Bread vs. Meat: Replicating Koenker (1977) Arianto A. Patunru Department of Economics, University of Indonesia 2004

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1 read v. Meat: Replicating Koenker (1977) Arianto A. Patunru Department of Economic, Univerity of Indoneia Introduction Thi exercie wa baed on my cla homework of an econometric coure in Univerity of Illinoi taught by Profeor Roger Koenker. It erve a a review of ome baic demand theory a well a ome baic idea of hypothei teting. In practice, we are intereted to tet the nature of bread (i.e. wa it Giffen or not?) in 18 th century Englih rural houehold. Thi i in part a replication of Koenker Wa read Giffen? The Demand for Food in England Circa 1790 (Review of Economic and Statitic, 59(2), 1977) which in turn wa baed on the claical tudie by Davie (The Cae of Labourer in Hubandry, 1795) and Eden (The State of the Poor, 1797). The data cover the period with 35 obervation. For our purpoe, we ummarize the data a follow 1 : Variable Art.Mean Geo. Mean Std. Dev. Median fam. ize income bread price meat price bread quant meat quant From the table above, we ee that income i quite pread relative to other variable. The cro correlation table i a follow: bread-qt income family bread-pr meat-pr bread-qt income family bread-pr meat-pr The table how ome relatively trong poitive correlation between family ize and income a well a between the price of bread and meat. Throughout the exercie, we would tet the nature of bread (and meat) uing the following concept: 1 The data et i provided by Roger Koenker of Univerity of Illinoi. It conit of expenditure (in old pence per week), price (in old pence per half peck loaf of bread and in old pence per lb of bacon), and family ize. We therefore imply divide the expenditure data with the repective price data to get the quantitie. Meanwhile, for analyi reaon, we ue the total expenditure to approximate the income. 1

2 Normal good g i / y > 0 Inferior good g i / y < 0 Giffen good g i / pi > 0 Luxury good > 1 Neceity good 0 < 1 iy < iy Subtitute h / p > 0 Complementary h / p < 0 i i j j where g i Marhallian demand, h i Hickian demand, y i income, p i price, and i elaticity (will be explained later). The ubcript i,j refer to the good (bread and meat). We would firt etimate two variant of linear equation for bread and then impoe ome hypothei teting. Next, we repeat thi procedure for meat. 2. Etimation and Teting for read We etimate the following two equation: Q = µ + α Y + u (1) Q = µ + α Y + γ S + β P + β P u (2) M M + where Q i the quantity of bread demanded, Y i income, S i family ize, P i the price of bread and P M i the price of meat. We aume that the error term, u follow the i.i.d. aumption. We obtain the following reult from etimating (1) bread Coef. Std. Err. t P> t income con F=11.94, R-quared=0.2656, Adj.R-quared= The hypothei that the Engle curve for bread i homogenou (i.e. H 0 : µ = 0 ) againt the alternative hypothei that familie have ome committed quantity of bread which they will purchae regardle of family income (i.e. H 1 : µ > 1 ) i teted. The t-tat aociated with the contant above how that the null hypothei i rejected 2. Thi implie that the familie do have ome committed quantity of bread regardle of their income. 2 Alternatively, we can execute an F-tet and obtain F-tat of 5.43 with a p-value of

3 We then etimate (2) and obtain the following reult: bread Coef. Std. Err. t P> t income fam ize bread price meat price con F=29.36, R-quared=0.7965, Adj.R-quared= aed on the reult above we tet the hypothee below: (i). Family ize and the price of bread and meat are not ignificant influence on bread conumption. That i, we tet H 0 : γ = β = β M = 0 againt H 1 : not all of them are zero. The tet give an F-tat of with a p-value of Thi mean, the null hypothei i ignificantly rejected; therefore the family ize and the price eem to be ignificant influence on bread conumption. (ii). read i a normal good. In regard with thi hypothei we tet an H 0 : α 0 againt H 1 : α > 0. We ue a one-tailed null hypothei o a to minimize Type-1 error in uch a way that the probability of the error hould be trictly le then the level of ignificance for any other value of the parameter. The tet can be done by oberving the t-tat in the regreion reult above. That i, with a t-tat of 3.07 and p-value of 0.01, we reject the null hypothei at 5 percent level. Therefore, bread i normal. (iii). The price of meat i not a ignificant factor in determining bread conumption. Thi hypothei can be teted by H 0 : β M = 0 againt H 1 : β M 0. The reult above how a t-tat of 3.53 with a p-value of Thi implie that the price of meat i a ignificant factor in bread conumption. 3. Elaticitie In thi ection we are intereted to ee the elaticity meaure. In particular, we analyze the income elaticity of bread, the uncompenated own price elaticity of bread, the compenated own price elaticity of bread, and the compenated cro (meat) price elaticity of bread. To calculate thee elaticitie we ue the following formula: Q Y Y = : income elaticity of bread Y Q Q P g = : uncompenated own price elaticity of bread P Q h h M P Q Y g PM QM = M + Y : compenated cro (meat) price elaticity of bread Y g = + Y : compenated own price elaticity of bread 3

