R as it is freely available and can be easily applied to our model.

  15. 15.

    We prefer to consider model 3 in all cases given that it is a more general model that also encompasses the case in which spatial parameters are equal to zero. However, we have also observed how the histograms of parameters of model 3 in Fig. 1 are altered when we consider instead model 1 for the cases in which the null of no spatial dependence has not been rejected at the 5 % level. The main conclusions are not altered if we had followed this alternative procedure. This other figure is available from the authors upon request.

    Fig. 1
    figure1figure1

    Histograms for the significant parameters in Model 3 (at 5 %)

References

  1. Andrés J, Ortega E, Vallés J (2008) Competition and inflation differentials in EMU. J Econ Dyn Control 32(3):848–874

    Article  Google Scholar 

  2. Altissimo F, Benigno P, Rodriguez-Palenzuela D (2005) Long-run determinants of inflation differentials in a Monetary Union. NBER WP 11473

  3. Anselin L (1987) Spatial dependence and spatial heterogeneity: a closer look at alternative modeling approaches, Working paper, Department of Geography, University of California, Santa Barbara, CA

  4. Anselin L (1988) Spatial econometrics, methods and models. Kluwer Academic, Boston

    Google Scholar 

  5. Arbia G (2006) Spatial econometrics. Springer, Berlin

    Google Scholar 

  6. Beck G, Hubrich K, Marcellino M (2009) Regional inflation dynamics within and across Euro Area countries and a comparison with the US. Econ Policy 24(57):141–184

    Article  Google Scholar 

  7. Beck G, Hubrich K, Marcellino M (2011) On the importance of sectoral and regional shocks for price-setting. CEPR Discussion Papers 8357, C.E.P.R. Discussion Papers

  8. Beck N, Katz J (2004) Time-series-cross-section issues: dynamics. New York University, New York

    Google Scholar 

  9. Boivin J, Giannoni M, Mihov I (2009) Sticky prices and monetary policy: evidence from disaggregated US data. Am Econ Rev 99:350–384

    Article  Google Scholar 

  10. Cecchetti S, Mark N, Sonora R (2002) Price index convergence among United States cities. Int Econ Rev 43:1081–1099

    Article  Google Scholar 

  11. Drukker DM, Prucha IR, Raciborski R (2011a) Maximum-likelihood and generalized spatial two-stage least-squares estimators for a spatial-autoregressive model with spatial-autoregressive disturbances. Department of Economics, University of Maryland, Mimeo

  12. Drukker DM, Prucha IR, Raciborski R (2011b) A command for estimating spatial-autoregressive models with spatial-autoregressive disturbances and additional endogenous variables. Department of Economics, University of Maryland, Mimeo

  13. Fujita M, Krugman P (1995) When is the economy monocentric?: von Thunen and Chamberlin unified. Reg Sci Urban Econ 25(4):505–528

    Article  Google Scholar 

  14. Fujita M, Krugman P, Venables A (1999) The spatial economy. Cities, regions and international trade. MIT Press, Cambridge

    Google Scholar 

  15. Hall AR (2005) Generalized method of moments. Oxford University Press, Oxford

    Google Scholar 

  16. Helpman E, Krugman P (1985) Market structure and foreign trade: increasing returns imperfect competition, and the international economy. MIT Press, Cambridge

    Google Scholar 

  17. Kelejian HH, Prucha IR (1998) A generalized spatial two stages least square procedure for estimating a spatial autoregressive model with autoregressive disturbances. J Real Estate Finance Econ 17(1):99–121

    Article  Google Scholar 

  18. Kelejian HH, Prucha IR, Yuzefovich Y (2004) Instrumental variable estimation of a spatial autoregressive model with autoregressive disturbances: large and small sample results. In: LeSage JP, Pace RK (eds) Advances in econometrics: spatial and spatio-temporal econometrics. Elsevier, Oxford, pp 163–198

    Google Scholar 

  19. Kelejian HH, Prucha IR (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroscedastic disturbances. J Econom 157(1):53–67

