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Regional inflation dynamics using space–time models


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.

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Fig. 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. 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. 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. Appendix 2 contains a detailed description of these variables.

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

  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. A summary of results is available from the authors.

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

  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. We thank an anonymous referee for suggesting this approach.

  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. 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
    figure 1figure 1

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


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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.

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Correspondence to Juan de Dios Tena Horrillo.


Appendix 1: First-order conditions in the theoretical model

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

$$\begin{aligned}&\displaystyle \hat{p}_{t} =n\hat{p}_{t} \left( c \right) +\left( {1-n} \right) \left[ {\hat{t}_t +\hat{p}_t^*\left( p \right) } \right] \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{p}_{t}^{*} =n\left[ {\hat{p}_{t} \left( c \right) +\hat{t}_t } \right] +\left( {1-n} \right) \hat{p}_{t}^*\left( p \right) \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{p}_t -\hat{p}_{t}^{*} =-n\hat{t}_1 +\left( {1-n} \right) \hat{t}_{t} \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{y}_t =\theta \left[ {\hat{p}_t -\hat{p}_{t} (c)} \right] +\hat{c}_{t}^{w} \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{y}_{t}^{*} =\theta \left[ {\hat{p}_t^*-\hat{p}_t^*(p)} \right] +\hat{c}_t^{w} \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{c}_{t+1} =\hat{c}_t +\frac{\delta }{1+\delta }\hat{r}_{t+1} \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{c}_{t+1}^{*} =\hat{c}_t^{*} +\frac{\delta }{1+\delta }\hat{r}_{t+1} \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{m}_t -\hat{p}_t =\hat{c}_t -\frac{r_{t+1} }{1+\delta }-\frac{\hat{p}_{t+1} -\hat{p}_t }{\delta } \end{aligned}$$
$$\begin{aligned}&\displaystyle \hat{m}_t -\hat{p}_t^*=\hat{c}_t^*-\frac{r_{t+1} }{1+\delta }-\frac{\hat{p}_{t+1}^*-\hat{p}_t^{*} }{\delta } \end{aligned}$$
$$\begin{aligned}&\displaystyle \bar{c} =\delta \bar{b}+\bar{p}\left( c \right) +\bar{y}-\bar{p} \end{aligned}$$
$$\begin{aligned} \bar{c}^{*}=-\left( {\frac{n}{1-n}} \right) \delta \bar{b}+\bar{p}^{*}\left( c \right) +\bar{y}^{*}-\bar{p}^{*} \end{aligned}$$

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

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

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: 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.


  • 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)

1.1 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.

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Marques, H., Pino, G. & de Dios Tena Horrillo, J. Regional inflation dynamics using space–time models. Empir Econ 47, 1147–1172 (2014).

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

JEL Classification

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