4 In addition, we alo etimate the log-log form to obtain the contant elaticity value, i.e.: lnq = µ + α lny + γ ln S + β ln P + β ln P u (3) M M + which give the following reult: - ln bread qt Coef. Std. Err. t P> t ln income ln family ln bread pr ln meat pr _con F=41.32, R-quared=0.8646, Adj.R-quared= The calculation reult in: Elaticity Inc. elat. of bread Uncompenated own price elat. of bread Compenated own price elat. of bread Compenated cro (meat) price elat. of bread At arith. mean At geo. mean At the median Contant elat. (log-log form) The reult above implie (auming arith. mean): (1) one percent increae in income yield 0.48 percent increae in the quantity demanded of bread, (2) one percent increae in the price of bread (oberved from income and price) lead to a 1.01 percent decreae in the quantity demanded of bread, (3) one percent increae in the price of bread lead to 0.69 percent decreae in the bread quantity in order to be remain in the ame level of utility, and (4) one percent increae in the price of meat lead to 1.02 percent increae in the bread quantity in order to be remain in the ame level of utility. 4. Etimation and Teting for Meat We now etimate the demand for meat uing the following equation: Q = µ + α Y + γ S + β P + β P u (4) M M M M M MM M + 3 For the compenated value, we ue arithmetic mean in the formula. 4

5 Our etimation give the following reult: - meat Coef. Std. Err. t P> t income fam ize bread price meat price con F=19.43, R-quared=0.7215, Adj.R-quared= For comparion, we etimate the log-log form of: lnq = µ + α lny + γ ln S + β ln P + β ln P u (5) M M M M MM M + that yield the following reult: ln meat qt Coef. Std. Err. t P> t ln income ln family ln bread pr ln meat pr _con F=6.15, R-quared=0.4861, Adj.R-quared= We are intereted to tet the following hypothee: (a). Meat i a luxury. Thi hypothei i the ame a aying that the income elaticity of meat i greater than one. Formally, we tet H 0 : > 1 againt H 1 : 1. Here we calculate: Q Y M MY = : income elaticity of meat Y QM MY MY The reult i at arithmetic mean, at geometric mean, and at the median. To ee the ignificance of coefficient being ued, we oberve the t-tat of the income coefficient. We have a t-tat of 5.15 with a p-value of Thi mean that meat i a luxury good for the 18 th century Englih rural houehold. On the other hand, uing log-log form, we obtain income elaticity of with t-tat of 2.81 and p-value of Thi confirm the reult from linear form. (b). Meat and bread are ubtitute. To tet thi hypothei we need to oberve the Slutky matrix. Prior to that, we have to make ure the ignificance of the coefficient for meat price and income in the bread equation (2) a well a the coefficient for bread price and income in meat equation (3). We ee from the previou table that the t-tat and the p-value confirm thi ignificance. Therefore we can proceed to the Slutky matrix uing the following formula: 5

6 ij ii h g g i i i = = + g j : Slutky cro decompoition Pj Pj Y h g g i i i = = + gi : Slutky own decompoition. Pi Pi Y The reult i (uing arithmetic mean): ii ji ij jj = where i i bread and j i meat. From the reult, therefore, we can conclude that the bread and the meat are ubtitute. From economic theory we know that the Slutky matrix i ymmetric. However, our reult above how otherwie. We argue a follow: a) Mipecification of the model: Thi might be due to bad data collection and inappropriate model pecification. Figure 1 and Figure 2 indicate that the linear bread model i inufficient to explain the variabilitie in the demand for bread, compared to the log-log bread model. Figure 3 and Figure 4 do not have an explicit difference in the pread of the reidual. Nonethele, the adjuted R-quare of both pecification indicate that they can explain only forty percent of the variabilitie in the demand for meat. The reidual plot (Figure 1 to Figure 4), therefore, alo ugget mipecification of the demand model for bread and meat. b) Correlation among independent variable: From our cro correlation matrix, it eem that income and family ize, and the price of meat and bread are poitively correlated, which inflate the tandard deviation of the model. In addition, thee relatively trong correlation undermine our aumption of IID independent variable. c) Miing explanatory variable: A we recall, the demand for meat, for example, were etimated uing price of only two good, depite the fact that more price variable could affect the quantity of meat. d) Violation of the aumption The aumption about conumer behavior, uch a binding budget contraint and nonatiation, may not be atified in the data et. 6

7 Appendix Figure 1: Reidual Plot for Model reid Fitted value Reidual Plot for ig read Model Figure 2: Reidual Plot for Model reidbl Fitted value Reidual Plot of ig Log read Model Figure3: Reidual Plot for Model 4 7

8 reidm Fitted value Reidual Plot of ig Meat Model Figure 4: Reidual Plot for Model reidml Fitted value Reidual Plot of ig Log Meat Model 8