University of Frankfurt am Main

Bachelor Seminar Business Cycle: Theory and Empirical Applications Country of interest: Netherlands Teacher: Prof. Ctirad Slavik Summer Semester 2013

Yisong Dong Student ID: 3903447 June 17.2013

Contents 1. Introduction……………………………………………………………………3 2. Data Work………………………...…………………………………………...3 2.1 2.2 2.3 2.4 2.5 Data……………………………………………………………………3 Detrending the data with Hodrick-Prescott Filter………………..……4 Basic Statistics for the detrended data………………………………...7 Construct the Solow residual without labor……………………...…..11 Construct the Solow residual with labor…………….………………12

3. Calibrating and simulating a simple stochastic RBC model…………………13 3.1 3.2 Two procedure for calibrating θ and calculating the I/K, K/Y and I/Y ratios……….…………………………………………………………13 Stimulation…………………………………………………………...16

4. Conclusion……………………………………………….………………...…21 References………………………………………………………………………..22

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1.

Introduction

Business cycle refers to economy-wide fluctuations in production, trade and economic activity in general over several months or years in an economy organized on freeenterprise principles.1 It has been a well-documented feature of economic life for two centuries or more. Business cycle is the upward and downward movements of levels of GDP2 and refers to the period of expansions and contractions in the level of economic activities (business fluctuations) around its long-term growth trend.3 These fluctuations occur around a long-term growth trend, and typically involve shifts over time between periods of relatively rapid economic growth (an expansion or boom), and periods of relative stagnation or decline (a contraction or recession). They are usually measured by considering the growth rate of real gross domestic product. Despite being termed cycles, these fluctuations in economic activity can prove unpredictable. In this paper I am going to evaluate the performance of Netherlands based on the basis of some relevant macroeconomic data such as Output (Y), Investment (I), Consumption (C), Capital (K) and Labor (N). In the first part I will use the HodrickPrescott filter to detrend the data and analyze the performance with standard deviations and correlations with output and autocorrelations. In the second part I will calibrate and simulate a simple stochastic Real Business Cycle model. In the third part of this paper I will discuss the successes and failures and perform my conclusions.

2.

Data Work 2.1 Data

The data I have used for this paper were from the International statistical yearbook (ISY) and OECD Economic Outlook No.90. The series are from 1968 to 2012, which is a total of 45 observations. The data from ISY and OECD Economic Outlook No.90 are highly identical. Because I didn’t find enough useful data for Capital from ISY, I

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A. F. Burns and W. C. Mitchell, Measuring business cycles, New York, National Bureau of Economic Research, 1946. 2 GDP=gross domestic product. 3 Madhani, P. M. (2010). Rebalancing Fixed and Variable Pay in a Sales Organization: A Business Cycle Perspective. Compensation & Benefits Review, 42(3), pp. 179-189.

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use the data from OECD NO,90. The data are annual adjusted. All values are presented in Euro. I use Eviews, Gretl and Excel to finish all the work To finish this paper I need data for the following five variables: Output(Y): Gross domestic product, volume, market prices in MN Euro Cnt Netherlands Labor (N): Total employment Cnt Netherlands Investment (I): Gross fixed capital formation, total, volume in MN Euro Cnt Netherlands Consumption(C): Private final consumption expenditure, volume in MN Euro Cnt Netherlands Capital (K): Oecd Economic Outlook No. 90

2.2 Detrending the data with Hodrick-Prescott Filter I first take logs of all the original data and then use the Hodrick-Prescott Filter with a smooth parameter equal to 100 for analyzing it. The following graphs show the detrended time series data for the relevant variables:

Figure 1: Output

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Figure 2: Labor

Figure 3: Investment

Figure 4: consumption

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Figure 5: capital

Figure 6: All the variables

The graphs of the time series show us that there is a fluctuation in past and recent years. Therefore we can draw some conclusions: 1. There was a recession between 1973 and 1983. It can be explained by the first

oil crisis and energy crisis in 1979. After that almost all the variables started to decrease till 1983. 2. 3. Another recession happens between 2001 and 2005.I think the reason is the Because of the financial crisis which happened at the end of 2007, we can internet bubble and 9-11 and. They cause a decline in GDP. observe a deep drop of GDP and investment. At the outbreak of the global financial crisis, the dutch economy was assessed to be relatively well prepared to weather the 6

storm. However, the negative effects of the financial crisis became more apparent in 2008. For 2009, GDP growth is expected to show the sharpest contraction ever.4 4. Investment is the most volatile variable among these five. It has the strongest fluctuations. And the fluctuations of consumption seem to be little higher than those of output. Labor and Capital are the less volatile at all.

2.3 Basic Statistics for the detrended data After detrending the data now I am supposed to compute the standard deviation, correlations with output and autocorrelation.

