1 investigaciones economicas,vol. XXI(2), 1997, ARETHEREANYSPECIALFEATURESINTHE SPANISH BUSINESS CYCLE? LUIS A. PUCH CEPREMAP OMAR LICANDRO FEDEA and Universidad Carlos III de Madrid In this paper we analyze the empirical performance for the Spanish economy of a standard real business cycle model. To this purpose, we de ne a set of measurements consistent with the structure of our model economy and we evalute both the long-run and business cycle properties of this reference dataset. Wesolvethemodel alternativelywith divisibleandindivisiblelabor and, in each case, with and without government consumption. We set the values of the structural parameters by combining calibration and estimation (GMM) techniques, and its implications on the results are evaluated. When we introduce indivisibilities in labor supply and government consumption the model's empirical performance is improved. In this respect, our results do not di er substantially from those obtained for the US economy. However, the model fails to explain the cyclical behavior of private consumption in the Spanish economy. (JEL E32, E37) 1. Introduction In this paper we evaluate the empirical performance for the Spanish economy of a standard real-business-cycle (RBC) model. The RBC approach has produced important advances in theinvestigation of the We thank Fabrice Collard, Jean-Fran»cois Fagnart, Patrick Fµeve, Javier D ³az- Gim enez, Juan F. Jimeno, Fran»cois Langot, Albert Marcet, Alfonso Novales, FranckPortier, Ram onruiz-tamarit, Sim onsosvilla, Javier Vall es, two anonymous referees and the editor for their multiple suggestions. Angel Estrada and Miguel Sebasti an gave us the data onconsumer durables and non-durables. Pilar Garc ³a Perea gave us the hours worked and employment series. We acknowledge nancial support from the Fundaci on Caja de Madrid and the CICYT(SEC ). L. Puch gratefully acknowledges the hospitality and the facilities of FEDEA and Universidad Carlos IIIde Madrid.
2 362 investigaciones economicas aggregate uctuations associated with the business cycle. However, there is a small number of applications of the RBC methodology to the analysis of the uctuations of the Spanish economy. 1 One of the main reasons underlying this circumstance is the lack of appropriate data. In fact, only recently National Accounts have been available on a quarterly basis. Moreover, the additional data sources, which are generallyneeded to round o the selection of parameter values, often lack an adequate homogeneity. 2 Consequently, the rst objective of this paper is to build an appropriate data set for the Spanish economy to ful ll the basic measurement requirements of RBC exercises. Not only the lack of reliable data justi es the absence of RBC models for the Spanish economy. One of the most recurrent arguments amongst the (Spanish) detractors of the RBC approach can be stated in terms of its inappropriateness to the study of the labor-market uctuations in economies with high unemployment. Another argument typically arises when discussing the role of the government sector in OECD economies other than the US. These two reasons lead us to choose as our standard RBC benchmark the speci cation proposed by Christiano and Eichenbaum (1992). Undoubtedly, as a variant of Hansen (1985) and Rogerson's (1988) indivisible labor model, Christiano and Eichenbaum's (1992) constitutes one of the most signi cant advances in the study of the key labor-market features in the RBC tradition. These authors modify the indivisible labor model by allowing government consumption shocks to in uence labor-market dynamics. Their empirical results indicate that this change improves the predictions of the model throughout its labor-market dimension and, in particular, with respect to the observed weak correlation between hours worked and wages, the so-called Dunlop-Tarshis observation. Of course, in the last seven years much progress has been made on the labor-market dimension of business cycle models, often through departures from the assumption of perfectly competitive labor markets. 3 1 SomeexceptionsareDoladoetal. (1993),Licandroetal. (1996)andOrtega (1994). 2 In this respect, recent works by Carbajo and Garc ³a-Perea (1988), Estrada and Sebasti an (1993)andGarc ³a Perea (1991), amongstothers, are extremely valuable. 3 SeeforexampleAndolfatto(1996),BeaudryandDiNardo(1995),Boldrinand
3 arethereanyspecial features inthespanishbusiness cycle? 363 However, none of these contributions belongs to the mainstream of the RBC research program. We would like to see whether the main conclusions of Christiano and Eichenbaum's (1992) RBC models hold when parameter values are chosen to t the Spanish data. Thus, the motivation of this paper is twofold: i) following Christiano (1987) and Cooley and Prescott (1995), to de ne a set of measurements of the Spanish economy consistent with the type of models under consideration, and ii) to evaluate the validity of the main conclusions of the RBC models on Spanish data, in particular in one of their most critical dimensions: labor-market uctuations. This will allow us to achieve a better characterization of both the cyclical properties and the long-run features of the Spanish economy. Also, we will beable to providea set of results that can beuseful for future research. This research should involve both extensions of the models and improvements in the data set. As has been stated above, the speci cation of a stochastic dynamic general equilibrium model we adopt is the one proposed by Christiano and Eichenbaum (1992). This speci cation incorporates: i) the divisible and indivisible labor hypothesis, and ii) either the presence or absence of the government sector. The indivisible labor model in Rogerson (1988) and Hansen (1985) assumes that individuals either work a xed number of hours or they do not work at all. If the individuals can choose the probability of working, then it is possible to widen the set of choices in such a way that the economy behaves as if there were no indivisibilities. This gives rise to uctuations in aggregate employment relatively more important than variations in the labor productivitysincethe marginaldisutilityof an extra unit of individuals at work is constant and independent of the number of individuals who work. Christiano and Eichenbaum (1992), building upon Hansen (1985), argue that the observed weak correlation between hours worked and productivity suggests that technology shocks cannot bethe onlyimpulse behind aggregate uctuations. Therationale for this is that, with technology shocks, movements in equilibrium wages and hours are mainly due to movements along the labor sup- Horvath(1995), Danthine and Donaldson(1990)and(1995), Fairise and Langot (1994)and Gali(1996).
