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Econometria
Eric Rebelo, Gabriela Peach, Lucas Simionato, Marion Mixéu, Natalia Gazige, Pollyanna Costa

Prof.: Priscila Fernandes Ribeiro

Objetivo:
Estimar uma regressão que coloque a renda como variável resposta e verificar o impacto de cada variável explicativa na variação das rendas das famílias.

Variáveis:
• • • • • • Soma de despesas Quantidade de bens duraveis Aluguel Gastos com veiculo Gastos com poupança Dummies , tem carro, paga aluguel

Tema:
Renda das unidades de consumo familiares brasileiras de acordo com os gastos com consumo obtidos com a Pesquisa de Orçamento Familiar(POF) do IBGE.

Modelo proposto:
Regressão: log(renda) = 5,733103 + 0,065849*(quantidade de bens duráveis) + 3,16E-05*(soma despesa) + 0,549274*[log(aluguel)] + 0,064763*[log(gasto com carro)] – 0,00765*[log(poupança)] – 2,544451*(dummy aluguel) + 0,261395*(dummy carro) + 0,036480*[(log(poupança)^2)] – 0,022365*[log(poupança)*log(aluguel)] – 0,003297*[log(aluguel)*(quantidade de bens duráveis)]

Ao analisar o impacto das variaveis, esperamos que a quantidade de bens duraeveis , os gastos com veiculo e os gastos com poupanca tenham um ipacto positivo na renda, ou seja, quanto maior a sua renda, maior seus gastos com essas variaveis. Por outro lado, esperamos que , ao tudo mais constantee , um aumento da renda perrmita que os gastos com aluguel diminua , pois pessoas que ganham mais ,tendem a poupar mais e assim , ter moradia propria ao invés de gastar mais com aluguel.

Resultado esperado:
Acreditamos que a quantidade de bens duráveis, a soma de despesas, o gasto com aluguel (no caso de existir aluguel, ou seja, somente o gasto dos que pagam aluguel) e o gasto com carro sejam diretamente proporcionais a renda. Desta maneira, temos que os betas seriam positivos. Quando tratamos das dummys, esperamos que a dummy do aluguel seja negativa, visto que pessoas que possuem casa própria tendem a ter uma renda maior do que as que pagam aluguel. Além disso, a dummy “tem carro” deve ter um beta positivo, visto que pessoas que possuem carro em geral têm maior renda. Quanto à poupança, esperamos que o log(poupança) seja negativo e o log(poupança)^2 seja positivo, assim teríamos um gráfico exponencial positivamente inclinado, o que significa que, quanto maior a poupança, maior a renda. Para o sinal da interação entre log(aluguel) e log(poupança) e a interação entre log(aluguel) e quantidade de bens duráveis, esperamos um sinal negativo, pois uma poupança maior pode propiciar a aquisição de imóvel. Com relação a quantidade de bens duráveis, esperamos que, uma família, quando paga aluguel, não adquire muitos bens duráveis, pois, muitas vezes, esse bem não pode ser levado para outros imóveis, então as famílias deixam para comprar mais bens duráveis quando elas adquirem o imóvel.

Gráficos: log Aluguel x Qdade bens duraveis
12 10

8

log aluguel

6

Aluguel

4

2

0 0 10 20 30 40 quantidade bens duraveis 50 60 70 80

Log Renda X log Poupanca
14

O que aconteceu:
C(1): quando a pessoa não possui quantidade de bens duráveis, não tem despesa, não paga aluguel, não tem gasto com carro (ou seja, não tem carro) e não tem dinheiro na poupança, esperamos que a renda dela seja exponencial(5,73), em média. C(2): a cada uma unidade a mais de bens duráveis, esperamos um aumento de 6,5849% em média, mantendo tudo mais constante. C(3): a cada um 1 real a mais em despesa, esperamos um aumento de 0,003% em média, mantendo tudo mais constante. C(4): 1% a mais no gasto com aluguel gera um aumento de renda de 0.549274% em média, mantendo tudo mais constante. C(5):1% a mais no gasto com carro gera um aumento de renda de 0.064763% em média, mantendo tudo mais constante. C(7): Uma pessoa que paga aluguel terá a renda menor, comparado a uma pessoa que não paga aluguel, em exponencial(-2,544), ceteris paribus C(8): Uma pessoa que tem carro terá renda maior que uma pessoa que não tem carro em exponencial(0,261395), ceteris paribus. C(9) e C(6): Esperamos que, quanto maior o log(poupança), menor seja o log(renda), mas isso só acontece até um certo ponto (quando poupança é igual a 0,06531). Após esse ponto, quanto maior for o log(poupança), maior será log(renda). log renda

12

10

8

Série1 6

4

2

0 -2 -1 0 1 2 3 log poupança 4 5 6 7 8

Ramsey RESET Test Equation: UNTITLED Specification: RENDA_L C QTD_BENS_DURAVEIS SOMA_DESPESA ALUGUEL_L CARRO_L POUPANCA_L PAGA_ALUGUEL TEM_CARRO POUPANCA_L^2 POUPANCA_L*ALUGUEL_L ALUGUEL_L*QTD_BENS_DURAVEIS Omitted Variables: Powers of fitted values from 2 to 3 Value 2.791197 5.611432 Df (2, 1960) 2 Probability 0.0616 0.0605

F-statistic Likelihood ratio

Teste RESET
Dependent Variable: RENDA_L Method: Least Squares Date: 11/05/12 Time: 20:45 Sample: 1 1973 Included observations: 1973 Variable C QTD_BENS_DURAVEIS SOMA_DESPESA ALUGUEL_L CARRO_L POUPANCA_L PAGA_ALUGUEL TEM_CARRO POUPANCA_L^2 POUPANCA_L*ALUGUEL_L ALUGUEL_L*QTD_BENS_DURAVEIS R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient 5.733103 0.065849 3.16E-05 0.549274 0.064763 -0.007650 -2.544451 0.261395 0.036480 -0.022365 -0.003297 0.711361 0.709890 0.774312 1176.334 -2289.395 483.5411 0.000000 Std. Error 0.259705 0.009353 1.09E-05 0.029879 0.014471 0.049413 0.200010 0.119404 0.006397 0.007171 0.001287 t-Statistic 22.07547 7.040477 2.888604 18.38319 4.475312 -0.154819 -12.72162 2.189159 5.702749 -3.118943 -2.562458 Prob. 0.0000 0.0000 0.0039 0.0000 0.0000 0.8770 0.0000 0.0287 0.0000 0.0018 0.0105 7.252447 1.437587 2.331875 2.363026 2.343321 1.985903

F-test summary: Sum of Sq. 3.340871 1176.334 1172.993 1172.993 df 2 1962 1960 1960 Mean Squares 1.670436 0.599558 0.598466 0.598466

Test SSR Restricted SSR Unrestricted SSR Unrestricted SSR LR test summary: Restricted LogL Unrestricted LogL

Value -2289.395 -2286.589

df 1962 1960

Conclusão:
O modelo proposto pelo grupo explica mais de 70% da variabilidade da renda das famílias brasileiras, o que é um número consideravelmente alto. Além disso, o teste RESET nos mostra que o modelo está bem especificado. Assim, conseguimos estimar brm a renda de uma família com base em apenas algumas variáveis.

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat

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