Table 1: Standard deviations Variable Output Labor Capital Investment Consumption Standard deviation 0.018232 0.010610 0.011739 0.051380 0.022929 Ratio to GDP 1 0.58 0.64 2.82 1.26

This table shows us that Investment has the highest standard deviation among all the five variables, which is 3 times higher than standard deviation of output. This conclusion matches the previous guess. Consumption is little more volatile than output. Capital and labor has relatively lower standard deviation. It can be explained by the durable low unemployment and the lack of shocks in the development of capital stocks over the period. In my case the data are match the conclusion in the Advanced Macroeconomics that employment is considerably less volatile over the business cycle than GDP and Investment is the most unstable component of aggregate demand.

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Maarten Masselink and Paul van den Noord, The global Financial Crisis and ist effects on the

Netherlands, in: Ecfin Country Focus, 2009, p. 6.

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Table 2: Correlation Correlation matrix Output Output 1 Labor 0.7548 Capital 0.6793 Investment 0.7830 Consumption 0.8081

Take a look at this table we can see the correlation between output and other variables. It is very interesting that all the variables have a significantly positive correlation with output, i.e they are all Pro-cyclical.

Table 3: Autocorrelation Autocorrelation of variables period 1 2 3 4 5 Y 0.5987 0.1550 -0.1397 -0.3584 -0.3535 L 0.6915 0.2725 -0.1229 -0.4116 -0.5020 C 0.7135 0.3090 -0.0220 -0.2773 -0.3547 I 0.5980 0.0533 -0.3855 -0.6274 -0.4972 K 0.8154 0.4167 -0.0233 -0.3791 -0.5664

Table 3 holds information about correlation of all the five variables. We can use the autocorrelation of a variable to measure its persistence. Capital has the highest autocorrelation among all the variables. In the first order all the variables have autocorrelations which are larger than 0.5900, which seem like persistence. We can read the data as following: If actual output goes up by 1%, output of next time period will also goes up by 0.5987%. Another interesting information is that the persistence decrease over time period, which can be confirm by the fact that from the third period all the variables have negative autocorrelations. Now I use the Gretl to perform a lead-lag analysis with respect to output. If P (Xt+n, Ct) is significantly different from 0 and numerically greater than P (Xt, Ct), we say that x is a lagging variable.. If P (Xt-n, Ct) is significantly different from 0 and numerically

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greater than P (Xt,Ct), we say that x is a leading indicator. So we can see the result as following figures.

Figure 7: Lead-lag analysis of Y and N

-3 0.0852

-2 0.3850

-1 0.6650

0 0.7548

1 0.3497

2 -0.1033

3 -0.2948

Figure 8: Lead-lag analysis of Y and I

-3 -0.4826

-2 -0.1625

-1 0.4511

0 0.7830

1 0.5819

2 0.2615

3 -0.0691

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Figure 9: Lead-lag analysis of Y and C

-3 0.0722

-2 0.3133

-1 0.5898

0 0.8081

1 0.5228

2 0.1322

3 -0.1551

Figure 10: Lead-lag analysis of Y and K

-3 0.3120

-2 0.6161

-1 0.7739

0 0.6793

1 0.2854

2 -0.0742

3 -0.2796

Looking at the figure 10 we can draw the conclusion that capital is leading indicator of output, and Investment, Consumption and Labor are neither leading indicator nor lagging variable. In my case the conclusion doesn’t match the conclusion in the Advanced Macroeconomics that Employment is a lagging variable.

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2.4 Construct the Solow residual without labor In this part I will construct the Solow residual from the data on Output and Capital. In project outline we know that Yt=exp(At)Kt and At is the total factor productivity. The basic empirical framework employed is based on a simple model of TFP At= β+ y.t + ut , where TFP refers to total factor productivity. I change the equation to At= lnYt lnKt. Then I detrend the TFP by running the regression on time with OLS: At= β+ y.t + ut, in Which t is time trend, y is the parameter of the time trend, β is a constant and ut is the detrended TFP.

Table 4

The table above shows us that At= -0.638 - 0.00411t + ut . The slope is negative, which means that TFP decreases over time, it seems like unrealistic. R-squared is 0.726833, it means that the Regression explains 72.68% of the variance in the model. It is a good value. The constant β is -0.638 and the time parameter y has the value -0.00411320 After analyzing the data we can use the new data to estimate the relevant parameters for AR(1) process.

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Table 5

Now we have Ȃt = 0.8675 Ȃt-1 + Ɛt R-squared is 0.762878, it means that Ȃt and Ȃt-1 have a linear relationship. It is a good value. The persistence parameter equals to 0.867523, which is really a high value. It shows that the detrednd component of TFP has a high persistence. The standard deviation of innovations is 0.014891, which is the standard error of regression in table 5.