4 364 investigaciones economicas ply curve, which results in a high positive correlation between these two variables. Consequently, when innovations in government expenditures are incorporated into the analysis the empirical performance of the model is improved. This is not the only contribution in Christiano and Eichenbaum (1992) though. In addition, their work represents one of the rst implementations of Hansen's (1982) Generalized Method of Moments (GMM) to the formal estimation of RBC models. We will pursue this methodology in our application to the Spanish economy. This means that we evaluate the conformity of the models with the data and we estimate the structural parameters of the model in order to have a metric to measure and test the model's implications. Our main motivation to incorporate the estimation and evaluation procedure comes frompractical reasons: to performcomparisons not only with the results for the US economy but also with comparable results for the French economy reported in Fµeve and Langot (1994). 4 As emphasized by Kydland and Prescott (1991) the evaluation of a model relies on the economic theory underlying it and not on any statistical measure of the discrepancy between the model and the data. Consequently, our strategy does not particularly stress the validation procedure; rather, it tries to take advantage of nearly ten years of GMM estimation to obtain additional insights into the performance of the models. Thus, we consider it useful to compare the parameter selection procedure used under calibration techniques with the GMM estimation of the structural parameters. 5 It is important to stress that RBC models integrate the study of aggregate uctuations within the framework of growth theory. Thus, before proceeding with the analysis it is important to evaluate whether the observations are consistent with the assumption of balanced growth. We nd that hours worked exhibit a marked downward trend until the middle of the eighties and that the capital-output ratio has 4 Tentative comparisons with results in Correia et al. (1995) and Kollintzas and Vassilatos(1996), for Portugal and Greece respectively, may be possible. 5 This argument is in line with part of the discussion in Canova and Ortega (1996). Increasingly, researchers are combining calibration and estimation techniquestoanalyzebusinesscycles,forinstancewhendevelopingthesmmapproach as inhairaultetal. (1996).
5 arethereanyspecial features inthespanishbusiness cycle? 365 a slight upward trend. It is for this reason that we will restrict the sample period to 1976:1-1994:4. This sampleapproximates the longrun properties of the Spanish economy better than the whole sample. Our main results suggest that theempirical behavior for Spanish data of the standard RBC models under consideration does not di er substantially from that for the US economy. All the models do well at matching output volatility and the volatility of investment relative to output. Also, when labor indivisibilities and innovations in government expenditures are incorporated into the analysis the empirical performance of the model with respect to the labor-market variables is somewhat improved. This might be taken as some evidence with respect to the fact that, in terms of aggregate uctuations at least, di erent economies behave in a similar way regardless of the level of unemployment, and only deviations of employment have relevant e ects on the cyclical properties of the economy. This opens the question of what is the role played by unemployment in the transmission of aggregate uctuations. As reported by Dolado et al. (1993), Spanish private consumption is more volatile than GDP, which contradicts the life-cycle hypothesis. They measure private consumption as the consumption of durable and non durablegoods. The substitution of consumer durables byan estimation of the ow of services derived fromthempartiallyanswers this puzzle, by reducing private consumption volatility below GDP volatility. Moreover, our proposed measure for production is more volatile than GDP, but the relative volatility of private consumption remains high. In any case, the models analyzed in this paper are not able to reproduce the high volatility of our measure of private consumption in Spain relative to our measure of production. This means basically that a lot of work remains to be done in order to explain what we would call the Dolado-et-al puzzle. Moreover, from the results in Christiano and Eichenbaum (1992) we know that labor indivisibilities and government consumption shocks are not enough to account for the Dunlop-Tarshis observation. Only when they incorporate measurement error in hours worked into the analysis the puzzle is resolved. Given that we do not have a reliable measure of hours worked, we leave for future research the exploration of this
6 366 investigaciones economicas feature of the model. The paper is organized as follows. Section 2 describes the model and its alternative speci cations. In Section 3 we analyze the main implications of our measurements of aggregate variables for the stylized facts of the Spanish economy. Section 4 discusses calibration and estimation. In Section 5 we report the main results and Section 6 concludes and evaluates the plausibility of some extensions. Appendix 1 contains the description of the data and the procedures used to construct our reference data set. 2. The economy As our benchmark RBC model we adopt Christiano and Eichenbaum's (1992) speci cation. This includes a version of the stochastic growth model with divisible labor and a version of Hansen's (1985) indivisible labor growth model. In both cases government consumption may be incorporated into the analysis as described below. The economy is inhabited by a large number of in nitely lived households that we normalize to one. As is standard in growth and business cycle models, the decentralized competitive equilibriumcan becharacterized bythe solution of a planning problem. Theplanner chooses the representative household's stochastic sequences of consumption and leisure to maximize X 1 E 0 t[ln(c t s ) + µ V (N n t )];  t=0 where represents the discount factor, C s t are per-capita consumption services, n t per-capita hours worked, N is the individual endowment of productive time, and µ is a positive parameter which represents the household's preferences for leisure. In the reference case V (N n t ) = ln(n n t ). Alternatively, if we assume that households' utility functions are linear in leisure then V (N n t ) = N n t, as in Hansen (1985). This speci cation is consistent with the existence of indivisibilities in the labor supply. 6 Notice that an appropriate manipulation implies that µ(n n t ) = µn(1 ¼ t ) + µ(n l)¼ t, where 6 Ifhouseholds'utilityfunctionsareseparableacrossconsumptionandleisure, Rogerson(1988)shows that a market structure in which agents choose the prob-
7 arethereanyspecial features inthespanishbusiness cycle? 367 ¼ t = n t =l represents the probability of nding a job with a xed number l of quarterly hours. Consumption services incorporate both per-capita private consumption C t and per-capita government consumption G t according to the function C s t = C t + G t ;  where is either 0 or 1. It is assumed that G t is a stochastic process beyond the planner's control. When = 1, private and public consumption are perfect substitutes. In this case, for any sequence of public consumption individuals may adjust private consumption in order to follow the same optimal path for total consumption. The equilibrium of this economy is formally the same as the one for an economy without government. Government consumption is incorporated into the analysis when = 0, implying that public consumption has no e ects on individual utility (it is a pure loss of resources). Crowding-out e ects coming from stochastic government spending should a ect the equilibriumpath. In particular, they should help to explain the Dunlop-Tarshis puzzle, since shocks to governement consumption move the labor supply curve, allowing for countercyclical responses of employment and wages. We will assume that per-capita aggregate output at time t, Y t, depends on per-capita capital stock, K t, and per-capita hours worked, n t, through a Cobb-Douglas production function of the form Y t = K (1 ) t (n t X t ) ;  where 0 < < 1 and X t represents the state of technology which evolves according to X t = X t 1 expf + v t g:  The technology shock v t is supposed to follow an i:i:d: process with zero mean and standard deviation ¾ v, and is a positive constant which represents the expected growth rate. ability of being at work some xed number of hours instead of hours worked guarantees a Pareto optimal allocationof consumptionandleisure.