    Article  Google Scholar 

  20. Krugman P (1991) Increasing returns and economic geography. J Political Econ 99(3):483–499

    Article  Google Scholar 

  21. Krugman P (1995) Innovation and agglomeration: two parables suggested by city-size distributions. Jpn World Econ 7(4):371–390

    Article  Google Scholar 

  22. LeSage J (1999a) Spatial econometrics: the web book of regional science. Regional Research Institute, West Virginia University, Morgantown

    Google Scholar 

  23. LeSage J (1999b) The theory and practice of spatial econometrics. A manual to accompany the spatial econometrics toolbox. http://www.spatial-econometrics.com

  24. Levin A, Lin Ch, James Chu Ch (2002) Unit root tests in panel data: asymptotic and finite-sample properties. J Econom 108:1–24

    Article  Google Scholar 

  25. Mackoviak B, Moench E, Wiederholt M (2009) Sectoral price data and models of price setting. J Monet Econ 56:78–99

    Article  Google Scholar 

  26. Obstfeld M, Rogoff K (1995) Exchange rate dynamics redux. J Political Econ 103:624–660

    Article  Google Scholar 

  27. Parsley D, Wei S-J (1996) Convergence to the law of one price without trade barriers of currency fluctuations. Quart J Econ 111:1211–1236

    Article  Google Scholar 

  28. Pesaran MH (2006) A simple panel unit root test in the presence of cross-section dependence. J Appl Econom 22(2):265–312

    Article  Google Scholar 

  29. Piras G (2010) Sphet: spatial models with heteroskedastic innovations. R. J Stat Softw 35(1):1–21. http://www.jstatsoft.org/v35/i01/

  30. Samuelson P (1952) The transfer problem and transport costs: the terms of trade when impediments are absent. Econ J 62:278–304

    Article  Google Scholar 

  31. Schumacher C, Breitung J (2008) Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data. Int J Forecast 24:386–398

    Article  Google Scholar 

  32. Stock J, Watson M (2002) Macroeconomic forecasting using diffusion indexes. J Business Econ Stat 20:147–162

    Article  Google Scholar 

  33. Tena JD, Espasa A, Pino G (2010) Forecasting Spanish inflation using the maximum disaggregation level by sectors and geographical areas. Int Reg Sci Rev 33:181–204

    Article  Google Scholar 

Download references

Acknowledgments

J. D. Tena acknowledges financial support from the British Academy under the Visiting Scholars Programme while working on this article. The authors are also grateful to the anonymous referees whose comments have greatly contributed towards improving the article. The usual disclaimer applies.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Juan de Dios Tena Horrillo.

Appendices

Appendix 1: First-order conditions in the theoretical model

The equilibrium (in log-linear form) is represented by the following system of equations:

$$\begin{aligned}&\displaystyle \hat{p}_{t} =n\hat{p}_{t} \left( c \right) +\left( {1-n} \right) \left[ {\hat{t}_t +\hat{p}_t^*\left( p \right) } \right] \end{aligned}$$
(8.1)
$$\begin{aligned}&\displaystyle \hat{p}_{t}^{*} =n\left[ {\hat{p}_{t} \left( c \right) +\hat{t}_t } \right] +\left( {1-n} \right) \hat{p}_{t}^*\left( p \right) \end{aligned}$$
(8.2)
$$\begin{aligned}&\displaystyle \hat{p}_t -\hat{p}_{t}^{*} =-n\hat{t}_1 +\left( {1-n} \right) \hat{t}_{t} \end{aligned}$$
(8.3)
$$\begin{aligned}&\displaystyle \hat{y}_t =\theta \left[ {\hat{p}_t -\hat{p}_{t} (c)} \right] +\hat{c}_{t}^{w} \end{aligned}$$
(8.4)
$$\begin{aligned}&\displaystyle \hat{y}_{t}^{*} =\theta \left[ {\hat{p}_t^*-\hat{p}_t^*(p)} \right] +\hat{c}_t^{w} \end{aligned}$$
(8.5)
$$\begin{aligned}&\displaystyle \hat{c}_{t+1} =\hat{c}_t +\frac{\delta }{1+\delta }\hat{r}_{t+1} \end{aligned}$$
(8.6)
$$\begin{aligned}&\displaystyle \hat{c}_{t+1}^{*} =\hat{c}_t^{*} +\frac{\delta }{1+\delta }\hat{r}_{t+1} \end{aligned}$$
(8.7)
$$\begin{aligned}&\displaystyle \hat{m}_t -\hat{p}_t =\hat{c}_t -\frac{r_{t+1} }{1+\delta }-\frac{\hat{p}_{t+1} -\hat{p}_t }{\delta } \end{aligned}$$
(8.8)
$$\begin{aligned}&\displaystyle \hat{m}_t -\hat{p}_t^*=\hat{c}_t^*-\frac{r_{t+1} }{1+\delta }-\frac{\hat{p}_{t+1}^*-\hat{p}_t^{*} }{\delta } \end{aligned}$$
(8.9)
$$\begin{aligned}&\displaystyle \bar{c} =\delta \bar{b}+\bar{p}\left( c \right) +\bar{y}-\bar{p} \end{aligned}$$
(8.10)
$$\begin{aligned} \bar{c}^{*}=-\left( {\frac{n}{1-n}} \right) \delta \bar{b}+\bar{p}^{*}\left( c \right) +\bar{y}^{*}-\bar{p}^{*} \end{aligned}$$
(8.11)