2.5

Construct the Solow residual with labor

Now I take labor into account. We know the fact that Yt =exp(At)Kt0.36Nt0.64. I convert this equation into that At= lnY-0.36 lnKt-0.64lnNt.The results shows as the following: Table 6

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The table above shows us that At = 6.75791 + 0.01144t + ut .The slope is positive, which means that TFP increases over time. R-squared is 0.929096, it means that the Regression explains 92.91% of the variance in the model. It is a very good value. The constant β is 6.7591 and the time parameter y has the value 0.0114413.

Table 7

Now we have Ȃt = 0.957248 Ȃt-1 + Ɛt R-squared is 0.844703, it means that Ȃt and Ȃt-1 have a linear relationship. It is a good value. The persistence parameter equals to 0.957248, which is close to one. The standard deviation of innovations is 0.015470.

3. Calibrating and simulating a simple stochastic RBC model 3.1 ratios I will use the following RBC model which is given in the project outline to solve the problem, 13

Two procedure for calibrating θ and calculating the I/K, K/Y and I/Y

In the first procedure I try to calibrate θ with set β = 0.96 and δ = 0.1 due to annual data. In the project online we are known that: Kt+1 =β [(1 − δ) Kt + θ exp (At) Kt ]. I use the condition that there is a steady state, i.e At =0 and Kt+1 = Kt =K* K*=β [(1 − δ) K* + θ exp(At ) K*] 1 = β [(1 − δ) + θ ] 1 = β- βδ + βθ θ = (1- β+ β δ) / β θ =(1-0.96+0.96x0.1) / 0.96 θ =0.142 In the outline we know that Ct + It = θ exp (At) Kt with the definition Kt+1= (1- δ) Kt + It So K*= (1- δ) K*+ I* K* = K*- δ K*+ I* I* = δ K * I/K = δ = 0.1 Y= θ exp(At) Kt K/Y = K* / Y* = K* / θ exp(At) K*= 1 / θ (3) (2)

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K/ Y = 1 / θ = 1/ 0.142=7.042 I / Y = (I/K) x (K/Y) I/Y = 0.1 x 0.7042 = 0.7042

(1)

In the second procedure I will use the condition that K/Y=3 in steady state, to calibrate δ and θ From (1) in the first procedure, we can calibrate θ = 1/3 = 0.333 From (2) in the first procedure, we can calibrate δ=1+ θ – 1/β =0.292 From (3) in the first procedure, we can calibrate I/K = 0.323 I/Y = (I/K) x (K/Y) = 0.323 x 3 = 0.969

Table 8 Parameters and ratios in steady state ratio Procedure 1 β θ δ I/K K/Y I/Y 0.96 0.142 0.1 0.1 7.042 0.704 Procedure 2 0.96 0.333 0.292 0.292 3 0.876

From the table above we can see that the capital-output ratio (K/Y) is much higher than other two ratios under the two procedures. It is nearly 7 times higher than the total output. This ratio will be higher when the capital is cheaper than other inputs. Besides, investment-output(I/Y) ratio are both very high, which are 70.4% and 96.9%. The capital-output ratio is always associated with the investment-output ratio. A larger capital-output ratio, a higher growth rate of investment.

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3.2 Stimulation I finish this part with Excel. The purpose of this part is using the variables to evaluating output, investment, consumption and capital with stochastic RBC model. First we creates a sequence of random numbers and we assume that Ɛt takes only two values, + Ɛt and - Ɛt with each possibility of them equals to 0.5.We have known that Ȃt = pa . Ȃt-1 + Ɛt Kt+1 =β [(1 − δ) Kt + θ exp(At) Kt ]. Ct + It = Yt Yt = θ exp (At) Kt It = Kt+1 - (1 − δ) Kt Now I use different pa and following: 1. 2. 3. 4. Ɛt = 0.014891 , p=0.867523 , δ=0.1, θ=0.142 Ɛt = 0.014891 , p=0.867523, δ=0.292, θ=0.333 Ɛt = 0.015470 , p=0.957248, δ=0.1, θ=0.142 (with labor) Ɛt = 0.015470 , p=0.957248, δ=0.292, θ=0.333(with labor)

ɕƐ value to do four simulations which seem like as the

Comparison of the results Simulation 1 Standard deviation Variable Output Investment Consumption Capital Standard deviation 0.013313 0.018215 0.17217 0.0034495

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Autocorrelations period 1 2 3 4 5 Output 0.4753 0.0668 -0.0628 -0.1390 -0.2617 Investment 0.4608 0.0485 -0.0736 -0.1393 -0.2714 Consumption -0.1196 -0.1068 -0.0902 -0.0723 -0.0546 Capital 0.8407 0.5580 0.2685 0.0056 -0.2143

Correlations with output Output Correlation 1.0000 Investment 0.9964 Consumption 0.076 Capital 0.0019