8 368 investigaciones economicas The aggregate resource constraint is given by C t + G t + K t+1 (1 ±)K t Y t :  Given the de nition of the state of technology and to keep the balanced growth properties of the model we assume that G t evolves according to G t = X t g t ;  where g t follows the law of motion ln(g t ) = (1 ½)ln(¹g) + ½ln(g t 1 ) + ² t :  ln(¹g) is the mean of the stationary component of government consumption, ln(g t ), 0 < ½ < 1, and ² t is the innovation to ln(g t ) which is assumed to follow an i:i:d: process with zero mean and standard deviation ¾ ². The planner chooses fy t ; C t ; K t+1 ; n t : t 0g to maximize  subject to  -  given K 0, X 1 and g 1. Finally, it is convenient to obtain a stationary representation of this social planning problem by normalizing with respect to the state of technology, X t. To this end we de ne the following detrended variables: c t = ln(c t =X t ); k t+1 = ln(k t+1 =X t ); and y t = ln(y t =X t ): Note that g t ; andn t are stationary Consistent measurements and stylized facts Business cycle theory aims at improving our understanding of the cyclical behavior of actual economies. The empirical evaluation of the capability of di erent models to reproduce the type of aggregate uctuations associated with the business cycle requires the set of measurements describing the actual economy to be consistent with the features of the model economy. The National Accounts of the Spanish Economy (Contabilidad Nacional de Espa~na; NA henceforth and NAq for the quarterly version) 7 Unlessotherwiseindicated,lowercaselettersdenotestationaryvariables.
9 arethereanyspecial features inthespanishbusiness cycle? 369 are somewhat inconsistent in their treatment of consumer durables and this has some e ects on the measures of output, consumption and investment. 8 More precisely, the NA data include consumption of durable goods as part of private consumption. However, the ow of services from these goods lasts for more than one period so that purchases of consumer durables should be computed as investment. Consequently, capital stock data have to match the de nition of investment, and the corresponding ow of services from the stock of consumer durables has to be imputed as part of measured output. In addition, in this paper we restrict ourselves to closed economy models so that we have to construct consistent measures of output and the components of demand. In particular, Christiano (1987) and Cooley and Prescott (1995) have proposed alternative de nitions of measurements consistent with closed economy models. These two approaches di er in their treatment of the balance of trade. Cooley and Prescott (1995) include net exports in the measure of investment, whereas Christiano (1987) excludes the foreign sector from the de nition of output. We choose to keep our de nition of variables closer to Christiano's (1987) proposal in order to make comparisons more straightforward. 9 We discuss below the main ingredients of our reference data set and we evaluate its implications on the stylized facts of the Spanish economy The data Following Christiano (1987), we de ne a setof measurements for the capital stock, employment, output and the components of demand. All series are quarterly for the period 1970:1-1994:4 and they were transformed to per capita terms using a measure of the labor force. See Appendix 1 for details. The capital stock, denoted by K t, includes public and private cap- 8 Cooley and Prescott (1995) discussed in detail the imperfections of the NationalIncomeandProductAccounts(NIPA)oftheUS.Theseimperfectionsare present in the Contabilidad Nacional de Espa~na. 9 Christiano (1988) and several subsequent papers use Christiano's (1987) measures.
10 370 investigaciones economicas ital, residential structures and a measure of the stock of consumer durables. The time series of hours worked we consider, H t, corresponds to hours worked by employed-person times the number of employed population and it is in per-capita terms. Private consumption, C t was measured as quarterly real expenditure in nondurables and services, plus an imputed ow of services from the stock of consumer durables. Gross Investment, I t, is the result of adding up the investment on xed capital series and the series of expenditure in durable goods. We have not included inventoryinvestment in our measure of gross investment, since in future work we expect to include this variableexplicitly into the analysis. Government consumption, which we denote G t, is the government consumption from the NAq divided by our measure of population. Finally, output per capita is the result of adding up the three previous components: Y t = C t +I t +G t. The main di erence between our measure of output and the corresponding GDP measure in the NAq is that we exclude net exports and inventory investment and we include the imputed ow of services of the stock of consumer durables. We would have liked to include a measure of the ow of services generated for the stock of public capital. Unfortunately a quarterly series for public investment is not available Stylized facts A rst and extensive description of the cyclical regularities of the Spanish economy was carried out by Dolado et al. (1993), using quarterly National Accounts (NAq) data. Our interest here is to brie ydiscuss some stylized facts relevant to our study. In particular, from the conclusions outlined by Dolado et al. (1993), we want to highlight the following: (a) the low volatilityof Spanish output when compared with output volatility in other industrialized economies, (b) in a seeming contradiction with the life-cycle hypothesis, consumption is more volatile than output, and (c) netexports are countercyclical. Table 1 reports some moments of interest for the original NAq data set in the 1970:1 1994:4 period. 10 Table 2 reports the results with 10 The trend component of the series is obtained by the use of the Hodrick-
11 arethereanyspecial features inthespanishbusiness cycle? 371 Variable x Table1 Second-moment properties of HP- ltered data. Relative Volatility National Accounts Data Period 1970:1 1994:4 Cross-correlations of GDP with x(t-3) x(t-2) x(t-1) x(t) x(t+1) x(t+2) x(t+3) GDP Private cons Govt' cons Fixed Invt' NX/ GDP National Accounts quarterly data for the period 1970:1 1994:4. All variables areinrealterms. ForthenetexportsoverGDPratio,XN/PIB,thereported value is absolute volatility (%). All variables are in logs except XN/PIB. Output volatility is 1:16%. our reference data set. The use of one or the other set of measurements is not innocuous and has some relevant e ects on the moments of the cyclical component of the Spanish economy's aggregate variables. In particular, when we move from NAq data to the reference data set there is an important increase in output volatility (from 1.16% to 1.46%), mainly as a result of the exclusion of net exports which are negatively correlated with GDP. As a consequence of the previous result, therelativevolatilityof the demand components decreases signi catively. Moreover, the substitution of the consumption of consumer durables by an estimate of the ow of services of the corresponding stock results in a smoothing of the consumption se- Prescott lter(hp),withtheusualvalueofthesmoothingparameterforquarterly data, i.e. = For comparisonpurposes, note that the sample period in Doladoetal. (1993)is1970:1-1991:4. Thesampleweareabletouseincludesthe last recession, which results in a slight increase in the volatility of all the series, andparticularlyingdp.