where for each variable \(x_t\), we define \(\hat{x}_{t} \equiv dx_{t} /x_{0}\) and \(\bar{x}\) corresponds to its value in equilibrium.

Equations (8.1) and (8.2) are the log-linear form of the central and peripheral price indexes under the assumption of asymmetry among each region’s producer, and the relationships between prices in the two regions are sketched in Eq. (8.3). The log-linear form for the demands of an individual good produced in the central and peripheral regions are described in Eqs. (2.14) and (2.15) in which we define world consumption as

$$\begin{aligned} \hat{c}_{t}^{w} =n\hat{c}_t +\left( {1+n} \right) \hat{c}_{t}^{*} =n\hat{y}_{t} +\left( {1+n} \right) \hat{y}_{t}^{*} =\hat{y}_{t}^{w} \end{aligned}$$
(8.12)

Equations (8.4) to (8.9) express the first-order conditions from the maximization of the individual utility function, whereas the last two equations derive from the integration of the individual’s period budget constraint over time and the imposition of the transversality condition.

Appendix 2: Time series

The time series considered in the analyses can be freely obtained from the Chilean National Statistical Institute at the following URL: http://www.ine.cl. The panel database consists of observations for 98 different items in 23 different Chilean cities on monthly basis for the period 2003:01–2006:09.

The cities and items in the sample are listed below:

  • Cities: Chillán, Copiapo, Quillota, Coihaique, Concepción, Linares, Iquique, Punta Arenas, Los Ángeles, Osorno, Rancagua, Arica, Los Andes, San Antonio, Valparaiso, Curicó, Puerto Montt, Talca, San Fernando, Valdivia, Temuco, Antofagasta, La Serena.

Items

  • Group 1: bread & cereals - r1: Normal bread (kg), r2: Special bread (no package) (kg), r3: Rice (kg), r4: Flour (kg), r5: Oats (500 g), r6: Noodles \(N^{\underline{\mathrm{o}}}\) 5 (400 g), r7: Noodles \(N^{\underline{\mathrm{o}}}\) 87 (400 g), r8: Spiral Noodles (400 g), r9: Quifaro Noodles (400 g), r10: Wafer biscuit (140 g), r11: Lemon biscuit (140 g), r12: Water biscuit (210 g), r13: Salted potatoes (230 g), r15: Pai (15 persons), r44: Cereal (box) (510 g)

  • Group 2: fresh meat - r16: Meat (best quality) (kg), r17: Beef ribs (kg), r18: Rump, Cap and Tail Off (kg), r19: Filet (kg), r20: Sirloin Tip (kg), r21: Shank (kg), r22: Minced meat 10 % fat (kg), r23: Pork chop (kg), r24: Pork rib cage (no seasoning) (kg), r25: Chicken (kg), r26: Chicken breast (kg), r27: Turkey breast (kg)