Lead-Lag analysis with output -3 Investment Capital -0.0297 -0.4278 Consumption 0.0235 -2 0.0948 0.0580 -0.3949 -1 0.4940 0.0748 -0.2934 0 0.9965 0.0761 0.0019 1 0.4358 -0.0374 0.5093 2 0.0163 -0.0368 0.6755 3 -0.1067 -0.320 0.6090

Simulation 2 Standard deviation Variable Output Investment Consumption Capital Standard deviation 0.013310 0.014409 0.17155 0.0075292

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Autocorrelations period 1 2 3 4 5 Output 0.5206 0.2247 0.0016 -0.1689 -0.2320 Investment 0.5009 0.1985 -0.0151 -0.1738 -0.2318 Consumption -0.1205 -0.1073 -0.0879 -0.0693 -0.0548 Capital 0.8387 0.5570 0.2549 -0.0081 -0.1930

Correlations with output Output Correlation 1.0000 Investment 0.9983 Consumption -0.0329 Capital 0.2823

Lead-Lag analysis with output -3 Investment Capital 0.0199 -0.3213 Consumption 0.0337 -2 0.2372 -0.0377 -0.2176 -1 0.5306 -0.0431 -0.0203 0 0.9983 -0.0329 0.2823 1 0.4912 0.0122 0.7589 2 0.1835 0.0005 0.8110 3 -0.0316 -0.0073 0.6763

Simulation 3 Standard deviation Variable Output Investment Consumption Capital Standard deviation 0.01298 0.017426 0.17126 0.0035534

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Autocorrelations period 1 2 3 4 5 Output 0.4622 0.0924 -0.0386 -0.2247 -0.3341 Investment 0.4512 0.0735 -0.0491 -0.2298 -0.3317 Consumption -0.1220 -0.1090 -0.0907 -0.0715 -0.0532 Capital 0.8079 0.4866 0.1686 -0.1101 -0.2985

Correlations with output Output Correlation 1.0000 Investment 0.9971 Consumption -0.0167 Capital -0.0441

Lead-Lag analysis with output -3 Investment Capital -0.0066 -0.4786 Consumption -0.0865 -2 0.1177 -0.0999 -0.4420 -1 0.4835 0.0377 -0.3364 0 0.9971 -0.0167 -0.0441 1 0.4268 0.0355 0.4923 2 0.0401 0.0219 0.6787 3 -0.0846 0.0127 0.6136

Simulation 4 Standard deviation Variable Output Investment Consumption Capital Standard deviation 0.014005 0.015200 0.17208 0.0080592

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Autocorrelations period 1 2 3 4 5 Output 0.5602 0.2330 0.0143 -0.1135 -0.1705 Investment 0.5419 0.2102 -0.0012 -0.1189 -0.1646 Consumption -0.1171 -0.1052 -0.0880 -0.0730 -0.0577 Capital 0.8415 0.5551 0.2467 -0.0325 -0.2597

Correlations with output Output Correlation 1.0000 Investment 0.9987 Consumption 0.0085 Capital 0.2992

Lead-Lag analysis with output -3 Investment Capital 0.0338 -0.3623 Consumption 0.1134 -2 0.2487 0.0353 -0.2326 -1 0.5707 0.0964 -0.0277 0 0.9987 0.0085 0.2992 1 0.5299 -0.0028 0.7581 2 0.1934 -0.0148 0.8223 3 -0.0208 -0.0216 0.6893

After analyzing the 4 tables, we can see that 1. GDP, investment and capital have smaller standard deviation than the actual data, but on the other hand, consumption has much more value in standard deviation than the actual data. Consumption is the most volatile variable, which has a conflict with the conclusion above. 2. Consumption has less persistence than the real data , which are all negative. 3. Capital become lagging variable, because it has the highest correlation value in lag order>0. Investment is neither a leading nor a lagging variable. Consumption varies with the simulation.

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4. Investment has a very high positive correlation with output, almost close to one. That is a little bit too high, which is almost impossible.

4. Conslusion As we see in this paper RBC model plays well to display some basic statistics , but not 100% exact. It can be improved. One major drawback of the model is it failed to take some other variables into consideration, such as Labor. It should add labor to the function. And another flaw is RBC model use constant δ and θ, which is fast impossible in the real world. But RBC model has also some strengths. It is very easy to use and evaluate the performance, they perform actually very well with the data I used. It is a good model for estimating the business cycle.

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Reference F. Burns and W. C. Mitchell, Measuring business cycles, New York, National Bureau of Economic Research, 1946. Madhani, P. M., Rebalancing Fixed and Variable Pay in a Sales Organization: A Business Cycle Perspective. Compensation & Benefits Review, 2010, 42(3), pp. 179189. Maarten Masselink and Paul van den Noord, The global Financial Crisis and ist effects on the Netherlands, in: Ecfin Country Focus, 2009.

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