12 372 investigaciones economicas Variable x Table2 Second-moment properties of HP- ltered data. Relative Volatility Reference data set Period 1970:1 1994:4 Cross-correlations of output with x(t-3) x(t-2) x(t-1) x(t) x(t+1) x(t+2) x(t+3) Output Private cons Govt' cons Fixed Invt' Reference quarterly data set for the period 1970:1 1994:4. All variables are in logs and real terms. All variables are in per capita terms. Output volatility is 1:46%. ries. This element further contributes to the decrease of the relative volatility of consumption. It can be seen that with the NAq data consumption is more volatile than production (the relative volatility is 1.07%), whereas in our reference data set the relative volatility of consumption is However, the correlations of the components of output with GDP are not substantially modi ed. Finally, it is important to evaluate whether the aggregate data of the Spanish economy during the period 1970:1-1994:4 are consistent with the required balanced growth assumptions. In this respect it is important to notice that hours worked exhibit a marked downward trend until the middle of the eighties. This is explained by an important reduction in the number of hours per worker during the seventies and, to a lesser extent, by a decrease in the employment rate in the eighties. The capital-output ratio exhibits some trend at the beginning of the sample. It can be argued that the unit root resulting from a stationarity test of the series is spurious though. More precisely, we nd that the capital-output ratio admits a change of mean around the second quarter of However, once the usual tests are performed, the hypothesis that the capital-output ratio is stationary
13 arethereanyspecial features inthespanishbusiness cycle? 373 with a change of mean is only acceptable up to a 10% signi cance level. When testing this hypothesis on the output series (both on GDP and on our measure of output) and the capital series we nd some evidence in favor of a segmented mean at 1975:2. This nding is consistent with the results reported in Andr es et al. (1990 p.103) and Bajo-Rubio and Sosvilla (1994 p.114) from annual data. For all these reasons, it is clear that the Spanish economy does not ful ll the balanced growth assumptions over the whole sample. We accept as a compromise solution that data from 1976:1 to 1994:4 might represent the long run properties of the Spanish economy better than the entire sample. As we will see when discussing our empirical results, this selection turns out to be particularly appropriate for the capital-output ratio, the outputgrowth rate and thelabor share, which are key elements of the model. Moreover, as can be checked by comparing Tables 2 and 6, second moment properties are very similar in both samples. However, as noted in Section 5, only some of the dimensions of the restricted sample are fully consistent with the balanced growth assumptions. 4. Calibration and estimation In this section we perform three tasks: a) we calibrate the model economy to obtain point estimates of the underlying parameters, b) we use a version of Hansen's (1982) generalized method-of-moments (GMM) to take into account parameter and sample uncertainty, and iii) we test from a statistical point of view the plausibility of the model's implications. It should be noticed that the labor share,, and the discount factor,, cannot be set independently. In this dimension, calibration implies taking from data and obtaining from the Euler condition at the steady state, whereas under a standard GMM approach the procedure consists of xing to estimate. To have consistent parameters coming from these two alternative methodologies, we set the value of the discount factor obtained from the calibration in order to obtain our GMM estimation of.
14 374 investigaciones economicas Table3 Calibrated parameter values. Individual's time endowments (1) N 1369 Subjective discount rate (3) 0:9891 Preference for leisure (3) µ Without Government Divisible labor 2:0684 Indivisible labor 0:0021 With Government Divisible Labor 2:4895 Indivisible Labor 0:0026 Labor share (1) 0:6529 Average depreciation (2) ± 0:0222 Growth rate (2) 0:0037 Standard deviation for tech. shock (4) ¾ v 0:0126 Government consumption share (2) g=y 0:1280 Correlation coef. for Govt' spending (4) ½ 0:9510 Standard deviation for Govt' shock (4) ¾ ² 0:0112 Calibration criteria: (1)External information, (2)sample averages (3) steadystate, and(4) stochastic properties Calibration To calibrate the model economy we follow the methods described in Cooley and Prescott (1995): parameter values are chosen so that the model economy produces values for the stationary variables which match the corresponding averages of actual data. This principle is based on the assumption that the Spanish economy is moving around its balanced growth path, which implies that stationary variables move around the observed averages. To this end we use the set of measurements discussed in Section 3.1 for the period 1976:1-1994:4. Table3 reports the calibrated parameter values. Following Christiano and Eichenbaum (1992) we xed the individual's productive time endowment, N, to 1369 hours per quarter. To calibrate the labor share,, we have corrected the NA data in order to take into account that a) a share of revenues corresponding to self-employed workers, imputed as capital revenues in the NA,
15 arethereanyspecial features inthespanishbusiness cycle? 375 should be registered as labor revenues 11 and b) an estimated ow of services of consumer durables is included as capital revenues. The labor share obtained after this correction is = 0:6529. All other parameters were chosen so that the balanced growth path conditions hold for the average data for the period 1976:1-1994:4. That is, the share on output of government expenditures, the quarterly growth rate, the depreciation rate, the capital labor ratio and the per-capita worked hours were set at their average values. Given all these values, we have solved the non-stochastic stationary conditions of each model in order to calibrate the subjective discount factor and the labor disutility parameter µ. To complete the calibration, the parameters corresponding to both the technological and government expenditure stochastic processes have to be set. The Solow residual measure is derived from equation  ln(x t ) = [ln(y t ) (1 )ln(k t ) ln(n t )]= :  The stochastic process for ln(x t ) is di erence-stationary and in accordance with equation  the innovations of this process should be taken as a measure of the sequence of technology shocks of the Spanish economy. Given X t, the stationary component of the government expenditures is solved and the corresponding parameters are estimated using equation  Econometric method In this section we brie y describe both the estimation procedure and the methods to evaluate the model's implications. As noted above, we focus on GMM estimation as implemented for RBC models by Christiano and Eichenbaum (1992). 11 As we point out in Appendix 1, following Bentolila and Blanchard (1990) we use the adjustment made byeuropean Economy (1994). The corresponding calculationofthelaborshareisinannualterms.