  • Group 3: fresh fish - r28: Fish (kg)

  • Group 4: canned & processed meat & fish - r29: Canned mackerel (425 g), r30: Canned tuna (184 g), r31: Canned sardines (125 g), r32: Ham (kg), r33: Culin bologna (kg), r34: Sausages (20 units), r35: Spicy sausages (kg), r36: Beef Paté (125 g), r50: Powered gelatine (160 g), r80: Chicken gravy cubes (8 units)

  • Group 5: fresh dairy products - r37: Mayonnaise (250 cc), r38: Eggs (12 units), r39: Milk (bag) (lt), r40: Milk (pack) (lt), r45: Salted butter (kg), r46: Cheese (kg), r47: Cream Cheese (kg), r48: Cheese (bag) (360 g), r49: Yogurt (175 g), r89: Ice cream (lt)

  • Group 6: preserved dairy products - r41: Powdered milk (1,6 kg), r42: Powdered milk (kg), r43: Sweetened condensed milk (400 g), r51: Powered caramel pudding (180 g), r82: Fortifier for milk (400 g)

  • Group 7: vegetable fats - r52: Vegetable oil(lt), r53: Sunflower oil(lt), r54: Salted Margarine (250g)

  • Group 8: fresh fruits & vegetables - r55: Avocado (kg), r56: Organic tomato (kg), r57: Normal tomato (Kg), r58: Lemons (kg), r59: Apples (kg), r60: Oranges (Kg), r61: Bananas (kg), r64: Potatoes (kg), r65: Garlics (3 units), r66: Onions (kg), r67: Lettuce (one), r68: White cabbage (one), r69: Carrots (bunch), r70: Pumpkin (kg), r73: Green beans (kg)

  • Group 9: canned & dried fruits & vegetables - r14: Olives (300 g), r62: Canned peaches (590 g), r63: Canned peas (310 g), r71: Lentils 5 mm (kg), r72: Beans (kg), r74: Tomato sauce (bottle) (250 g), r75: Tomato sauce (tetra) (215 g), r77: Marmalade (250 g), r79: Instantaneous soup (70 g)

  • Group 10: sugar & salt - r76: Sugar (kg), r78: Salt (kg)

  • Group 11: beverages - r81: Coffee (170 g), r83: Tea (250 g), r84: Tea bags (20 units), r85: Bottled soft drink (2 lt), r86: Canned soft drink (355 cc), r87: Organic juice (lt), r88: Powder juice (45 g), r90: Wine (lt), r91: Sparkling mineral water (1,6 lt), r92: Bottled beer (lt), r93: Canned beer (355 cc), r94: Pisco especial \(35^{\underline{\mathrm{o}}}\) (750 cc), r95: Pisco especial \(35^{\underline{\mathrm{o}}}\) (645 cc)

  • Group 12: gasoline - r97: Gasoline 95 octanes (lt), r98: Gasoline 97 octanes (lt), r96: Gasoline 93 octanes (lt)

Macroeconomic national factor

The macroeconomic national factors were obtained by principal components from the following variables:

  • Source: EcoWin. Production, Manufacturing, Index, 2002 = 100 (Ew:clp02005); Labour Cost, Real, total, Constant Prices, Index, 2006M1 = 100 (ew:clp10020); Inactivity, Economic inactive population, total (ew:clp09030); Chile, Money supply M3, CLP (ew:clp12005); Light Crude Futures 33-Pos, Nymex, Close (ew:com2431510); OPEC Reference Basket Price, Average (ew:com2121010).

  • Source: Central Bank of Chile. Interbank loan rate (1 day); Exchange rate from the central bank of Chile.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Marques, H., Pino, G. & de Dios Tena Horrillo, J. Regional inflation dynamics using space–time models. Empir Econ 47, 1147–1172 (2014). https://doi.org/10.1007/s00181-013-0763-9

Download citation

Keywords

  • Regional inflation dynamics
  • Space–time models
  • Common factors
  • Chile

JEL Classification

  • E31
  • E52
  • E58
  • R11
  • C23
  • C21