16 376 investigaciones economicas Estimation The criterion for choosing parameters is setting to zero the discrepancy between certain model and data rst and second moments. To this end, we use some moment restrictions implied by the model. In particular, fromthemodel presented in Section 2, we consider the following vector of parameters Ã 1 = fµ; ; ±; ; ¾ v ; ¹g; ½; ¾ ² g:  Parameters and N are not estimated: is set to imply a 4.5% annual subjective discount rate 12 and N is xed at 1369 hours per quarter. Parameter is set to one or zero alternatively. In addition, we are interested in a set Ã 2 of second-order moments of the cyclical component of the data: Ã 2 = f¾ c =¾ y ; ¾ i =¾ y ; ¾ g =¾ y ; ¾ n =¾ y ; ¾ n =¾ y=n ; ¾ y g;  where ¾ z is the standard deviation of the cyclical component (logged and HP-detrended) of the variable z with z = fy hp ; c hp ; i hp ; g hp ; n hp ; (y=n) hp g, (y=n) being average labor productivity. The combined parameter vector Ã = (Ã 1 ; Ã 2 ) can be estimated through moment conditions of the form 13 Eff([Z t ;z t ] 0 ;Ã)g = 0;  where Z t = fy t ; C t ; I t ; G t ; n t ; K t g. Thus, the entire parameter vector Ã is estimated by GMM. A GMM estimator of Ã can be obtained by minimizing a quadratic form in the sample moments, i.e. choose ^Ã = ( ^Ã 1 ; ^Ã 2 ) to minimize J T = g T (Ã) 0 W T g T (Ã);  12 Whichroughlycorrespondstoourcalibrationresult. 13 SeeAppendix2foradetailedpresentationoftheorthogonalityconditions.
18 Withoutgovernment( =1) Withgovernment( =0) Divisiblelabor Indivisiblelabor Divisiblelabor Indivisiblelabor Exactly Over Exactly Over Exactly Over Exactly Over identi ed identi ed identi ed identi ed identi ed identi ed identi ed identi ed µ (.0364) (.0377) (.0000) (.0000) (.0512) (.0514) (.0000) (.0000) (.0059) (.0057) (.0059) (.0057) (.0065) (.0063) (.0065) (.0063) ± (.0003) (.0003) (.0003) (.0003) (.0003) (.0003) (.0003) (.0003) (.0009) (.0009) (.0009) (.0009) (.0009) (.0009) (.0009) (.0009) ¾ v (.0012) (.0009) (.0012) (.0009) (.0012) (.0009) (.0012) (.0009) ¹g (7.482) (7.870) (7.496) (8.033) (7.233) (7.021) (7.273) (7.004) ½ (.0226) (.0251) (.0226) (.0252) (.0229) (.0250) (.0229) (.0252) ¾ ² (.0012) (.0006) (.0012) (.0006) (.0012) (.0006) (.0012) (.0006) J ::: ::: ::: ::: [.002] [.002] [.002] [.002] Allofthestatisticsforthemodelsareaverages,across100simulateddatasets, each with 75 observations. Numbers in parentheses are the standard deviations across data sets. Under the null hypothesis that the model moments and the data moments are equal, W» Â 2 (l). The degrees of freedom, l, are equal to the number of restrictions to be tested. 5. Empirical results In this section we discuss our empirical results for the four models under consideration. As can be seen from Tables 3 and 4 (under the exactly identi ed heading) nearly all the calibrated parameters are in the con dence intervals of the estimated parameters. This is particularly true for the labor share and, consequently, for the variance of the technology shock ¾ v. 17 Table 4 also displays our parameter estimates for all the models when 17 NoticethatthelaborshareisnotinthedatasetutilizedfortheGMMestimation. However,anappropriatechoiceof intheestimationstageiscrucialto obtainavaluefor consistentwiththelaborsharedata.
19 arethereanyspecial features inthespanishbusiness cycle? 379 we impose the orthogonality between the innovation in the technology shocks and the innovation in the government spending shocks. A rst test of the model consists of imposing the overidentifying restriction E(º t ² t ) = 0 by using Hansen's (1982) J-statistic. As can be expected fromthe previous literature on this issue, the overidenti ed system is rejected at less than the 0:5% signi cance level. However, given our reference data set and the speci cation for the shocks processes, the pointestimates of themodel's parameters do notmoveto inadmissible values. 18 Table 5 reports the implications of our point estimates for some rstmoment properties of the models under consideration. First, our estimate of Ã 1 implies steady state ratios that lie in the con dence interval of the corresponding empirical averages. This is particulary true for the capital-output ratio, which is the only ratio explicitly included in the orthogonality conditions. Secondly, as discussed in Section 3.2, the capital stock at the beginning of the sample grows at a higher rate than output and hours worked evolve with a marked downward trend. For these reasons, the growth rate of capital is greater than the growth rate of output 19 and the growth rate of hours is di erent from zero. Indeed, the unconditional growth rate of capital in the models correspond to the growth rate of output and the unconditional growth rate of hours is zero. However, the growth rates of the data exhibit a high variability and the short length of the sample does not allow a proper evaluation of whether the Spanish economy is on its balanced growth path. Tables 6 and 7 present a selection of second-moment properties for the HP- ltered data corresponding to simulations of the calibrated 18 This ndingscallfortheinvestigationoftheeconomicreasonsunderlyingthe non-exogeneityof thesolowresidual forthe Spanisheconomy. Indeed, thenonexogeneityof the Solowresidual has beenextensivelydiscussedinthe literature, for instance in Burnside et al. (1993). 19 Therateofgrowthofcapitaldependscruciallyonthedepreciationrate,which is far from being correctly measured. In particular, obsolescence is not considered inthe standardmeasurements of the capital stock, evenif itcouldhave playeda crucial role in the Spanish accumulation process during the seventies. A better measurement of the depreciationrate would be necessary to evaluate if, during the seventies, the Spanish economy was on the balancedgrowth path or it was convergingtothebalancedgrowthpath.
20 380 investigaciones economicas Table5 First moment properties for the reference data set. Estimatedeconomies Period76:194:3 Moments data C p t =Y t (.023) G t=y t (.015) I t =Y t (.019) K t+1 =Y t (.456) n t (43.8) lnc p t (.006) lnk t (.005) lng t (.007) lny t (.008) lnn t (.010) Withoutgovernment( =1) Divisiblelabor Indivisiblelabor (.008) (.003) (.007) (.175) (2.53) (.000) (.008) (.003) (.007) (.174) (3.83) (.000) Withgovernment( =0) Divisiblelabor Indivisiblelabor (.007) (.002) (.007) (.179) (3.09) (.000) (.007) (.002) (.007) (.176) (4.46) (.000) Allofthestatisticsforthemodelsareaverages,across100simulateddata sets, each with 75 observations. Numbers in parentheses are the standard deviations across data sets. economies and the estimated economies, respectively. As can be seen by comparing both tables, the cyclical behavior of the arti cial economies is quite similar, irrespective of the methodology underlying the selection of parameter values. This is an expected result given how close the corresponding sets of parameter values are. Consequently, we will concentrate the analysis on the estimated economies, since this allows to have a metric for the distance between simulated and observed second moments, and to perform comparisons with previous results for other economies. A rst result is that all the models perform poorly at matching the volatility of consumption relative to output. As has been stated in
Why Does Consumption Lead the Business Cycle? Yi Wen Department of Economics Cornell University, Ithaca, N.Y. email@example.com Abstract Consumption in the US leads output at the business cycle frequency.
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
Real Business Cycle Models Lecture 2 Nicola Viegi April 2015 Basic RBC Model Claim: Stochastic General Equlibrium Model Is Enough to Explain The Business cycle Behaviour of the Economy Money is of little
Chapter 5 Real business cycles 5.1 Real business cycles The most well known paper in the Real Business Cycles (RBC) literature is Kydland and Prescott (1982). That paper introduces both a specific theory
Real Business Cycle Theory Guido Ascari University of Pavia () Real Business Cycle Theory 1 / 50 Outline Introduction: Lucas methodological proposal The application to the analysis of business cycle uctuations:
CENTRAL BANK OF THE REPUBLIC OF TURKEY WORKING PAPER NO: 0/08 Interest Rates and Real Business Cycles in Emerging Markets May 200 S. Tolga TİRYAKİ Central Bank of the Republic of Turkey 200 Address: Central
Homework #1 1. In 1900 GDP per capita in Japan (measured in 2000 dollars) was $1,433. In 2000 it was $26,375. (a) Calculate the growth rate of income per capita in Japan over this century. (b) Now suppose
Normalization and Mixed Degrees of Integration in Cointegrated Time Series Systems Robert J. Rossana Department of Economics, 04 F/AB, Wayne State University, Detroit MI 480 E-Mail: firstname.lastname@example.org
Estimating baseline real business cycle models of the Australian economy Don Harding and Siwage Negara y University of Melbourne February 26, 2008 1 Introduction This paper is concerned with the issues
UNIVERSITY OF OSLO DEPARTMENT OF ECONOMICS Exam: ECON4310 Intertemporal macroeconomics Date of exam: Thursday, November 27, 2008 Grades are given: December 19, 2008 Time for exam: 09:00 a.m. 12:00 noon
Topic 5: Stochastic Growth and Real Business Cycles Yulei Luo SEF of HKU October 1, 2015 Luo, Y. (SEF of HKU) Macro Theory October 1, 2015 1 / 45 Lag Operators The lag operator (L) is de ned as Similar
Real Business Cycle Theory Marco Di Pietro Advanced () Monetary Economics and Policy 1 / 35 Introduction to DSGE models Dynamic Stochastic General Equilibrium (DSGE) models have become the main tool for
Franck Portier TSE Macro II 29-21 Chapter 3 Real Business Cycles 36 3 The Standard Real Business Cycle (RBC) Model Perfectly competitive economy Optimal growth model + Labor decisions 2 types of agents
Dynamic Macroeconomics I Introduction to Real Business Cycle Theory Lorenza Rossi University of Pavia these slides are based on my Course of Advanced Macroeconomics II held at UPF and bene t of the work
Indeterminacy, Aggregate Demand, and the Real Business Cycle Jess Benhabib Department of Economics New York University email@example.com Yi Wen Department of Economics Cornell University Yw57@cornell.edu
The Real Business Cycle Model Ester Faia Goethe University Frankfurt Nov 2015 Ester Faia (Goethe University Frankfurt) RBC Nov 2015 1 / 27 Introduction The RBC model explains the co-movements in the uctuations
Business School, Brunel University MSc. EC5501/5509 Modelling Financial Decisions and Markets/Introduction to Quantitative Methods Prof. Menelaos Karanasos (Room SS69, Tel. 018956584) Lecture Notes 3 1.
Chapter 3 Credit and Business Cycles Here I present a model of the interaction between credit and business cycles. In representative agent models, remember, no lending takes place! The literature on the
Intermediate Macroeconomics: The Real Business Cycle Model Eric Sims University of Notre Dame Fall 2012 1 Introduction Having developed an operational model of the economy, we want to ask ourselves the
Business Cycle Accounting for South Africa May 20 Albert Touna Mama University of Cape Town firstname.lastname@example.org Nicola Viegi University of Pretoria and ERSA email@example.com Abstract Quantitative
Employment Protection and Business Cycles in Emerging Economies Ruy Lama IMF Carlos Urrutia ITAM August, 2011 Lama and Urrutia () Employment Protection August, 2011 1 / 38 Motivation Business cycles in
Debt in the U.S. Economy Kaiji Chen z Ayşe Imrohoro¼glu zz This Version: May 2013 Abstract In 2011, the publicly held debt-to-gdp ratio in the United States reached 68% and is expected to continue rising.
In ation Tax and In ation Subsidies: Working Capital in a Cash-in-advance model George T. McCandless March 3, 006 Abstract This paper studies the nature of monetary policy with nancial intermediaries that
ECON 5010 Class Notes Business Cycles and the Environment Here, I outline a forthcoming paper by Garth Heutel in the Review of Economic Dynamics. The title is "How Should Environmental Policy Respond to
Endogenous Growth Theory Motivation The Solow and Ramsey models o er valuable insights but have important limitations: Di erences in capital accummulation cannot satisfactorily account for the prevailing
Fiscal and Monetary Policy in Australia: an SVAR Model Mardi Dungey and Renée Fry University of Tasmania, CFAP University of Cambridge, CAMA Australian National University September 21 ungey and Fry (University
Comments on \Do We Really Know that Oil Caused the Great Stag ation? A Monetary Alternative", by Robert Barsky and Lutz Kilian Olivier Blanchard July 2001 Revisionist history is always fun. But it is not
Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence Zeldes, QJE 1989 Background (Not in Paper) Income Uncertainty dates back to even earlier years, with the seminal work of
The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian
Prof. Dr. Thomas Steger Advanced Macroeconomics II Lecture SS 13 2. Real Business Cycle Theory (June 25, 2013) Introduction Simplistic RBC Model Simple stochastic growth model Baseline RBC model Introduction
A Quantitative Assessment of the Decline in the U.S. Saving Rate Kaiji Chen y Ayşe Imrohoro¼glu z Selahattin Imrohoro¼glu z First Version October 2005; this Version January 2007 Abstract The saving rate
A Review of the Literature of Real Business Cycle theory By Student E XXXXXXX Abstract: The following paper reviews five articles concerning Real Business Cycle theory. First, the review compares the various
Chapter 4 Real Business Cycle Theory This section of the textbook focuses on explaining the behavior of the business cycle. The terms business cycle, short-run macroeconomics, and economic fluctuations
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
Universidad de Montevideo Macroeconomia II Danilo R. Trupkin Class Notes (very preliminar) The Ramsey-Cass-Koopmans Model 1 Introduction One shortcoming of the Solow model is that the saving rate is exogenous
Chapter 11 Economic Growth This chapter examines the determinants of economic growth. A startling fact about economic growth is the large variation in the growth experience of different countries in recent
Current Accounts in Open Economies Obstfeld and Rogoff, Chapter 2 1 Consumption with many periods 1.1 Finite horizon of T Optimization problem maximize U t = u (c t ) + β (c t+1 ) + β 2 u (c t+2 ) +...
Indeterminacy, Aggregate Demand, and the Real Business Cycle Jess Benhabib Department of Economics New York University firstname.lastname@example.org Yi Wen Department of Economics Cornell University Yw57@cornell.edu
1 CHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM) This model is the main tool in the suite of models employed by the staff and the Monetary Policy Committee (MPC) in the construction
Introduction General equilibrium analysis looks at how multiple markets come into equilibrium simultaneously. With many markets, equilibrium analysis must take explicit account of the fact that changes
WORING PAPERS IN ECONOMICS No 448 Conditional Investment-Cash Flow Sensitivities and Financing Constraints Stephen R. Bond and Måns Söderbom May 2010 ISSN 1403-2473 (print) ISSN 1403-2465 (online) Department
Secular Trends in U.S. Consumption and Saving Kaiji Chen y Ayşe Imrohoro¼glu z Selahattin Imrohoro¼glu z First Version October 2005; This Version September 2006 Abstract The saving rate in the U.S. has
Towards a Structuralist Interpretation of Saving, Investment and Current Account in Turkey MURAT ÜNGÖR Central Bank of the Republic of Turkey http://www.muratungor.com/ April 2012 We live in the age of
Reexamination of Real Business Cycles in A Small Open Economy Jang-Ting Guo University of California, Riverside y Zuzana Janko z University of Calgary January 29, 2008 Abstract Standard dynamic small open
MA Advanced Macroeconomics: 7. The Real Business Cycle Model Karl Whelan School of Economics, UCD Spring 2015 Karl Whelan (UCD) Real Business Cycles Spring 2015 1 / 38 Working Through A DSGE Model We have
0. Fixed-Income Securities Fixed-income securities (FIS) are bonds that have no default risk and their payments are fully determined in advance. Sometimes corporate bonds that do not necessarily have certain
14.461: Advanced Macroeconomics I Suman S. Basu, MIT Recitation 9: Empirical Evidence on Labor Market Dynamics Part II of 14.461 covers topics in the macroeconomic analysis of labor markets. The purpose
Lecture 14 More on Real Business Cycles Noah Williams University of Wisconsin - Madison Economics 312 Optimality Conditions Euler equation under uncertainty: u C (C t, 1 N t) = βe t [u C (C t+1, 1 N t+1)
GROWTH, INCOME TAXES AND CONSUMPTION ASPIRATIONS Gustavo A. Marrero Alfonso Novales y July 13, 2011 ABSTRACT: In a Barro-type economy with exogenous consumption aspirations, raising income taxes favors
From Pawn Shops to Banks: The Impact of Banco Azteca on Households Credit and Saving Decisions Claudia Ruiz UCLA January 2010 Abstract This research examines the e ects of relaxing credit constraints on
Phd Macro, 2007 (Karl Whelan) 1 Real Business Cycle Models The Real Business Cycle (RBC) model introduced in a famous 1982 paper by Finn Kydland and Edward Prescott is the original DSGE model. 1 The early
SIMULATING THE TURKISH TAX SYSTEM ADEM İLERİ Middle East Technical University Department of Economics email@example.com PINAR DERİN-GÜRE Middle East Technical University Department of Economics firstname.lastname@example.org
Chapter 4 Cash in advance model 4.1 Motivation In this lecture we will look at ways of introducing money into a neoclassical model and how these methods can be developed in an effort to try and explain
Solutions Problem Set 2 Macro II (4.452) Francisco A. Gallego 4/22 We encourage you to work together, as long as you write your own solutions. Intertemporal Labor Supply Consider the following problem.
Name: Number: Nova School of Business and Economics Macroeconomics, 1103-1st Semester 2013-2014 Prof. André C. Silva TAs: João Vaz, Paulo Fagandini, and Pedro Freitas Final Maximum points: 20. Time: 2h.
The Credit Spread Cycle with Matching Friction Kevin E. Beaubrun-Diant and Fabien Tripier y June 8, 00 Abstract We herein advance a contribution to the theoretical literature on nancial frictions and show
Changing income shocks or changed insurance - what determines consumption inequality? Johannes Ludwig Ruhr Graduate School in Economics & Ruhr-Universität Bochum Abstract Contrary to the implications of
The Cyclical Behavior of Debt and Equity Finance Web ppendix Francisco B. Covas and Wouter J. Den Haan December 15, 2009 bstract This appendix gives details regarding the construction of the data set and
Chapter 6 Econometrics 6.1 Introduction We re going to use a few tools to characterize the time series properties of macro variables. Today, we will take a relatively atheoretical approach to this task,
Can we rely upon fiscal policy estimates in countries with a tax evasion of 15% of GDP? Raffaella Basile, Ministry of Economy and Finance, Dept. of Treasury Bruno Chiarini, University of Naples Parthenope,
Jakub Gazda 42 Jakub Gazda, Real Business Cycle Theory Methodology and Tools, Economics & Sociology, Vol. 3, No 1, 2010, pp. 42-48. Jakub Gazda Department of Microeconomics Poznan University of Economics
INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. Its
A New Perspective on The New Rule of the Current Account Cedric Tille Graduate Institute of International and Development Studies, Geneva CEPR 1 Eric van Wincoop University of Virginia NBER 2 1 Corresponding
Business Cycles, Theory and Empirical Applications Seminar Presentation Country of interest France Jan Krzyzanowski June 9, 2012 Table of Contents Business Cycle Analysis Data Quantitative Analysis Stochastic
Time Preference and the Distributions of Wealth and Income Richard M. H. Suen This Version: February 2010 Abstract This paper presents a dynamic competitive equilibrium model with heterogeneous time preferences
The Real Business Cycle Model for Lesotho Tanka Tlelima University of Cape Town, South Africa October 27, 29 Abstract This paper modi es Hansen s model of indivisible labour, to include labour exports,
GENERAL EQUILIBRIUM WITH BANKS AND THE FACTOR-INTENSITY CONDITION Emanuel R. Leão Pedro R. Leão Junho 2008 WP nº 2008/63 DOCUMENTO DE TRABALHO WORKING PAPER General Equilibrium with Banks and the Factor-Intensity
Working Paper 07-60 Departamento de Economía Economic Series (34) Universidad Carlos III de Madrid July 2007 Calle Madrid, 126 28903 Getafe (Spain) Fax (34) 916249875 Intermediate Goods and Total Factor
Chapter 3: The Multiple Linear Regression Model Advanced Econometrics - HEC Lausanne Christophe Hurlin University of Orléans November 23, 2013 Christophe Hurlin (University of Orléans) Advanced Econometrics
Working Paper 09-4 Departamento de Economía Economic Series (09) Universidad Carlos III de Madrid February 2009 Calle Madrid, 26 28903 Getafe (Spain) Fax (34) 96249875 The Structural Transformation Between
The Stock Market, Monetary Policy, and Economic Development Edgar A. Ghossoub University of Texas at San Antonio Robert R. Reed University of Alabama July, 20 Abstract In this paper, we examine the impact
How Much Insurance in Bewley Models? Greg Kaplan New York University email@example.com Giovanni L. Violante New York University, CEPR, and NBER firstname.lastname@example.org This Draft: February 2008 PRELIMINARY AND INCOMPLETE
Margin Requirements and Equilibrium Asset Prices Daniele Coen-Pirani Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA Abstract This paper studies
Macroeconomics Lecture 1: The Solow Growth Model Richard G. Pierse 1 Introduction One of the most important long-run issues in macroeconomics is understanding growth. Why do economies grow and what determines
Economic Quarterly Volume 100, Number 1 First Quarter 2014 Pages 51 85 A Business Cycle Analysis of Debt and Equity Financing Marios Karabarbounis, Patrick Macnamara, and Roisin McCord The recent turmoil
Summing up 4310 ECON4310 Lecture Asbjørn Rødseth University of Oslo 27/11 2013 Asbjørn Rødseth (University of Oslo) Summing up 4310 27/11 2013 1 / 20 Agenda Solow, Ramsey and Diamond Real Business Cycle
Japanese Saving Rate Kaiji Chen y Ayşe Imrohoro¼glu z Selahattin Imrohoro¼glu z First Version April 2004 This Version: January 22, 2005 Abstract Japanese and U.S. saving rates have been signi cantly di
Learning objectives This chapter presents an overview of recent work in two areas: Real Business Cycle theory New Keynesian economics Advances in Business Cycle Theory slide 1 The Theory of Real Business
A Quantitative Assessment of the Decline in the U.S. Saving Rate and the Current Account Balance Kaiji Chen y Ayşe Imrohoro¼glu z Selahattin Imrohoro¼glu z First Version October 2005; this Version April
ECON 3312 Macroeconomics Exam 3 Fall 2014 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Everything else held constant, an increase in net
Research Division Federal Reserve Bank of St. Louis Working Paper Series Comment on "Taylor Rule Exchange Rate Forecasting During the Financial Crisis" Michael W. McCracken Working Paper 2012-030A http://research.stlouisfed.org/wp/2012/2012-030.pdf
Lecture 1: The intertemporal approach to the current account Open economy macroeconomics, Fall 2006 Ida Wolden Bache August 22, 2006 Intertemporal trade and the current account What determines when countries
1 Endogenous Growth We present two models that are very popular in the, so-called, new growth theory literature. They represent economies where, notwithstanding the absence of exogenous technical progress,